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Java-based LeetCode algorithm problem solutions, regularly updated

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package g2501_2600.s2523_closest_prime_numbers_in_range;

// #Medium #Math #Number_Theory #2023_04_19_Time_1_ms_(100.00%)_Space_39.9_MB_(97.74%)

/**
 * 2523 - Closest Prime Numbers in Range\.
 *
 * Medium
 *
 * Given two positive integers `left` and `right`, find the two integers `num1` and `num2` such that:
 *
 * *   `left <= nums1 < nums2 <= right` .
 * *   `nums1` and `nums2` are both **prime** numbers.
 * *   `nums2 - nums1` is the **minimum** amongst all other pairs satisfying the above conditions.
 *
 * Return _the positive integer array_ `ans = [nums1, nums2]`. _If there are multiple pairs satisfying these conditions, return the one with the minimum_ `nums1` _value or_ `[-1, -1]` _if such numbers do not exist._
 *
 * A number greater than `1` is called **prime** if it is only divisible by `1` and itself.
 *
 * **Example 1:**
 *
 * **Input:** left = 10, right = 19
 *
 * **Output:** [11,13]
 *
 * **Explanation:** 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.
 *
 * **Example 2:**
 *
 * **Input:** left = 4, right = 6
 *
 * **Output:** [-1,-1]
 *
 * **Explanation:** There exists only one prime number in the given range, so the conditions cannot be satisfied.
 *
 * **Constraints:**
 *
 * *   1 <= left <= right <= 10⁶
**/
public class Solution {
    public int[] closestPrimes(int left, int right) {
        int diff = -1;
        int x = -1;
        int y = -1;
        int prev = -1;
        for (int i = left; i <= right; i++) {
            boolean isPrime = isPrime(i);
            if (isPrime) {
                if (prev != -1) {
                    int d = i - prev;
                    if (diff == -1 || d < diff) {
                        diff = d;
                        x = prev;
                        y = i;
                        if (diff <= 2) {
                            return new int[] {x, y};
                        }
                    }
                }
                prev = i;
            }
        }
        return new int[] {x, y};
    }

    private boolean isPrime(int x) {
        if (x == 1) {
            return false;
        }
        double sqrt = Math.sqrt(x);
        for (int i = 2; i <= sqrt; i++) {
            if (x % i == 0) {
                return false;
            }
        }
        return true;
    }
}