650. 2 Keys Keyboard

There is only one character ‘A’ on the screen of a notepad. You can perform one of two operations on this notepad for each step:

• Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).
• Paste: You can paste the characters which are copied last time.

Given an integer n, return the minimum number of operations to get the character ‘A’ exactly n times on the screen.

class Solution {
public:
    int minSteps(int n) {
        vector<int> dp(n + 1, 987654321);
        dp[1] = 0;
        for(int i = 1; i < n; i++) {
            for(int j = i + i; j <= n; j += i) {
                dp[j] = min(dp[j], dp[i] + j / i);
            }
        }
        return dp[n];
    }
};