最大子序列和问题

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问题描述：

给定一个整数序列，a0, a1, a2, …… , an（项可以为负数），求其中最大的子序列和。如果所有整数都是负数，那么最大子序列和为0；
例如：对于序列-2， 11， -4， 13， -5， –2。所求的最大子序列和为20（从11到13，即从a1到a3）。

package com.ql;import java.util.Arrays;/** * @author Administrator * */public class MaxSubSum {    public static void main(String[] args){        int [] a={-2,11,-4,13,-5,-2};        //System.out .println(maxSubSum1(a));        //System.out .println(maxSubSum2(a));        //System.out .println(maxSubSum3(a));        System.out .println(maxSubSum4(a));    }    /**     * @author Administrator     * 运行时间为O(N^3)     */     public static int maxSubSum1(int [] a){        int maxSum = 0;        for(int i = 0;i<a.length;i++)            for(int j = i;j<a.length;j++){                int thisSum = 0;                for(int k = i;k<=j;k++){                    thisSum += a[k];                    if(thisSum>maxSum)                        maxSum=thisSum;                }            }        return maxSum;    }    /**     * @author Administrator     * 运行时间为O(N^2)     */     public static int maxSubSum2(int [] a){        int maxSum = 0;        for(int i = 0;i < a.length;i++){            int thisSum = 0;            for(int j = i;j<a.length;j++){                thisSum += a[j];                if(thisSum>maxSum)                    maxSum=thisSum;            }        }        return maxSum;    }    /**     * @author Administrator     * 运行时间为O(NlogN)     */    private static int maxSumRec(int a[],int left,int right){        if(left == right)            if(a[left]>0)                return a[left];            else                return 0;        int center = (left + right)/2;        int maxLeftSum = maxSumRec(a, left, center);        int maxRightSum = maxSumRec(a, center+1, right);        int maxLeftBorderSum = 0,leftBorderSum = 0;        for(int i = center;i>=left;i--){            leftBorderSum += a[i];            if(leftBorderSum>maxLeftBorderSum)                maxLeftBorderSum = leftBorderSum;        }        int maxRightBorderSum = 0,rightBorderSum = 0;        for(int i = center+1;i<=right;i++){            rightBorderSum += a[i];            if(rightBorderSum>maxRightBorderSum)                maxRightBorderSum = rightBorderSum;        }        return max3(maxLeftSum,maxRightSum,maxLeftBorderSum+maxRightBorderSum);    }    private static int max3(int maxLeftSum, int maxRightSum, int i) {        int[] str = {maxLeftSum,maxRightSum,i};        Arrays.sort(str);        return str[2];    }    public static int maxSubSum3(int [] a){        return maxSumRec(a, 0, a.length-1);    }    /**     * @author Administrator     * 运行时间为O(N)     */    public static int maxSubSum4(int [] a){        int maxSum = 0,thisSum = 0;        for(int j = 0;j < a.length;j++){            thisSum += a[j];            if(thisSum > maxSum)                maxSum = thisSum;            else if(thisSum < 0)                thisSum = 0;        }        return maxSum;    }}

先贴代码，有时间再详细注解，欢迎指正！

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