<p>There is only one character <code>&#39;A&#39;</code> on the screen of a notepad. You can perform one of two operations on this notepad for each step:</p>

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

<p>Given an integer <code>n</code>, return <em>the minimum number of operations to get the character</em> <code>&#39;A&#39;</code> <em>exactly</em> <code>n</code> <em>times on the screen</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> Initially, we have one character &#39;A&#39;.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get &#39;AA&#39;.
In step 3, we use Paste operation to get &#39;AAA&#39;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

class Solution {
public:
    unordered_map<string, int> memo;
    int minOperations(int currentCount, int clipboard, int target) {
        if (currentCount == target) {
            return 0;
        }
        if (currentCount > target) {
            return 1001; //larger then Constraint
        }

        string key = to_string(currentCount) + "," + to_string(clipboard);

        if (memo.find(key) != memo.end()) {
            return memo[key];
        }

        // Option 1: "Copy All" and then "Paste"
        int copyAndPaste = INT_MAX;
        if (clipboard != currentCount) { // Only copy when clipboard is different to avoid redundant copy
            copyAndPaste = 2 + minOperations(currentCount + currentCount, currentCount, target);
        }

        // Option 2: "Paste"
        int paste = INT_MAX;
        if (clipboard > 0) { // Only paste if something is in the clipboard
            paste = 1 + minOperations(currentCount + clipboard, clipboard, target);
        }
        memo[key] = min(copyAndPaste, paste);
        return memo[key];

    }
    int minSteps(int n) {
        return minOperations(1, 0, n);
    }
};
45563