背包问题

有N个重量和价值分别为wi和vi的物品。

从这些物品中挑选出总重量不超过W的物品，求所有挑选方案中价值总和的最大值。

#define MAX_N 1000
// input
int N, W, w[MAX_N], v[MAX_N];
int dp[MAX_N][MAX_N]; // remember array to reduce recursive

int rec(int i, int weight)
{
    if(dp[i][weight] >= 0)
        return dp[i][weight];

    int ans;

    if(i == N) // no product left
        ans = 0; 

    if(w[i] > weight) // can not include this product
        ans = rec(i+1, weight);
    else
        ans = max(rec(i+1, weight), rec(i+1, weight - w[i]) + v[i]);

    return dp[i][weight] = ans;
}

void solve()
{
    printf("%d\n", rec(0, W));
}