Maximum Subarray

April 3, 2020

Introduction

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4], Output: 6 Explanation: [4,-1,2,1] has the largest sum = 6. Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

Solution

This is an O(n) simple solution by using maxSoFar with left and right sides.

func maxSubArray(nums []int) int {
	n := len(nums)
	if n == 0 {
		return 0
	}
	left := make([]int, n+1)
	for i, val := range nums {
		left[i+1] = max(left[i] + val, 0)
	}
	maxSoFar := nums[0]
	right := 0
	for j := n-1; j >= 0; j-- {
		maxSoFar = max(maxSoFar, left[j] + nums[j] + right)
		right = max(right + nums[j], 0)
	}
	return maxSoFar
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}