最大字段和 暴力 分治 动态规划时间对比

//============================================================================// Name        : maxsum.cpp// Author      : judyge// Version     :// Copyright   : Your copyright notice// Description : Hello World in C++, Ansi-style//============================================================================#include <iostream>#include<time.h>#include<windows.h>using namespace std;/*简单算法:**v[0]不保存数据**T(n)=O(n^2).*/int MaxSum(int *v,int n,int *besti,int *bestj){    int sum=0;    int i,j;    for (i=1;i<=n;i++)    {        int thissum=0;        for (j=i;j<=n;j++)        {            thissum+=v[j];            if (thissum>sum)            {                sum=thissum;                *besti=i;                *bestj=j;            }        }    }    return sum;}

int main() {int 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v[24]={1,2,3,4,5,6,7,-1,8,9,-23,45,34,67,-200,45,67,89,6,7,8-100,2,4};int m=0;int n=0;clock_t start,finish;    double time;    start=clock();MaxSum(v,24,&m,&n);cout<<m<<","<<n<<endl;MaxSum(k,10000,&m,&n);cout<<m<<","<<n<<endl;finish=clock();       time=(double)((finish-start)/CLOCKS_PER_SEC);       printf("start:%ld\t\tfinish:%ld\tfinish-start:%ld\truntime:%f\n",start,finish,finish-start,time);return 0;}

运行结果 

15,193261,7418start:1finish:361finish-start:360runtime:0.000000

编译器的优化 没有超时 ACM肯定不过  O(10000^2) 肯定超时。

/*分治法:**将a[1n]分成a[1n/2]和a[n/2+1n],则a[1n]的最大字段和有三种情况:**(1)a[1n]的最大子段和与a[1n/2]的最大子段和相同**(2)a[1n]的最大子段和与a[n/2n]的最大子段和相同**(3)a[1n]的最大子段和为ai++aj,1<=i<=n/2,n/2+1<=j<=n**T(n)=2T(n/2)+O(n)**T(n)=O(nlogn)*/int MaxSum_DIV(int *v,int l,int r){    int k,sum=0;    if(l==r)        return v[l]>=0?v[l]:0;    else    {        int center=(l+r)/2;        int lsum=MaxSum_DIV(v,l,center);        int rsum=MaxSum_DIV(v,center+1,r);        int s1=0;        int lefts=0;        for (k=center;k>=l;k--)        {            lefts+=v[k];            if(lefts>s1)                s1=lefts;        }        int s2=0;        int rights=0;        for (k=center+1;k<=r;k++)        {            rights+=v[k];            if(rights>s2)                s2=rights;        }        sum=s1+s2;        if(sum<lsum)            sum=lsum;        if(sum<rsum)            sum=rsum;    }    return sum;}/*动态规划算法:**b[j]=max{a[i]++a[j]},1<=i<=j,且1<=j<=n,则所求的最大子段和为max b[j]，1<=j<=n。**由b[j]的定义可易知，当b[j-1]>0时b[j]=b[j-1]+a[j]，否则b[j]=a[j]。故b[j]的动态规划递归式为:**b[j]=max(b[j-1]+a[j],a[j])，1<=j<=n。**T(n)=O(n)*/int MaxSum_DYN(int *v,int n){    int sum=0,b=0;    int i;    for (i=1;i<=n;i++)    {        if(b>0)            b+=v[i];        else            b=v[i];        if(b>sum)            sum=b;    }    return sum;}

int main() {int 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v[24]={1,2,3,4,5,6,7,-1,8,9,-23,45,34,67,-200,45,67,89,6,7,8-100,2,4};int m=0;int n=0;clock_t start,finish;    double time;    start=clock();//MaxSum(v,24,&m,&n);//cout<<m<<","<<n<<endl;cout<<MaxSum_DIV(k,1,10000)<<endl;cout<<MaxSum_DYN(k,10000);finish=clock();       time=(double)((finish-start)/CLOCKS_PER_SEC);       printf("start:%ld\t\tfinish:%ld\tfinish-start:%ld\truntime:%f\n",start,finish,finish-start,time);return 0;}

运行结果

8188681886start:1finish:3finish-start:2runtime:0.000000