算法导论——最大子数组和

来源：互联网发布：阿提拉全面战争知乎编辑：程序博客网时间：2024/04/28 13:04
import java.io.IOException;import java.util.ArrayList;import java.util.List;import org.junit.Test;public class MaxSumOfSubArray {            @Test    public void test() throws IOException{        //int a[] = {13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7};                String s = MyFileUtil.read("src/test/java/lily/utils/arrays.txt");        System.out.println(s);        String[] ss = s.split(",");        System.out.println(ss.length);        List<Integer> list = new ArrayList<Integer>();        for(int i=0;i<ss.length;i++){            list.add(Integer.parseInt(ss[i]));        }                //List<Integer> list = Arrays.asList(13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7);        SubArray max = divideConqueMethod(list);        System.out.println(list.subList(max.maxLeft, max.maxRight+1));        System.out.println(max.maxSum);                max = linearMethod(list);        System.out.println(list.subList(max.maxLeft, max.maxRight+1));        System.out.println(max.maxSum);                    }                /**     * 分治法     * @param list     * @return     */    public SubArray divideConqueMethod(List<Integer> list){        if(list==null || list.size()==0){            return null;        }        return divideConqueMethod(list,0,list.size()-1);    }        public SubArray divideConqueMethod(List<Integer> list,int left, int right){                if(left==right){            return new SubArray(left,left,list.get(left));        }else{            int mid = (left+right)/2;            SubArray leftMaxArray = divideConqueMethod(list, left, mid);            SubArray rightMaxArray = divideConqueMethod(list, mid+1, right);            SubArray midMaxArray = getMaxArray(list,left,mid,right);            if(leftMaxArray.maxSum>=rightMaxArray.maxSum && leftMaxArray.maxSum>=midMaxArray.maxSum){                return leftMaxArray;            }            if(rightMaxArray.maxSum>=leftMaxArray.maxSum && rightMaxArray.maxSum>=midMaxArray.maxSum){                return rightMaxArray;            }            return midMaxArray;        }    }         private SubArray getMaxArray(List<Integer> list, int left, int mid, int right) {        int leftMax=Integer.MIN_VALUE,rightMax=Integer.MIN_VALUE;        int leftMaxPosition=mid,rightMaxPosition=mid;        int leftSum=0,rightSum=0;        for(int i=mid; i>=left;i--){            leftSum += list.get(i);            if(leftSum>leftMax){                leftMaxPosition=i;                leftMax =leftSum;            }        }        for(int j=mid+1;j<=right;j++){            rightSum += list.get(j);            if(rightSum>rightMax){                rightMaxPosition=j;                rightMax=rightSum;            }        }        return new SubArray(leftMaxPosition, rightMaxPosition, rightMax+leftMax);    }         class SubArray{        public int maxLeft;        public int maxRight;        public int maxSum;        public SubArray(int maxLeft, int maxRight, int maxSum){            this.maxLeft = maxLeft;            this.maxRight = maxRight;            this.maxSum = maxSum;        }    }        /**     * 线性算法     */    public SubArray linearMethod(List<Integer> list){        int maxLeft=0,maxRight=0;        int maxSum=list.get(0);                for(int i=1;i<list.size();i++){            int tempMaxLeft=i;            int tempMaxSum=Integer.MIN_VALUE;            int tempSum=0;            for(int j=i;j>=0;j--){                tempSum+=list.get(j);                if(tempSum>tempMaxSum){                    tempMaxSum=tempSum;                    tempMaxLeft=j;                }            }                        if(tempMaxSum>maxSum){                maxSum=tempMaxSum;                maxLeft=tempMaxLeft;                maxRight=i;            }        }                return new SubArray(maxLeft, maxRight, maxSum);    }         }
可稍加修改，使用https://leetcode.com/problems/maximum-subarray/进行验证
使用分治法时，通过；使用线性方法时，超时了，证明当list的size较大时，分治法的效率更高
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