Find the index of the subarray whose sum is minimum

Question

Given an array of length n, with integers(can be negative or positive). Find the starting and ending index of the subarray with minimum sum possible.

Answer 1

As you specified this is about Kadanes Algorithm, it is easy to find a lot of references about it. GeeksForGeeks : Smallest sum contiguous subarray kindly explains about the algorithm and provides implementations in a few languages.

Based on the python code from that page, I have revised it to return begin/end indices rather than the sum value. The idea is keeping the range indices along with the sum value.

import sys

def smallestSumSubarr(arr, n):
    min_ending_here = sys.maxint
    min_so_far = sys.maxint
    min_so_far_range = (-1, 0) # save indices

    for i in range(n):
        if (min_ending_here > 0):
            min_ending_here = arr[i]
            min_ending_here_range = (i, i) # start over
        else:
            min_ending_here += arr[i]
            min_ending_here_range = (min_so_far_range[0], i) # extend the range

        if min_so_far > min_ending_here: # update both value and range
            min_so_far = min_ending_here
            min_so_far_range = min_ending_here_range

    return min_so_far_range # return range instead of value


# Usage
arr = [3, -4, 2, -3, -1, 7, -5]
n = len(arr)
print "Smallest sum range(inclusive): ", smallestSumSubarr(arr, n)

On STDOUT, you will see

Smallest sum range(inclusive):  (1, 4)