【LeetCode.53】Maximum Subarray（最大子序和 | 动态规划）

最新推荐文章于 2021-09-01 09:36:25 发布

cuiccc2014

最新推荐文章于 2021-09-01 09:36:25 发布

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分类专栏：算法

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本文介绍了一种求解最大子数组和问题的有效算法。通过动态规划方法，该算法能在O(n)的时间复杂度内找到给定整数数组中具有最大和的连续子数组。文章以示例形式展示了算法的具体实现过程。

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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.


class Solution {
    public int maxSubArray(int[] nums) {
        if(nums.length == 0){
            return 0;
        }
        int[] dp = new int[nums.length];
        dp[0] = nums[0];
        for(int i = 1; i < nums.length; i++){
            /** 状态转移方程 */
            dp[i] = Math.max(nums[i], dp[i - 1] + nums[i]);
        }
        int res = dp[0];
        for(int i = 1; i < dp.length; i++){
            res = Math.max(res, dp[i]);
        }
        return res;
    }
}