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Author: jimit105

3243-count-the-number-of-powerful-integers/README.md

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+<p>You are given three integers <code>start</code>, <code>finish</code>, and <code>limit</code>. You are also given a <strong>0-indexed</strong> string <code>s</code> representing a <strong>positive</strong> integer.</p>
+
+<p>A <strong>positive</strong> integer <code>x</code> is called <strong>powerful</strong> if it ends with <code>s</code> (in other words, <code>s</code> is a <strong>suffix</strong> of <code>x</code>) and each digit in <code>x</code> is at most <code>limit</code>.</p>
+
+<p>Return <em>the <strong>total</strong> number of powerful integers in the range</em> <code>[start..finish]</code>.</p>
+
+<p>A string <code>x</code> is a suffix of a string <code>y</code> if and only if <code>x</code> is a substring of <code>y</code> that starts from some index (<strong>including </strong><code>0</code>) in <code>y</code> and extends to the index <code>y.length - 1</code>. For example, <code>25</code> is a suffix of <code>5125</code> whereas <code>512</code> is not.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> start = 1, finish = 6000, limit = 4, s = &quot;124&quot;
+<strong>Output:</strong> 5
+<strong>Explanation:</strong> The powerful integers in the range [1..6000] are 124, 1124, 2124, 3124, and, 4124. All these integers have each digit &lt;= 4, and &quot;124&quot; as a suffix. Note that 5124 is not a powerful integer because the first digit is 5 which is greater than 4.
+It can be shown that there are only 5 powerful integers in this range.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> start = 15, finish = 215, limit = 6, s = &quot;10&quot;
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> The powerful integers in the range [15..215] are 110 and 210. All these integers have each digit &lt;= 6, and &quot;10&quot; as a suffix.
+It can be shown that there are only 2 powerful integers in this range.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> start = 1000, finish = 2000, limit = 4, s = &quot;3000&quot;
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> All integers in the range [1000..2000] are smaller than 3000, hence &quot;3000&quot; cannot be a suffix of any integer in this range.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= start &lt;= finish &lt;= 10<sup>15</sup></code></li>
+	<li><code>1 &lt;= limit &lt;= 9</code></li>
+	<li><code>1 &lt;= s.length &lt;= floor(log<sub>10</sub>(finish)) + 1</code></li>
+	<li><code>s</code> only consists of numeric digits which are at most <code>limit</code>.</li>
+	<li><code>s</code> does not have leading zeros.</li>
+</ul>

3243-count-the-number-of-powerful-integers/solution.py

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+# Approach 2: Combinatorial mathematics
+
+# Time: O(log(finish))
+# Space: O(log(finish))
+
+class Solution:
+    def numberOfPowerfulInt(self, start: int, finish: int, limit: int, s: str) -> int:
+        start_ = str(start - 1)
+        finish_ = str(finish)
+
+        return self.calculate(finish_, s, limit) - self.calculate(start_, s, limit)
+
+    def calculate(self, x, s, limit):
+        if len(x) < len(s):
+            return 0
+
+        if len(x) == len(s):
+            return 1 if x >= s else 0
+
+        suffix = x[len(x) - len(s) :]
+        count = 0
+        pre_len = len(x) - len(s)
+
+        for i in range(pre_len):
+            if limit < int(x[i]):
+                count += (limit + 1) ** (pre_len - i)
+                return count
+            count += int(x[i]) * (limit + 1) ** (pre_len - 1 - i)
+
+        if suffix >= s:
+            count += 1
+
+        return count
+
+