[leetcode53]最长子数组 Maximum Subarray Kadane's算法

【题目】

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.

【思路】

• Kadane's Algorithm 位置的移动通过判断cur正负，为负置0。

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https://blog.csdn.net/sinat_34976604/article/details/80970936

update 2021.08.22 DP动态规划

从后往前倒推，握手问题

第一个数的最长序列L1=MAX(L1本身值，后面数最长序列L2+L1本身值）

答案ans=MAX（当前ans，当前数最长序列Ln）

【代码】

Kadane's Algorithm 原代码

class Solution {
    public int maxSubArray(int[] nums) {
        int sum=Integer.MIN_VALUE;
        int cur=0;
        for(int i=0;i<nums.length;i++){
            cur+=nums[i];
            sum=Math.max(sum,cur);
            cur=cur<0?0:cur;
        }
        return sum;
    }
}

动态规划 二刷

    public int maxSubArray(int[] nums) {
        if(nums.length==1)
            return nums[0];

        
        int sum[]=new int[nums.length];
        sum[nums.length-1]=nums[nums.length-1];
        int ans=sum[nums.length-1];//注意ans最初赋值
        for(int i=nums.length-1;i>0;i--){
            sum[i-1]=Math.max(nums[i-1]+sum[i],nums[i-1]);
            ans=Math.max(sum[i-1],ans);
        }
        return ans;
    }