dp06

322. 零钱兑换

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> dp(amount + 1, INT_MAX);
        dp[0] = 0;
        for (int i = 0; i < coins.size(); i++){
            for (int j = coins[i]; j <= amount; j++){
                if (dp[j - coins[i]] != INT_MAX) {   
                    dp[j] = min(dp[j], dp[j - coins[i]] + 1);
             }
            }
        }
        return dp[amount] == INT_MAX ? -1 : dp[amount];
    }
};

279. 完全平方数

class Solution {
public:
    int numSquares(int n) {
        vector<int> dp(n + 1, INT_MAX);
        dp[0] = 0;
        for (int i = 1; i <= 100; i++){
            for (int j = i * i; j <= n; j++){
                if (dp[j - i * i] != INT_MAX)
                    dp[j] = min(dp[j], dp[j - i * i] + 1);
            }
        }
        return dp[n];
    }
};
# 139. 单词拆分
```C++
class Solution {
public:
    bool wordBreak(string s, vector<string>& wordDict) {
        unordered_set<string> wordSet(wordDict.begin(), wordDict.end());
        int n = s.size();
        vector<bool> dp(n + 1, false);
        dp[0] = true;
        for (int j = 1; j <= n; j++){
            for (int i = 0; i < j; i++){
                string word = s.substr(i, j - i);
                if (wordSet.find(word) != wordSet.end() && dp[i] == true){
                    dp[j] = true;
                }
            }
        }
        return dp[n];
    }
};

多重背包

#include <iostream>
#include <vector>

using namespace std;

int main(){
    int c, n;
    cin >> c >> n;
    vector<int> w(n + 1, 0);
    vector<int> v(n + 1, 0);
    vector<int> k(n + 1, 0);

    for (int i = 0; i < n; i++) cin >> w[i];
    for (int i = 0; i < n; i++) cin >> v[i];
    for (int i = 0; i < n; i++) cin >> k[i];


    vector<int> dp(c + 1, 0);
    for (int i = 0; i < n; i++){
        for (int j = c; j >= w[i]; j--){
            for (int q = 1; (j - q * w[i] >= 0) && (q <= k[i]); q++){
                dp[j] = max(dp[j], dp[j - q * w[i]] +q * v[i]);
            }
        }

    }
    cout << dp[c];
    return 0;
}