53. Maximum Subarray
Tags: ‘Array’, ‘Divide and Conquer’, ‘Dynamic Programming’
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
方法1： DP, 类似还有134 Gas Station / 517 Washing Machines
public int maxSubArray(int[] nums) {
int n = nums.length;
int[] dp = new int[n]; // dp[i] is the maximum subarray sum ending with nums[i]
dp[0] = nums[0];
int max = dp[0];
for (int i = 1; i < n; i++) {
dp[i] = nums[i] + (dp[i - 1] > 0 ? dp[i - 1] : 0);
max = Math.max(max, dp[i]);
}
return max;
}
方法2： divide and conquer 类似merge sort