Question

I am trying to a C++ implementation of this knapsack problem using branch and bounding. There is a Java version on this website here: Implementing branch and bound for knapsack

I’m trying to make my C++ version print out the 90 that it should, however it’s not doing that, instead, it’s printing out 5.

Does anyone know where and what the problem may be?

#include <queue>
#include <iostream>
using namespace std;

struct node
{
    int level;
    int profit;
    int weight;
    int bound;
};

int bound(node u, int n, int W, vector<int> pVa, vector<int> wVa)
{
    int j = 0, k = 0;
    int totweight = 0;
    int result = 0;

    if (u.weight >= W)
    {
        return 0;
    }
    else
    {
        result = u.profit;
        j = u.level + 1;
        totweight = u.weight;

        while ((j < n) && (totweight + wVa[j] <= W))
        {
            totweight = totweight + wVa[j];
            result = result + pVa[j];
            j++;
        }

        k = j;

        if (k < n)
        {
            result = result + (W - totweight) * pVa[k]/wVa[k];
        }
        return result;
    }
}

int knapsack(int n, int p[], int w[], int W)
{
    queue<node> Q;
    node u, v;
    vector<int> pV;
    vector<int> wV;
    Q.empty();

    for (int i = 0; i < n; i++)
    {
        pV.push_back(p[i]);
        wV.push_back(w[i]);
    }

    v.level = -1; 
    v.profit = 0;
    v.weight = 0;

    int maxProfit = 0;

    //v.bound = bound(v, n, W, pV, wV);
    Q.push(v);

    while (!Q.empty())
    {
        v = Q.front();
        Q.pop();

        if (v.level == -1)
        {
            u.level = 0;
        }
        else if (v.level != (n - 1))
        {
            u.level = v.level + 1;
        }

        u.weight = v.weight + w[u.level];
        u.profit = v.profit + p[u.level];

        u.bound = bound(u, n, W, pV, wV);

        if (u.weight <= W && u.profit > maxProfit)
        {
            maxProfit = u.profit;
        }

        if (u.bound > maxProfit)
        {
            Q.push(u);
        }

        u.weight = v.weight;
        u.profit = v.profit;

        u.bound = bound(u, n, W, pV, wV);

        if (u.bound > maxProfit)
        {
            Q.push(u);
        }
    }
    return maxProfit;
}

int main()
{
    int maxProfit;
    int n = 4;
    int W = 16;
    int p[4] = {2, 5, 10, 5};
    int w[4] = {40, 30, 50, 10};

    cout << knapsack(n, p, w, W) << endl;

    system("PAUSE");
}

Answer 1

I think you have put the profit and weight values in the wrong vectors. Change:

int p[4] = {2, 5, 10, 5};
int w[4] = {40, 30, 50, 10};

to:

int w[4] = {2, 5, 10, 5};
int p[4] = {40, 30, 50, 10};

and your program will output 90.