Sync LeetCode submission Runtime - 853 ms (98.41%), Memory - 18.9 MB (98.41%)

Author: jimit105

3548-find-the-count-of-good-integers/README.md

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+<p>You are given two <strong>positive</strong> integers <code>n</code> and <code>k</code>.</p>
+
+<p>An integer <code>x</code> is called <strong>k-palindromic</strong> if:</p>
+
+<ul>
+	<li><code>x</code> is a <span data-keyword="palindrome-integer">palindrome</span>.</li>
+	<li><code>x</code> is divisible by <code>k</code>.</li>
+</ul>
+
+<p>An integer is called <strong>good</strong> if its digits can be <em>rearranged</em> to form a <strong>k-palindromic</strong> integer. For example, for <code>k = 2</code>, 2020 can be rearranged to form the <em>k-palindromic</em> integer 2002, whereas 1010 cannot be rearranged to form a <em>k-palindromic</em> integer.</p>
+
+<p>Return the count of <strong>good</strong> integers containing <code>n</code> digits.</p>
+
+<p><strong>Note</strong> that <em>any</em> integer must <strong>not</strong> have leading zeros, <strong>neither</strong> before <strong>nor</strong> after rearrangement. For example, 1010 <em>cannot</em> be rearranged to form 101.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 3, k = 5</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">27</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p><em>Some</em> of the good integers are:</p>
+
+<ul>
+	<li>551 because it can be rearranged to form 515.</li>
+	<li>525 because it is already k-palindromic.</li>
+</ul>
+</div>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 1, k = 4</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">2</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p>The two good integers are 4 and 8.</p>
+</div>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 5, k = 6</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">2468</span></p>
+</div>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 10</code></li>
+	<li><code>1 &lt;= k &lt;= 9</code></li>
+</ul>

3548-find-the-count-of-good-integers/solution.py

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+class Solution:
+    def countGoodIntegers(self, n: int, k: int) -> int:
+        dictionary = set()
+        base = 10 ** ((n - 1) // 2)
+        skip = n & 1
+        # Enumerate the number of palindrome numbers of n digits
+        for i in range(base, base * 10):
+            s = str(i)
+            s += s[::-1][skip:]
+            palindromicInteger = int(s)
+            # If the current palindrome number is a k-palindromic integer
+            if palindromicInteger % k == 0:
+                sorted_s = "".join(sorted(s))
+                dictionary.add(sorted_s)
+
+        fac = [factorial(i) for i in range(n + 1)]
+        ans = 0
+        for s in dictionary:
+            cnt = [0] * 10
+            for c in s:
+                cnt[int(c)] += 1
+            # Calculate permutations and combinations
+            tot = (n - cnt[0]) * fac[n - 1]
+            for x in cnt:
+                tot //= fac[x]
+            ans += tot
+
+        return ans