Maximum Subarray

最新推荐文章于 2025-05-15 16:32:28 发布

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最新推荐文章于 2025-05-15 16:32:28 发布

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本文介绍了一种寻找具有最大和的连续子数组的有效算法。通过动态规划方法解决了给定问题，示例中使用了整数数组[-2,1,-3,4,-1,2,1,-5,4]，并找到了最大和子数组[4,-1,2,1]，其和为6。

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<span style="font-family: Arial, Helvetica, sans-serif; background-color: rgb(255, 255, 255);">Question:</span>

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4],
the contiguous subarray [4,−1,2,1] has the largest sum = 6.

Answer:

--Thought 1: divide to left and right part, compare largest subarray of left, subarray of right part and the cross-over of left and right subs. In recursive way

--Thought 2: DP

public class Solution {
    public int maxSubArray(int[] A) {
        if(A.length == 0) return 0;
        if(A.length == 1) return A[0];
        int[] sum = new int[A.length];
        sum[0] = A[0];
        for(int i=1; i<A.length; i++){
            sum[i] = Math.max(sum[i-1] + A[i], A[i]);
        }
        Arrays.sort(sum);
        return sum[A.length-1];
    }
}