{"id":15871,"date":"2023-01-26T17:12:26","date_gmt":"2023-01-26T11:42:26","guid":{"rendered":"https:\/\/www.interviewbit.com\/blog\/?post_type=web-story&#038;p=15871"},"modified":"2023-02-07T23:47:32","modified_gmt":"2023-02-07T18:17:32","slug":"how-to-solve-coin-change-problem","status":"publish","type":"web-story","link":"https:\/\/www.interviewbit.com\/blog\/web-stories\/how-to-solve-coin-change-problem\/","title":{"rendered":"How to Solve Coin Change Problem?"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link href=\"https:\/\/fonts.googleapis.com\/css2?display=swap&amp;family=Roboto%3Awght%40400%3B700&amp;family=Darker+Grotesque%3Awght%40400%3B700&amp;family=Anton\" 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style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.2658227848101267% 1.2658227848101267% 1.2658227848101267% 1.2658227848101267%\" id=\"el-95a17566-0eff-4d0a-a9a1-c1eab9f25976\">\n<h1 id=\"how-to-solve-coin-change-problem\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.3597705696202531% 0;font-family:&quot;Roboto&quot;,sans-serif;font-size:0.809061em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">How to Solve Coin Change Problem?<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:5.58252%;top:81.06796%;width:91.26214%;height:5.66343%;opacity:1\">\n<div 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1.25% 1.25% 1.25%\" id=\"el-01463911-9ace-441d-a6f8-4307552a5552\">\n<h2 id=\"given-an-array-of-coins-and-a-total-sum-find-the-fewest-number-of-coins-needed-to-make-the-sum-return-1-if-impossible\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Given an array of coins and a total sum, find the fewest number of coins needed to make the sum. Return -1 if impossible.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:11.65049%;opacity:1\">\n<div id=\"anim-647f5454-eaef-404e-b017-07b7133c7c9c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a49fc4bb-5ba6-4a93-ac7b-d2e208c07a20\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 2.7777777777777777% 2.7777777777777777% 2.7777777777777777% 2.7777777777777777%;background-clip:content-box;background-color:#052258\" id=\"el-982eeb26-c459-4fd0-82c3-a697d1dcf9c9\">\n<h1 id=\"problem-statement\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Problem Statement<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Banner-13.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/coin-change-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=coin-change-problem\" rel=\"\">Explore now<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"89c46d12-909f-4a7b-b582-777f409a4ac2\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5f1d4d44-339c-41ec-ad75-24bd2f37ddaa [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-034ef67f-2af7-4fd0-89bc-5232790bd83d\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-92e81889-4f0f-426b-a87c-df469a4d4810\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f3f3f3\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-5f1d4d44-339c-41ec-ad75-24bd2f37ddaa\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-76638dd5-e923-4c37-8934-99f03447a159\">\n<div style=\"position:absolute;width:266.31253%;height:100%;left:-83.15627%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max\" alt=\"photography of three women sits beside table inside room during daytime\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max 6016w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4812&amp;h=3212&amp;fit=max 4812w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3609&amp;h=2409&amp;fit=max 3609w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2406&amp;h=1606&amp;fit=max 2406w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1203&amp;h=803&amp;fit=max 1203w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=227&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 120vh, 267vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-90701d05-70b8-48ba-9066-72199e99b3ce\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.25243%;top:26.86084%;width:85.43689%;height:50.32362%;opacity:1\">\n<div id=\"anim-034ef67f-2af7-4fd0-89bc-5232790bd83d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-92e81889-4f0f-426b-a87c-df469a4d4810\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 0.6430868167202572% 0.6430868167202572% 0.6430868167202572% 0.6430868167202572%\" id=\"el-beb9cd08-b670-4372-bebb-c5ab5af8e430\">\n<h2 id=\"example-input-12598sum-17output-2explanation-two-coins-require-to-make-the-desired-sum-98\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #347eff\">Example-&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">Input: <\/span><span style=\"color: #fff\">[1,2,5,9,8]<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">Sum: <\/span><span style=\"color: #fff\">17<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">Output: <\/span><span style=\"color: #fff\">2<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">Explanation: <\/span><span style=\"color: #fff\">Two coins require to make the desired sum [9,8]<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" 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type=\"application\/json\">[{\"selector\":\"#anim-6d423f63-8c1d-48a4-8218-e080f945fb50\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-d385c560-61d6-4eff-94c2-c0116404e3cd\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#d9d9d9\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-e91a9091-d788-4237-b6eb-2b3908bd1b59\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-76638dd5-e923-4c37-8934-99f03447a159\">\n<div style=\"position:absolute;width:266.31253%;height:100%;left:-83.15627%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max\" alt=\"photography of people inside room during daytime\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max 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1203w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=227&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 120vh, 267vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ca607fc3-47ce-46f2-be0f-336346011aab\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.73786%;top:32.68608%;width:82.76699%;height:35.76052%;opacity:1\">\n<div id=\"anim-4243953e-6ca4-441a-a7eb-a934d3881490\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a1cea293-68b7-42cf-92cf-71cca11bf1eb\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5865102639296188% 0.5865102639296188% 0.5865102639296188% 0.5865102639296188% \/ 0.904977375565611% 0.904977375565611% 0.904977375565611% 0.904977375565611%\" id=\"el-91e1f96d-98c1-4640-bbd8-2ceb2f611100\">\n<h2 id=\"use-recursion-to-check-all-possible-combinations-of-coins-to-find-the-minimum-number-of-coins-needed-to-create-the-given-sum-update-the-number-of-coins-needed-with-each-iteration\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.565982404692082% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Use recursion to check all possible combinations of coins to find the minimum number of coins needed to create the given sum. Update the number of coins needed with each iteration.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:11.48867%;opacity:1\">\n<div id=\"anim-6d423f63-8c1d-48a4-8218-e080f945fb50\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-d385c560-61d6-4eff-94c2-c0116404e3cd\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 2.8169014084507045% 2.8169014084507045% 2.8169014084507045% 2.8169014084507045%;background-clip:content-box;background-color:#052258\" id=\"el-9b799116-f7f3-4f88-aafc-d52d5a3ec37c\">\n<h1 id=\"simple-approach\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Simple Approach<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Banner-11.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/coin-change-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=coin-change-problem\" rel=\"\">See code implementation<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"9e5d6a53-c17c-415a-b590-e6df6d6fd3f4\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-6ca8f587-405a-4bd5-a165-5c658d6f12e3 [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-2982b9d0-1795-4823-b7b6-dd65e77e849e\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-dccc3857-a790-456c-aa9b-00cce21362c0\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f3a673\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-6ca8f587-405a-4bd5-a165-5c658d6f12e3\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-27f2951c-8b6e-4772-8cc9-8a5b431fd5c6\">\n<div style=\"position:absolute;width:266.31253%;height:100%;left:-83.15627%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max\" alt=\"people sitting beside rectangular brown table with laptops\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max 6016w,https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4812&amp;h=3212&amp;fit=max 4812w,https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3609&amp;h=2409&amp;fit=max 3609w,https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2406&amp;h=1606&amp;fit=max 2406w,https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1203&amp;h=803&amp;fit=max 1203w,https:\/\/images.unsplash.com\/photo-1573165759995-5865a394a1aa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw2M3x8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjY5OTAyNjU0&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=227&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 120vh, 267vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f24b57dc-e5b9-416a-be22-4a071ebd4794\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:32.20065%;width:85.43689%;height:26.05178%;opacity:1\">\n<div id=\"anim-2982b9d0-1795-4823-b7b6-dd65e77e849e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-dccc3857-a790-456c-aa9b-00cce21362c0\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 1.2422360248447204% 1.2422360248447204% 1.2422360248447204% 1.2422360248447204%\" id=\"el-9cdf83be-84a7-4e37-9e13-228230d7f1b6\">\n<h2 id=\"time-complexity-exponential-every-recursive-call-is-making-n-recursive-callsspace-complexity-o1\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #347eff\">Time complexity:<\/span><span style=\"color: #347eff\"> <\/span><span style=\"color: #fff\">Exponential. (every recursive call is making n recursive calls)<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #347eff\">Space complexity:<\/span><span style=\"color: #347eff\"> <\/span><span style=\"color: #fff\">O(1)<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Banner-11.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/coin-change-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=coin-change-problem\" rel=\"\">Explore other approach<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"8df77031-9e15-4779-a2a9-fe68c9e86633\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-979cbea8-fa86-49f0-bda9-02aaea13af9b\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5e02eed2-31d7-482c-9b3e-4a4573c9ba2d\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-cdd25856-ebc2-4f32-9ee7-0e92f1c0b40c [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-59716949-11b4-4303-9cfc-c4e32b144b1b\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e9c4ccea-1f61-4f8a-9b3f-0c227717797b\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f3f3f3\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-cdd25856-ebc2-4f32-9ee7-0e92f1c0b40c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-abc994fd-18e5-4821-9439-6a805f711046\">\n<div style=\"position:absolute;width:118.67612%;height:100%;left:-9.33806%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4016&amp;h=6016&amp;fit=max\" alt=\"shallow focus photo of woman using gray laptop computer\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4016&amp;h=6016&amp;fit=max 4016w,https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3212&amp;h=4812&amp;fit=max 3212w,https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2409&amp;h=3609&amp;fit=max 2409w,https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1606&amp;h=2406&amp;fit=max 1606w,https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=803&amp;h=1203&amp;fit=max 803w,https:\/\/images.unsplash.com\/photo-1573495627094-cbfef909a47b?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw4MHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjczNDQzODM1&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=509&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 53vh, 119vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0a76cce9-5584-441b-bdfc-8adb40d0cc18\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:5.09709%;top:41.26214%;width:89.80583%;height:35.76052%;opacity:1\">\n<div id=\"anim-979cbea8-fa86-49f0-bda9-02aaea13af9b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-5e02eed2-31d7-482c-9b3e-4a4573c9ba2d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5405405405405406% 0.5405405405405406% 0.5405405405405406% 0.5405405405405406% \/ 0.904977375565611% 0.904977375565611% 0.904977375565611% 0.904977375565611%\" id=\"el-68dc11dc-e204-44c0-b174-4c7e4f8d8ead\">\n<h2 id=\"solve-the-problem-by-breaking-it-down-into-smaller-subproblems-and-using-a-bottom-up-approach-to-compute-dpi-1isubproblems-which-stores-the-minimum-number-of-coins-needed-to-create\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.4432432432432432% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Solve the problem by breaking it down into smaller subproblems and using a bottom-up approach to compute&nbsp;<\/span><br \/>\n<span style=\"color: #fff\">dp[i] (1&lt;=i&lt;=subproblems) which stores the minimum number of coins needed to create the sum.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:25.40453%;opacity:1\">\n<div id=\"anim-59716949-11b4-4303-9cfc-c4e32b144b1b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e9c4ccea-1f61-4f8a-9b3f-0c227717797b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 1.2738853503184715% 1.2738853503184715% 1.2738853503184715% 1.2738853503184715%;background-clip:content-box;background-color:#052258\" id=\"el-c443c2c6-2783-4348-9cb4-4ac952ad3b88\">\n<h1 id=\"efficient-approach-dynamic-programming\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Efficient Approach: Dynamic Programming<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Banner-11.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/coin-change-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=coin-change-problem\" rel=\"\">Check out its algorithm<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"9cf6163f-6d49-4cd9-b20d-820dab8f09f4\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4ec960fd-c651-4e6c-a06e-85d339bbf33f\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-fd7dfa93-652f-4e93-b9d3-4ffc2447f351\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-40f6b0e9-1eac-4445-a21b-d410e0a80d30 [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#262626\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-40f6b0e9-1eac-4445-a21b-d410e0a80d30\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-1a4302e2-14d2-4e1b-a167-83e3c20cc912\">\n<div style=\"position:absolute;width:118.51852%;height:100%;left:-9.25926%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=4000&amp;h=6000&amp;fit=max\" alt=\"media\/unsplash:7wLQNYKL3Rw\" srcSet=\"https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=4000&amp;h=6000&amp;fit=max 4000w,https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=3200&amp;h=4800&amp;fit=max 3200w,https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=2400&amp;h=3600&amp;fit=max 2400w,https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=1600&amp;h=2400&amp;fit=max 1600w,https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=800&amp;h=1200&amp;fit=max 800w,https:\/\/images.unsplash.com\/photo-1631624210938-539575f92e3c?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwyNHx8c29mdHdhcmUlMjBkZXZlbG9wbWVudHxlbnwwfHx8fDE2NjYwMDQwNzM&amp;ixlib=rb-1.2.1&amp;fm=jpg&amp;w=340&amp;h=510&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 53vh, 119vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-714d4b27-56b9-4059-86b7-f96b9aebf636\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:41.58576%;width:85.43689%;height:26.05178%;opacity:1\">\n<div id=\"anim-4ec960fd-c651-4e6c-a06e-85d339bbf33f\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-fd7dfa93-652f-4e93-b9d3-4ffc2447f351\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 1.2422360248447204% 1.2422360248447204% 1.2422360248447204% 1.2422360248447204%\" id=\"el-9e7f24fa-f710-4cd5-96c0-5fca546c5906\">\n<h2 id=\"time-complexity-onsum-n-no-of-distinct-coins-sum-desired-sum-space-complexity-osum\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #347eff\">Time complexity: <\/span><span style=\"color: #fff\">O(n*sum) &nbsp;n- no of distinct coins, sum- desired sum.<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #347eff\">Space complexity:<\/span><span style=\"color: #fff\"> O(sum)<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Banner-11.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/coin-change-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=coin-change-problem\" rel=\"\">See code implementation<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"936b559d-4dc0-423a-9d89-b4d4ba99b081\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0ba830e7-8086-4084-b651-d452d45b05d5\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-44293ae2-6ebb-4803-9fc8-b2729963bf38\",\"keyframes\":{\"transform\":[\"translate3d(-112.4161%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1000,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-dc995e89-543a-4d45-a6df-c291bc31a3fc\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-2a2c7709-1b19-4f44-9b51-ae9cbc882b99\",\"keyframes\":{\"transform\":[\"translate3d(-109.375%, 0px, 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src=\"https:\/\/images.unsplash.com\/photo-1451187580459-43490279c0fa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwzfHxiaWclMjBkYXRhfGVufDB8fHx8MTY3MjY2MDQyNA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4256&amp;h=2832&amp;fit=max\" alt=\"photo of outer space\" srcSet=\"https:\/\/images.unsplash.com\/photo-1451187580459-43490279c0fa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwzfHxiaWclMjBkYXRhfGVufDB8fHx8MTY3MjY2MDQyNA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4256&amp;h=2832&amp;fit=max 4256w,https:\/\/images.unsplash.com\/photo-1451187580459-43490279c0fa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwzfHxiaWclMjBkYXRhfGVufDB8fHx8MTY3MjY2MDQyNA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3404&amp;h=2265&amp;fit=max 3404w,https:\/\/images.unsplash.com\/photo-1451187580459-43490279c0fa?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwzfHxiaWclMjBkYXRhfGVufDB8fHx8MTY3MjY2MDQyNA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2553&amp;h=1699&amp;fit=max 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template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-380e77ec-becc-4e13-b03c-a3c1bed377c3\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 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style=\"position:absolute;pointer-events:none;left:8.00971%;top:77.6699%;width:85.43689%;height:11.97411%;opacity:1\">\n<div id=\"anim-dc995e89-543a-4d45-a6df-c291bc31a3fc\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-2a2c7709-1b19-4f44-9b51-ae9cbc882b99\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-109.375%, 0px, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 2.7027027027027026% 2.7027027027027026% 2.7027027027027026% 2.7027027027027026%\" id=\"el-faf98ac9-3bde-42ce-ba57-b4ed553c9aaf\">\n<h2 id=\"click-on-the-link-below-to-start-your-journey\" class=\"fill text-wrapper\" 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