Practice
Resources
Contests
Online IDE
New
Free Mock
Events New Scaler
Practice
Improve your coding skills with our resources
Contests
Compete in popular contests with top coders
Events
Attend free live masterclass hosted by top tech professionals
New
Scaler
Explore Offerings by SCALER

# Rod Cutting

Problem Description

There is a rod of length N lying on the x-axis with its left end at x = 0 and right end at x = N. Now, there are M weak points on this rod denoted by positive integer values(all less than N) A1, A2, ..., AM. You have to cut the rod at all these weak points. You can perform these cuts in any order. After a cut, the rod gets divided into two smaller sub-rods. The cost of making a cut is the length of the sub-rod in which you are making a cut.

Your aim is to minimize this cost. Return an array denoting the sequence in which you will make cuts. If two different sequences of cuts give the same cost, return the lexicographically smallest.

Notes:
• Sequence a1, a2 ,..., an is lexicographically smaller than b1, b2 ,..., bm, if and only if at the first i where ai and bi differ, ai < bi, or if no such i found, then n < m.
• N can be up to 109.

Problem Constraints
0 <= A <= 109
1 <= |B| <= 100

Input Format
The first argument is an integer A, representing the value of N.
The second argument is an integer array B, representing the weak points of rod.

Output Format
Return an array denoting the sequence in which you will make cuts.

Example Input
A = 6
B = [1, 2, 5]

Example Output
[2, 1, 5]

Example Explanation
```N = 6
A = [1, 2, 5]

If we make cuts in order [1, 2, 5], let us see what total cost would be.
For first cut, the length of rod is 6.
For second cut, the length of sub-rod in which we are making cut is 5(since we already have made a cut at 1).
For third cut, the length of sub-rod in which we are making cut is 4(since we already have made a cut at 2).
So, total cost is 6 + 5 + 4.

Cut order          | Sum of cost
(lexicographically | of each cut
sorted)           |
________________|____________
[1, 2, 5]          | 6 + 5 + 4 = 15
[1, 5, 2]          | 6 + 5 + 4 = 15
[2, 1, 5]          | 6 + 2 + 4 = 12
[2, 5, 1]          | 6 + 4 + 2 = 12
[5, 1, 2]          | 6 + 5 + 4 = 15
[5, 2, 1]          | 6 + 5 + 2 = 13

So, we return [2, 1, 5].
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Hints
• Hint 1
• Solution Approach
• Complete Solution

## Discussion

Free Mock Assessment
Fill up the details for personalised experience.
Phone Number *
OTP will be sent to this number for verification
+1 *
+1
Change Number
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
*Enter the expected year of graduation if you're student
Current Employer
Company Name
College/University Name
Job Title
Job Title
Software Development Engineer (Backend)
Software Development Engineer (Frontend)
Software Development Engineer (Full Stack)
Data Scientist
Android Engineer
iOS Engineer
Devops Engineer
Support Engineer
Research Engineer
Engineering Intern
QA Engineer
Co-founder
SDET
Product Manager
Product Designer
Backend Architect
Program Manager
Release Engineer