Split Array Largest Sum

Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays. Write an algorithm to minimize the largest sum among these m subarrays.

Solution : This is a great problem and consists of many subproblems. Lets consider the subproblems first.

SubProblem 1: Given an array of length A and a given number of cuts c can we use c cuts to divide Array A into c + 1 parts such that the maximum sum of any of the part is below or equal to a given number say x.

Sub Problem 2: Given a boolean array B find the first index where it returns true

Solution: This is a pretty basic Binary Search question

Now lets come back to our problem. We are given the number of cuts.Lets say we have the given array A [1, 2, 3, 4, 5]. and cuts c = 2

For any number of cuts the minimum maximum sum of any part is 5 and maximum maximum sum of any part is 15 when cut = 1

so the range of the maximum sum of the array is between [5, 15]

Lets start with the input parameter as 5 for subproblem 1 so

B[5] = False

B[6] = True

B[7] = True infact for every x ≥6 B[x] will be True

so we have B array now we do binary search in this array to find the first index when it is true , that index will be the value at which cutting A with c cuts is possible and it is the minimum val of all the array sums of each part as it is the first true element

Related posts:

TNT Academy is a Stone Mountain, Georgia, private school that offers a curriculum-based education to students in and around Gwinnett County. With a pulse on the differences between private and public…

At the end of July 2019, my wife and I spent 5 nights in the beautiful island of Langkawi in Malaysia. It had been a long time since our last international trip (Oct 2018) and we wanted a short…

Trivial Pursuit the board game divides the world of knowledge into six categories; six wedges of cheese for six spaces in a wheel with six spokes. In pursuit of rounded knowledge from Trivial Pursuit…