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# Merge sort algorithm

Merge sort is one of the most efficient sorting algorithms. It works on the principle of Divide and Conquer. Merge sort repeatedly breaks down a list into several sublists until each sublist consists of a single element and merging those sublists in a manner that results into a sorted list.

## A merge sort works as follows:

### Top-down Merge Sort Implementation:

The top-down merge sort approach is the methodology which uses recursion mechanism. It starts at the Top and proceeds downwards, with each recursive turn asking the same question such as “What is required to be done to sort the array?” and having the answer as, “split the array into two, make a recursive call, and merge the results.”, until one gets to the bottom of the array-tree.

Example: Let us consider an example to understand the approach better.

1. Divide the unsorted list into n sublists, each comprising 1 element (a list of 1 element is supposed sorted).

Top-down Implementation

1. Repeatedly merge sublists to produce newly sorted sublists until there is only 1 sublist remaining. This will be the sorted list.

### Merging of two lists done as follows:

The first element of both lists is compared. If sorting in ascending order, the smaller element among two becomes a new element of the sorted list. This procedure is repeated until both the smaller sublists are empty and the newly combined sublist covers all the elements of both the sublists.

Merging of two lists

## Implementation Of Merge Sort

``````// example of merge sort in C/C++
// merge function take two intervals
// one from start to mid
// second from mid+1, to end
// and merge them in sorted order

void merge(int *Arr, int start, int mid, int end) {
// create a temp array
int temp[end - start + 1];

// crawlers for both intervals and for temp
int i = start, j = mid+1, k = 0;

// traverse both arrays and in each iteration add smaller of both elements in temp
while(i <= mid && j <= end) {
if(Arr[i] <= Arr[j]) {
temp[k] = Arr[i];
k += 1; i += 1;
}
else {
temp[k] = Arr[j];
k += 1; j += 1;
}
}

// add elements left in the first interval
while(i <= mid) {
temp[k] = Arr[i];
k += 1; i += 1;
}

// add elements left in the second interval
while(j <= end) {
temp[k] = Arr[j];
k += 1; j += 1;
}

// copy temp to original interval
for(i = start; i <= end; i += 1) {
Arr[i] = temp[i - start]
}
}

// Arr is an array of integer type
// start and end are the starting and ending index of current interval of Arr

void mergeSort(int *Arr, int start, int end) {

if(start < end) {
int mid = (start + end) / 2;
mergeSort(Arr, start, mid);
mergeSort(Arr, mid+1, end);
merge(Arr, start, mid, end);
}
}``````
``````// example of merge sort in Java
// merge function take two intervals
// one from start to mid
// second from mid+1, to end
// and merge them in sorted order

void merge(int Arr[], int start, int mid, int end) {

// create a temp array
int temp[] = new int[end - start + 1];

// crawlers for both intervals and for temp
int i = start, j = mid+1, k = 0;

// traverse both arrays and in each iteration add smaller of both elements in temp
while(i <= mid && j <= end) {
if(Arr[i] <= Arr[j]) {
temp[k] = Arr[i];
k += 1; i += 1;
}
else {
temp[k] = Arr[j];
k += 1; j += 1;
}
}

// add elements left in the first interval
while(i <= mid) {
temp[k] = Arr[i];
k += 1; i += 1;
}

// add elements left in the second interval
while(j <= end) {
temp[k] = Arr[j];
k += 1; j += 1;
}

// copy temp to original interval
for(i = start; i <= end; i += 1) {
Arr[i] = temp[i - start]
}
}

// Arr is an array of integer type
// start and end are the starting and ending index of current interval of Arr

void mergeSort(int Arr[], int start, int end) {

if(start < end) {
int mid = (start + end) / 2;
mergeSort(Arr, start, mid);
mergeSort(Arr, mid+1, end);
merge(Arr, start, mid, end);
}
}``````
``````# example of merge sort in Python
# merge function take two intervals
# one from start to mid
# second from mid+1, to end
# and merge them in sorted order
def merge(Arr, start, mid, end) :

# create a temp array
temp[] =  * (end - start + 1)

# crawlers for both intervals and for temp
i, j, k = start, mid+1, 0

# traverse both lists and in each iteration add smaller of both elements in temp
while(i <= mid and j <= end) :
if(Arr[i] <= Arr[j]) :
temp[k] = Arr[i]
k += 1; i += 1
else :
temp[k] = Arr[j]
k += 1; j += 1

# add elements left in the first interval
while(i <= mid) :
temp[k] = Arr[i]
k += 1; i += 1

# add elements left in the second interval
while(j <= end) :
temp[k] = Arr[j]
k += 1; j += 1

# copy temp to original interval
for i in range (start, end+1) :
Arr[i] = temp[i - start]

# Arr is an array of integer type
# start and end are the starting and ending index of current interval of Arr

def mergeSort(Arr, start, end) {

if(start < end) :
mid = (start + end) / 2
mergeSort(Arr, start, mid)
mergeSort(Arr, mid+1, end)
merge(Arr, start, mid, end)``````

### Bottom-Up Merge Sort Implementation:

The Bottom-Up merge sort approach uses iterative methodology. It starts with the “single-element” array, and combines two adjacent elements and also sorting the two at the same time. The combined-sorted arrays are again combined and sorted with each other until one single unit of sorted array is achieved.

Example: Let us understand the concept with the following example.

1. Iteration (1)

Merge pairs of arrays of size 1

2. Iteration (2)

Merge pairs of arrays of size 2

3. Iteration (3)

Merge pairs of arrays of size 4

Thus the entire array has been sorted and merged.

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## Arrays Problems

Array math
Value ranges
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Max Min 150
17:31
Merge Intervals 225 78:57
Merge Overlapping Intervals 225 48:24
Simulation array
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Perfect Peak of Array 200 49:13
Move Zeroes 200 27:19
Make equal elements Array 200 33:22
Segregate 0s and 1s in an array 200 15:27
Array Sum 200 34:32
Kth Row of Pascal's Triangle 225
28:32
Spiral Order Matrix II 225 48:40
Pascal Triangle 225 26:46
Anti Diagonals 225 41:46
Bucketing
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Triplets with Sum between given range 200
76:15
Balance Array 200 62:17
Find Duplicate in Array 450 40:13
Maximum Consecutive Gap 450 58:46
Arrangement
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Sort array with squares! 200 31:22
Largest Number 225 70:26
Rotate Matrix 300 60:26
Next Permutation 300 63:13
Find Permutation 300 56:00
Hash search
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Occurence of Each Number 200 26:15
Sorting
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Noble Integer 200 43:30
Reorder Data in Log Files 200 42:17
Set Intersection 200 56:13
Wave Array 225 22:08
Hotel Bookings Possible 225 66:06
Max Distance 250 68:14
Maximum Unsorted Subarray 250 68:52
Space recycle
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Set Matrix Zeros 300 48:04
First Missing Integer 300 64:38
Maximum Sum Square SubMatrix 300 57:15
Missing / repeated number
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First Missing Integer 300 64:38
Repeat and Missing Number Array 350 63:55
N/3 Repeat Number 600
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