53. Maximum Subarray #

Problem #

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.

Problem Summary #

Given an integer array nums, find the contiguous subarray with the largest sum (the subarray must contain at least one element) and return its maximum sum.

Solution Approach #

• This problem can be solved with DP or without DP.
• The problem asks for the maximum value of the sum of numbers within some interval in the array. dp[i] represents the maximum sum among all subarrays within the [0,i] interval. The state transition equation is dp[i] = nums[i] + dp[i-1] (dp[i-1] > 0), dp[i] = nums[i] (dp[i-1] ≤ 0).

Code #

package leetcode

// Solution 1 DP
func maxSubArray(nums []int) int {
	if len(nums) == 0 {
		return 0
	}
	if len(nums) == 1 {
		return nums[0]
	}
	dp, res := make([]int, len(nums)), nums[0]
	dp[0] = nums[0]
	for i := 1; i < len(nums); i++ {
		if dp[i-1] > 0 {
			dp[i] = nums[i] + dp[i-1]
		} else {
			dp[i] = nums[i]
		}
		res = max(res, dp[i])
	}
	return res
}

// Solution 2 Simulation
func maxSubArray1(nums []int) int {
	if len(nums) == 1 {
		return nums[0]
	}
	maxSum, res, p := nums[0], 0, 0
	for p < len(nums) {
		res += nums[p]
		if res > maxSum {
			maxSum = res
		}
		if res < 0 {
			res = 0
		}
		p++
	}
	return maxSum
}