dp05

完全背包

#include <iostream>
#include <vector>

using namespace std;

int main(){
    
    int n; int v;
    cin >> n >> v;
    vector<int> W(n + 1, 0), V(n + 1, 0);
    for (int i = 0; i < n; i++){
        cin >> W[i] >> V[i];
    }
    vector<int> dp(v + 1, 0);
    for (int i = 0; i < n; i++){
        for (int j = W[i]; j <= v; j++){
            dp[j] = max(dp[j], dp[j - W[i]] + V[i]);
        }

    }
    cout << dp[v];

    return 0;
}

518. 零钱兑换 II

class Solution {
public:
    int change(int amount, vector<int>& coins) {
        vector<int> dp(amount + 1, 0);
        dp[0] = 1;
        for (int i = 0; i < coins.size(); i++){
            for (int j = coins[i]; j <= amount; j++){
                 if (dp[j] < INT_MAX - dp[j - coins[i]]) { //防止相加数据超int
                    dp[j] += dp[j - coins[i]];
                }
            }
        }
        return dp[amount];
    }
};

377. 组合总和 Ⅳ

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        vector<unsigned long long> dp(target + 1, 0);
        dp[0] = 1;
        for (int j = 0; j <= target; j++){
            for (int i = 0; i < nums.size(); i++){
                if (j >= nums[i])
                    dp[j] += dp[j - nums[i]];
            }
        }
        return dp[target];
    }
};

70. 爬楼梯（进阶版）

#include <iostream>
#include <vector>

using namespace std;
int main(){
    int n, m;
    cin >> n >> m;
    vector<int> dp(n + 1, 0);
    dp[0] = 1;
    for (int j = 0; j <= n; j++){
        for (int i = 1; i <= m; i++){
            if (j >= i)
                dp[j] += dp[j - i];
        }
    }
    cout << dp[n];
    return 0;
}