Knapsack Problem(背包问题)

#include <bits/stdc++.h>

using namespace std;

int w[4]={2, 1, 3, 2};
int v[4]={3, 2, 4, 2};
int n=4, W=5;

// Recursion algorithm
int REC(int num, int rem)
{
    int res;
    if(num == n) res = 0;
    else if(rem < w[num]) res = REC(num + 1, rem);
    else res = max(REC(num + 1, rem), REC(num + 1, rem-w[num]) + v[num]);
    return res;
}

int dp[5][6]={0};

int DP(int rem)
{
    int i=0, j=0;
    for(i = 0; i < n; i++)
    {
        for(j = 0; j <= W; j++)
        {
            if(w[i] > j) dp[i+1][j] = dp[i][j];
            else dp[i+1][j] = max(dp[i][j], dp[i][j-w[i]]+v[i]);
        }
    }
    return dp[n][rem];
}

// Complete Knapsack Problem
int DP2(int rem)
{
    int i=0, j=0;
    for(i = 0; i < n; i++)
    {
        for(j = 0; j <= W; j++)
        {
            if(w[i] > j) dp[i+1][j] = dp[i][j];
            else dp[i+1][j] = max(dp[i][j], dp[i+1][j-w[i]]+v[i]);
        }
    }
    return dp[n][rem];
}

int main()
{
    int res;
    res = REC(0, W);
    res = DP(W);
    res = DP2(W);
    cout << res;
    return 0;
}