Sync LeetCode submission Runtime - 1485 ms (58.79%), Memory - 35.2 MB (18.21%)

Author: jimit105

2610-closest-prime-numbers-in-range/README.md

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+<p>Given two positive integers <code>left</code> and <code>right</code>, find the two integers <code>num1</code> and <code>num2</code> such that:</p>
+
+<ul>
+	<li><code>left &lt;= num1 &lt; num2 &lt;= right </code>.</li>
+	<li>Both <code>num1</code> and <code>num2</code> are <span data-keyword="prime-number">prime numbers</span>.</li>
+	<li><code>num2 - num1</code> is the <strong>minimum</strong> amongst all other pairs satisfying the above conditions.</li>
+</ul>
+
+<p>Return the positive integer array <code>ans = [num1, num2]</code>. If there are multiple pairs satisfying these conditions, return the one with the <strong>smallest</strong> <code>num1</code> value. If no such numbers exist, return <code>[-1, -1]</code><em>.</em></p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> left = 10, right = 19
+<strong>Output:</strong> [11,13]
+<strong>Explanation:</strong> The prime numbers between 10 and 19 are 11, 13, 17, and 19.
+The closest gap between any pair is 2, which can be achieved by [11,13] or [17,19].
+Since 11 is smaller than 17, we return the first pair.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> left = 4, right = 6
+<strong>Output:</strong> [-1,-1]
+<strong>Explanation:</strong> There exists only one prime number in the given range, so the conditions cannot be satisfied.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= left &lt;= right &lt;= 10<sup>6</sup></code></li>
+</ul>
+
+<p>&nbsp;</p>
+<style type="text/css">.spoilerbutton {display:block; border:dashed; padding: 0px 0px; margin:10px 0px; font-size:150%; font-weight: bold; color:#000000; background-color:cyan; outline:0; 
+}
+.spoiler {overflow:hidden;}
+.spoiler > div {-webkit-transition: all 0s ease;-moz-transition: margin 0s ease;-o-transition: all 0s ease;transition: margin 0s ease;}
+.spoilerbutton[value="Show Message"] + .spoiler > div {margin-top:-500%;}
+.spoilerbutton[value="Hide Message"] + .spoiler {padding:5px;}
+</style>

2610-closest-prime-numbers-in-range/solution.py

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+# Approach 1: Sieve of Eratosthenes
+
+# Time: O(R log(log R) + R - L)
+# Space: O(R)
+
+class Solution:
+    def _sieve(self, upper_limit):
+        sieve = [True] * (upper_limit + 1)
+        sieve[0] = sieve[1] = False # 0 and 1 are not prime
+
+        for number in range(2, int(upper_limit ** 0.5) + 1):
+            if sieve[number]:
+                # Mark all multiple of `number` as non-prime
+                for multiple in range(number * number, upper_limit + 1, number):
+                    sieve[multiple] = False
+        
+        return sieve
+
+    def closestPrimes(self, left: int, right: int) -> List[int]:
+        sieve_array = self._sieve(right)
+
+        prime_numbers = [num for num in range(left, right + 1) if sieve_array[num]]
+
+        # Find closest prime pair
+        if len(prime_numbers) < 2:
+            return -1, -1
+
+        min_diff = float('inf')
+        closest_pair = (-1, -1)
+
+        for index in range(1, len(prime_numbers)):
+            diff = prime_numbers[index] - prime_numbers[index - 1]
+            if diff < min_diff:
+                min_diff = diff
+                closest_pair = prime_numbers[index - 1], prime_numbers[index]
+
+        return closest_pair
+