01背包、完全背包、多重背包问题的C++实现及路径记录

这里主要实现路径记录，只求最值问题移步

01背包、完全背包、多重背包问题的C++实现

以下均打印输出路径，即装入背包的物品序号，和最大值。

01背包问题

#include <iostream>
#include<algorithm>

using namespace std;

int main()
{
    int total_weight = 10;
    int w[6] = { 0,5,4,3,2,1 };
    int v[6] = { 0,1,2,3,4,5 };
    int dp[11] = { 0 };
    int path[6][11] = { 0 };

    for (int i = 1; i <= 5; i++)
        for (int j = 10; j >= w[i]; j--)
            if (dp[j] < dp[j - w[i]] + v[i])
            {
                dp[j] = dp[j - w[i]] + v[i];
                path[i][j] = 1;
            }

    int i = 5, j = 10;
    while (i > 0 && j > 0)
    {
        if (path[i][j] == 1)
        {
            cout << i << ' ';
            j -= w[i];
        }
        i--;
    }
    cout << endl;

    cout << "总的价值为: " << dp[10] << endl;
    return 0;
}

完全背包问题

#include <iostream>
#include<algorithm>

using namespace std;

int main()
{
    int total_weight = 10;
    int w[6] = { 0,5,4,3,2,1 };
    int v[6] = { 0,1,2,3,4,5 };
    int dp[11] = { 0 };
    int path[6][11] = { 0 };

    for (int i = 1; i <= 5; i++)
        for (int j = w[i]; j <= 10; j++)
            if (dp[j] < dp[j - w[i]] + v[i])
                {
                    dp[j] = dp[j - w[i]] + v[i];
                    path[i][j]=1;
                }

    int i = 5, j = 10;
    while (i > 0 && j > 0)
    {
        if (path[i][j] == 1)
        {
            cout << i << ' ';
            j -= w[i];
        }
        else
            i--;
    }
    cout << endl;

    cout << "总的价值为: " << dp[10] << endl;
    return 0;
}

多重背包问题

#include <iostream>
#include<algorithm>

using namespace std;

int main()
{
    int total_weight = 10;
    int w[6] = { 0,5,4,3,2,1 };
    int v[6] = { 0,1,2,3,4,5 };
    int cot[6] = { 0,1,2,1,2,1 };
    int dp[11] = { 0 };
    int path[6][11] = { 0 };

    for (int i = 1; i <= 5; i++)
        for (int k = 1; k <= cot[i]; k++)
            for (int j = 10; j >= w[i]; j--)
                if (dp[j] < dp[j - w[i]] + v[i])
                {
                    dp[j] = dp[j - w[i]] + v[i];
                    path[i][j] = 1;
                }

    int i = 5, j = 10;
    while (i > 0 && j > 0)
    {
        if (path[i][j] == 1&&cot[i])
        {
            cout << i << ' ';
            j -= w[i];
            cot[i]--;
        }
        else
            i--;
    }
    cout << endl;

    cout << "总的价值为: " << dp[10] << endl;
    return 0;
}