动态规划法求解01背包问题C++代码

动态规划法求解01背包问题

以下代码为动态规划法求解01背包问题并统计代码运行300遍的平均运行时间。

#include <iostream>
#include <windows.h>
#include <iomanip>
#include <time.h>

using namespace std;

int KnapSack(int w[], int v[], int n, int C){
    int V[n+1][C+1];
    int i, j;
    int x[n+1];
    for(i=0; i<=n; i++) //a[0] 到 a[n]
        V[i][0] = 0;    //初始化第0列
    for(j=0; j<=C; j++)
        V[0][j] = 0;    //初始化第0行

    for(i=1; i<=n; i++)
        for(j=1; j<=C; j++)
            if(j<w[i])
                V[i][j] = V[i-1][j];
            else
                V[i][j] = max(V[i-1][j],V[i-1][j-w[i]]+v[i]);
    for(j=C,i=n; i>0; i--){
        if(V[i][j]>V[i-1][j]){
            x[i]=1;
            j=j-w[i];
        }
        else
            x[i]=0;
    }
    return V[n][C];
}

int main()
{


    LARGE_INTEGER nFreq;
    LARGE_INTEGER nBeginTime;
    LARGE_INTEGER nEndTime;
    double time;

    int w[] = {0,2,2,6,5,4};
    int v[] = {0,6,3,5,4,6};
    int n=5, C = 10;	//5个物品，背包最大重量为10
    int m;

    int i=0;
    double SumTime=0.0;
    QueryPerformanceFrequency(&nFreq);
    while(i<300){
        QueryPerformanceCounter(&nBeginTime);

        m = KnapSack(w,v,n,C);

        QueryPerformanceCounter(&nEndTime);
        time=(double)(nEndTime.QuadPart-nBeginTime.QuadPart)*1000000000/(double)(nFreq.QuadPart);
        SumTime+=time;
        i++;
    }
    time = SumTime/300.0;
    cout << "Max Value is " << m << endl;
    cout << "Average running time is : "  << time << " ns."; //单位是纳秒.
    return 0;
}