<p>We are given <code>n</code> different types of <code>stickers</code>. Each sticker has a lowercase English word on it.</p>

<p>You would like to spell out the given string <code>target</code> by cutting individual letters from your collection of stickers and rearranging them. You can use each sticker more than once if you want, and you have infinite quantities of each sticker.</p>

<p>Return <em>the minimum number of stickers that you need to spell out </em><code>target</code>. If the task is impossible, return <code>-1</code>.</p>

<p><strong>Note:</strong> In all test cases, all words were chosen randomly from the <code>1000</code> most common US English words, and <code>target</code> was chosen as a concatenation of two random words.</p>

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

<pre>
<strong>Input:</strong> stickers = [&quot;with&quot;,&quot;example&quot;,&quot;science&quot;], target = &quot;thehat&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can use 2 &quot;with&quot; stickers, and 1 &quot;example&quot; sticker.
After cutting and rearrange the letters of those stickers, we can form the target &quot;thehat&quot;.
Also, this is the minimum number of stickers necessary to form the target string.
</pre>

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

<pre>
<strong>Input:</strong> stickers = [&quot;notice&quot;,&quot;possible&quot;], target = &quot;basicbasic&quot;
<strong>Output:</strong> -1
Explanation:
We cannot form the target &quot;basicbasic&quot; from cutting letters from the given stickers.
</pre>

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

<ul>
	<li><code>n == stickers.length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= stickers[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= target.length &lt;= 15</code></li>
	<li><code>stickers[i]</code> and <code>target</code> consist of lowercase English letters.</li>
</ul>

#include <vector>
#include <string>
#include <unordered_map>
#include <numeric> // For std::accumulate

using namespace std;
    int helper(vector<int>& dp, const vector<string>& stickers, const string& target, int mask) {
        const int n = target.size();
        if (dp[mask] != -1) return dp[mask]; // Return memoized result
        dp[mask] = numeric_limits<int>::max(); // Initialize with max value
        int originalMask = mask;
        for (const string& sticker : stickers) {
            int leftMask = mask;
            vector<int> count(26, 0); // Count characters in the sticker
            for (char c : sticker) ++count[c - 'a'];
            for (int i = 0; i < n; ++i) {
                if (((mask >> i) & 1) && count[target[i] - 'a'] > 0) {
                    --count[target[i] - 'a'];
                    leftMask ^= (1 << i); // Remove character i from the mask
                }
            }
            if (leftMask < mask) { // Ensure the sticker contributes to the target
                int subProblem = helper(dp, stickers, target, leftMask);
                if (subProblem != numeric_limits<int>::max()) {
                    dp[mask] = min(dp[mask], 1 + subProblem);
                }
            }
        }
        // Check if no progress was made with any sticker
        if (dp[mask] == numeric_limits<int>::max() && originalMask == mask) {
            dp[mask] = -1; // Indicate that it's impossible to form the target
        }
        return dp[mask];
    }

class Solution {
public:
    int minStickers(vector<string>& stickers, string target) {
          // Combined frequency count for all stickers
        vector<int> combinedStickerCount(26, 0);
        for (const string& sticker : stickers) {
            for (char c : sticker) {
                combinedStickerCount[c - 'a'] = 1; // Mark presence of character
            }
        }

        // Frequency count for target
        vector<int> targetCount(26, 0);
        for (char c : target) {
            targetCount[c - 'a']++;
        }

        // Check if all characters in the target can be formed
        for (int i = 0; i < 26; ++i) {
            if (targetCount[i] > 0 && combinedStickerCount[i] == 0) {
                return -1; // Cannot form target
            }
        }

        const int n = target.size();
        vector<int> dp(1 << n, -1); // DP table for memoization
        dp[0] = 0; // Base case: 0 stickers needed for an empty target
        return helper(dp, stickers, target, (1 << n) - 1);
    
    }
};
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