求一个数组的子数组的最大和

/**
 * Created by elvalad on 2014/12/4.
 * 求一个数组的子数组的最大和
 */
import java.util.ArrayList;
import java.util.Scanner;

public class MaxSubArray {
    /* 暴力遍历所有子数组的和 */
    public static int maxSubArray1(ArrayList<Integer> a) {
        int sum = 0;
        int max = Integer.MIN_VALUE;
        for (int i = 0; i < a.size(); i++) {
            sum = 0;
            for (int j = i; j < a.size(); j++) {
                sum += a.get(j);
                if (sum > max) {
                    max = sum;
                }
            }
        }
        return max;
    }

    /* 递归实现 */
    public static int maxSubArray2(ArrayList<Integer> a, int low, int high) {
        int max = Integer.MIN_VALUE;
        int max1 = Integer.MIN_VALUE;
        int max2 = Integer.MIN_VALUE;
        int max3 = Integer.MIN_VALUE;
        int max4 = Integer.MIN_VALUE;
        int sum = 0;

        if (low < high) {
            int mid = low + (high - low)/2;
            /* 最大子数组为左半部分的子数组最大值 */
            max1 = maxSubArray2(a, low, mid);
            /* 最大子数组为右半部分的子数组最大值 */
            max2 = maxSubArray2(a, mid + 1, high);
            /* 最大子数组跨越mid元素，所以最大值必定为mid向左的最大值加上mid向右的最大值 */
            for (int i = mid; i >= low; i--) {
                sum += a.get(i);
                if (sum > max3) {
                    max3 = sum;
                }
            }
            sum = 0;
            for (int i = mid + 1; i <= high; i++) {
                sum += a.get(i);
                if (sum > max4) {
                    max4 = sum;
                }
            }
            return Math.max(Math.max(max1, max2), (max3 + max4));
        } else {
            return a.get(0);
        }
    }

    /* 动态规划 */
    public static int maxSubArray3(ArrayList<Integer> a) {
        int max = Integer.MIN_VALUE;
        int sum = 0;

        /* 每个元素更新sum的值，当sum<0时清零，同时如果sum>max时更新max */
        for (int i = 0; i < a.size(); i++) {
            sum += a.get(i);
            if (sum > max) {
                max = sum;
            } else if (sum < 0) {
                sum = 0;
            }
        }
        return max;
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        ArrayList<Integer> array = new ArrayList<Integer>();
        while (scan.hasNext()) {
            array.add(scan.nextInt());
        }
        System.out.println("The max sub array is :" + maxSubArray1(array));
        System.out.println("The max sub array is :" + maxSubArray2(array, 0, array.size()-1));
        System.out.println("The max sub array is :" + maxSubArray3(array));
    }
}