[动态规划] leetcode 650 2Keys Keyboard

problem:https://leetcode.com/problems/2-keys-keyboard/

         重做此题，发现依然只能写出N2的算法，水平并没有提升TAT

class Solution {  
public:
    int minSteps(int n) {
        vector<vector<int>> dp(n + 1, vector<int>(n + 1, 10000));
        if(n == 1) return 0;
        dp[1][1] = 1;
        for(int i = 2;i <= n;i++)
        {
            int minnum = INT_MAX;
            for(int j = 1; j < i; j++) // do parse
            {
                dp[i][j] = min(dp[i][j], dp[i - j][j] + 1);
                minnum = min(dp[i][j], minnum);
            }
            dp[i][i] = minnum + 1; // do copy
        }
        return *min_element(dp[n].begin(), dp[n].end());
    }
};

        从评论区拿到的advance版本。这道题的标准解法是分解质因数。最优解的证明已经涉及到一些数学上的问题了。

class Solution {
public:
    int minSteps(int n) {
        vector<int> dp(n + 1, INT_MAX);
        
        dp[1] = 0;

        for (int i = 2; i <= n; i++) {
            dp[i] = i;
            for (int j = i/2; j > 1; j--) {
                if (i % j == 0) {
                    dp[i] = dp[j] + (i / j);
                    break;
                }
            }
        }

　　　　return dp[n]; 
} };