[leetcode] Maximum Subarray

標籤：style   class   blog   code   java   http   

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.

More practice:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

https://oj.leetcode.com/problems/maximum-subarray/

思路1：Kadane演算法，複雜度O(n)。

思路2：分治。對於每次遞迴，將數組分半，最大和可能存在

1. 完全在左面部分（遞迴求解）
   
2. 完全在右面部分（遞迴求解）
3. 橫跨左右兩個部分（從中間(必須包含中間元素，否則左右無法串連)向兩邊加，記錄最大值）
   

注意點：注意負數的處理，此題最大值為負數時依然返回最大的負數，也有題目負數時要求返回0。注意兩種情況下最大值的初始化等細節的區別。

 

思路1代碼：

public class Solution {public int maxSubArray(int[] A) {int n = A.length;int i;int maxSum = A[0];int thisSum = 0;for (i = 0; i < n; i++) {thisSum += A[i];if (thisSum > maxSum)maxSum = thisSum;if (thisSum < 0)thisSum = 0;}return maxSum;}public static void main(String[] args) {System.out.println(new Solution().maxSubArray(new int[] { -2, 1, -3, 4,-1, 2, 1, -5, 4 }));}}

思路2代碼：

public class Solution {    public int maxSubArray(int[] A) {        return maxSub(A, 0, A.length - 1);    }    private int maxSub(int[] a, int left, int right) {        if (left == right)            return a[left];        int mid = (left + right) / 2;        int maxLeft = maxSub(a, left, mid);        int maxRight = maxSub(a, mid + 1, right);        int leftHalf = 0, leftHalfMax = Integer.MIN_VALUE;        int rightHalf = 0, rightHalfMax = Integer.MIN_VALUE;        for (int i = mid; i >= left; i--) {            leftHalf += a[i];            if (leftHalf > leftHalfMax)                leftHalfMax = leftHalf;        }        for (int i = mid + 1; i <= right; i++) {            rightHalf += a[i];            if (rightHalf > rightHalfMax)                rightHalfMax = rightHalf;        }        return Math.max(Math.max(maxLeft, maxRight), (leftHalfMax + rightHalfMax));    }    public static void main(String[] args) {        System.out.println(new Solution().maxSubArray(new int[] { -2, -1, -3, -2, -5 }));    }}

參考：

Data Structures and Algorithm Analysis in C

http://blog.csdn.net/xshengh/article/details/12708291