2 keys keyboard

[leetcode]2 keys keyboard

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

Question

Initially on a notepad only one character ‘A’ is present. You can perform two operations on this notepad for each step:

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

Given a number n. You have to get exactly n ‘A’ on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to get n ‘A’.

Example

Input: 3
Output: 3
Explanation:
Intitally, we have one character 'A'.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get 'AA'.
In step 3, we use Paste operation to get 'AAA'.

Solution

class Solution {
public:
  #define inf 0x3fffffff
  int minSteps(int n) {
    // dp[i]表示得到i个A所需要的最少的操作次数
    vector<int> dp;
    dp.resize(n+1, inf);
    dp[1] = 0;
    for (int i = 2; i <= n; i++)
      for (int k = 1; k <= i; k++)
        // 因为操作肯定是CP..CP..CP..，也就是说最后肯定是P结尾，不会以C结尾
        // 这样的话找遍所有C的前一个位置，也就是这里的k(条件是i必须整除k)
        if (i % k == 0) dp[i] = min(dp[i], dp[k] + i/k);
    return dp[n];
  }
};

思路：因为操作肯定是CP..CP..CP..，也就是说最后肯定是P结尾，不会以C结尾。这样的话找遍所有C的前一个位置，也就是这里的k(条件是i必须整除k)。dp[i]表示得到i个A所需要的最少的操作次数。