动态规划实战8 leetcode-53. Maximum Subarray

确定状态

这道题难就在确定状态。因为根据给定的输入，我们可能在中间找到最大值，而不是在最后找到最大值。

但是我们可以用一个变量去保存全局的最大值

dp[i]表示从下标0至下标i最大的子序列和

状态转移方程

dp[i] = max(dp[i-1]+nums[i],nums[i])\

初始条件和边界条件

dp[0] = =nums[0]

计算的顺序

dp[0] ..... dp[n-1]

代码

class Solution {public int maxSubArray(int[] nums) {int n = nums.length;int[] dp = new int[n];//dp[i] means the maximum subarray ending with A[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;}
}

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