Algorithm splitting array into sub arrays where the maximum sum among all sub arrays is as low as possible

Question

Let\'s say we have an array of ints: a = {2,4,3,5}

And we have k = 3.

We can split array a in k (3) sub arrays in which the order of the array cannot be chan

Answer 1

We can use binary search to solve this problem.

So, assume that the maximum value for all sub-array is x, so, we can greedily choose each sub-array in O(n) so that the sum of each subarray is maximum and less than or equals to x. After creating all subarray, if the number of sub-array is less than or equal to k, so x is one possible solution, or else, we increase x.

Pseudocode:

int start = Max_Value_In_Array;
int end = Max_Number;

while(start <= end)
   int mid = (start + end)/2;
   int subSum = 0;
   int numberOfSubArray = 1;
   for(int i = 0; i < n; i++){
      if(subSum + data[i] > mid){
          subSum = data[i];
          numberOfSubArray++;
      }else{
          subSum += data[i];
      }
   }
   if(numberOfSubArray <= k)
       end = mid - 1;
   else
       start = mid + 1;

Time complexity O(n log k) with k is the maximum sum possible.