代码随想录Day44、45、46

// 完全背包问题，对于for循环的先后顺序没有要求，可以先物品，也可以先背包

// 先便利物品，再便利背包
void test_CompletePack() {
    vector<int> weight = {1, 3, 4};
    vector<int> value = {15, 20 ,30};
    int bagWeight = 4;
    vector<int> dp(bagWeight + 1, 0);
    for (int i = 0; i < weight.size(); i++) {
        for (int j = weight[i]; j <= bagWeight; j++) {
            dp[j] = max(dp[j], dp[j - weight[i]] + value[i]);
        }
    }
    cout << dp[bagWeight] << endl;
}

void test2_CompletePack() {
    vector<int> weight = {1, 3, 4};
    vector<int> value = {15, 20 ,30};
    int bagWeight = 4;
    vector<int> dp(bagWeight + 1, 0);
    for (int j = 0; j <= bagWeight; j++) {
        for (int i = 0; i < weight.size(); i++) {
            if (j - weight[i] >= 0) {
                dp[j] = max(dp[j], dp[j - weight[i]] + value[i]);
            }
        }
    }
}

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        vector<int> dp(target + 1, 0);
        dp[0] = 1;
        for (int i = 0; i <= target; ++i) {
            for (int j = 0; j < nums.size(); ++j) {
                if (i - nums[j] >= 0 && dp[i] < INT32_MAX - dp[i- nums[j]]) {
                    dp[i] += dp[i - nums[j]];
                }
            }
        }
        return dp[target];
    }
};

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++) {
                dp[j] += dp[j - coins[i]];
            }
        }
        return dp[amount];
    }
};

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> dp(amount + 1, INT64_MAX);
        dp[0] = 0;
        for (int i = 0; i < coins.size(); i++) { // 遍历物品
            for (int j = coins[i]; j <= amount; j++) { // 遍历背包
                if (dp[j - coins[i]] != INT64_MAX) { // 如果dp[j - coins[i]]是初始值则跳过
                    dp[j] = min(dp[j - coins[i]] + 1, dp[j]);
                }
            }
        }
        if (dp[amount] == INT64_MAX) return -1;
        return dp[amount];
    }
};

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> dp(amount + 1, INT64_MAX);
        dp[0] = 0;
        for (int i = 0; i < coins.size(); i++) { // 遍历物品
            for (int j = coins[i]; j <= amount; j++) { // 遍历背包
                if (dp[j - coins[i]] != INT64_MAX) { // 如果dp[j - coins[i]]是初始值则跳过
                    dp[j] = min(dp[j - coins[i]] + 1, dp[j]);
                }
            }
        }
        if (dp[amount] == INT64_MAX) return -1;
        return dp[amount];
    }
};

class Solution {
public:
    bool wordBreak(string s, vector<string>& wordDict) {
        unordered_set<string> wordSet(wordDict.begin(), wordDict.end());
        vector<bool> dp(s.size() + 1, false);
        dp[0] = true;
        for (int i = 1; i <= s.size(); i++) {
            for (int j = 0; j < i ; j++) {
                string word = s.substr(j, i - j);
                if (wordSet.find(word) != wordSet.end() && dp[j]) {
                    dp[i] = true;
                }
            }
        }
        return dp[s.size()];
    }
};

void test_multi_pack() {
    vector<int> weight = {1, 3, 4};
    vector<int> value = {15, 20, 30};
    vector<int> nums = {2, 3, 2};
    int bagWeight = 10;
    vector<int> dp(bagWeight + 1, 0);


    for(int i = 0; i < weight.size(); i++) { // 遍历物品
        for(int j = bagWeight; j >= weight[i]; j--) { // 遍历背包容量
            // 以上为01背包，然后加一个遍历个数
            for (int k = 1; k <= nums[i] && (j - k * weight[i]) >= 0; k++) { // 遍历个数
                dp[j] = max(dp[j], dp[j - k * weight[i]] + k * value[i]);
            }
        }
        // 打印一下dp数组
        for (int j = 0; j <= bagWeight; j++) {
            cout << dp[j] << " ";
        }
        cout << endl;
    }
    cout << dp[bagWeight] << endl;
}