650 2 Keys Keyboard

650. 2 Keys Keyboard

1. 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 numbern. You have to getexactlyn'A' on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to getn'A'.

Example 1:

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'.

Note:

1. Thenwill be in the range [1, 1000].

2. Implementation

(1) DP

class Solution {
    public int minSteps(int n) {
        if (n <= 1) {
            return 0;
        }
        int[] dp = new int[n + 1];

        for (int i = 1; i <= n; i++) {
            dp[i] = i;
            for (int j = i - 1; j >= 1; j--) {
                if (i % j == 0) {
                    dp[i] = Math.min(dp[i], dp[j] + i / j);
                }
            }
        }
        return dp[n];
    }
}

3. Time & Space Complexity

DFS + Memoization: 时间复杂度O(k ^(mn)), k是offer的数量, m是item的个数，n是每个item要买的个数，空间复杂度O(mn)?