Sync LeetCode submission Runtime - 2348 ms (61.76%), Memory - 17.8 MB (54.45%)

Author: jimit105

2202-sum-of-k-mirror-numbers/README.md

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+<p>A <strong>k-mirror number</strong> is a <strong>positive</strong> integer <strong>without leading zeros</strong> that reads the same both forward and backward in base-10 <strong>as well as</strong> in base-k.</p>
+
+<ul>
+	<li>For example, <code>9</code> is a 2-mirror number. The representation of <code>9</code> in base-10 and base-2 are <code>9</code> and <code>1001</code> respectively, which read the same both forward and backward.</li>
+	<li>On the contrary, <code>4</code> is not a 2-mirror number. The representation of <code>4</code> in base-2 is <code>100</code>, which does not read the same both forward and backward.</li>
+</ul>
+
+<p>Given the base <code>k</code> and the number <code>n</code>, return <em>the <strong>sum</strong> of the</em> <code>n</code> <em><strong>smallest</strong> k-mirror numbers</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 2, n = 5
+<strong>Output:</strong> 25
+<strong>Explanation:
+</strong>The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:
+  base-10    base-2
+    1          1
+    3          11
+    5          101
+    7          111
+    9          1001
+Their sum = 1 + 3 + 5 + 7 + 9 = 25. 
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 3, n = 7
+<strong>Output:</strong> 499
+<strong>Explanation:
+</strong>The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:
+  base-10    base-3
+    1          1
+    2          2
+    4          11
+    8          22
+    121        11111
+    151        12121
+    212        21212
+Their sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> k = 7, n = 17
+<strong>Output:</strong> 20379000
+<strong>Explanation:</strong> The 17 smallest 7-mirror numbers are:
+1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>2 &lt;= k &lt;= 9</code></li>
+	<li><code>1 &lt;= n &lt;= 30</code></li>
+</ul>

2202-sum-of-k-mirror-numbers/solution.py

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+# Time: O(log n)
+# Space: O(n)
+
+class Solution:
+    def createPalindrome(self, num: int, odd: bool) -> int:
+        x = num
+        if odd:
+            x //= 10
+        while x > 0:
+            num = num * 10 + x % 10
+            x //= 10
+        return num
+
+    def isPalindrome(self, num: int, base: int) -> bool:
+        digits = []
+        while num > 0:
+            digits.append(num % base)
+            num //= base
+        return digits == digits[::-1]
+
+    def kMirror(self, k: int, n: int) -> int:
+        total = 0
+        length = 1
+        while n > 0:
+            for i in range(length, length * 10):
+                if n <= 0:
+                    break
+                p = self.createPalindrome(i, True)
+                if self.isPalindrome(p, k):
+                    total += p
+                    n -= 1
+            for i in range(length, length * 10):
+                if n <= 0:
+                    break
+                p = self.createPalindrome(i, False)
+                if self.isPalindrome(p, k):
+                    total += p
+                    n -= 1
+            length *= 10
+        return total