算法刷题Day 44 完全背包理论基础+零钱兑换+组合综合IV

Day 44 动态规划

完全背包理论基础

求组合:先物品再背包

求排列:先背包再物品

518. 零钱兑换

完全背包问题,求组合

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];
    }
};

377. 组合总和IV

完全背包问题,求排列

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] < INT_MAX - dp[i - nums[j]])
                {
                    dp[i] += dp[i - nums[j]];
                }
            }
        }

        return dp[target];
    }
};

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