+ problem 2523

Author: fruit-in

Problemset/2523-Closest Prime Numbers in Range/README.md

@@ -0,0 +1,76 @@
+# 2523. Closest Prime Numbers in Range
+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:
+<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>
+
+#### Example 2:
+<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>
+
+#### Constraints:
+* <code>1 <= left <= right <= 10<sup>6</sup></code>
+
+## Solutions (Rust)
+
+### 1. Solution
+```Rust
+impl Solution {
+    pub fn closest_primes(left: i32, right: i32) -> Vec<i32> {
+        let mut is_prime = vec![true; right as usize + 1];
+        let mut primes = vec![];
+        let mut ret = vec![-1, i32::MAX - 1];
+
+        for nums2 in 2..=right {
+            if ret[1] - ret[0] < 3 {
+                break;
+            }
+
+            if is_prime[nums2 as usize] {
+                if let Some(&nums1) = primes.last() {
+                    if nums1 >= left && nums2 - nums1 < ret[1] - ret[0] {
+                        ret = vec![nums1, nums2];
+                    }
+                }
+
+                primes.push(nums2);
+            }
+
+            for prime in &primes {
+                if prime * nums2 > right {
+                    break;
+                }
+
+                is_prime[(prime * nums2) as usize] = false;
+
+                if nums2 % prime == 0 {
+                    break;
+                }
+            }
+        }
+
+        if ret[0] == -1 {
+            ret[1] = -1;
+        }
+
+        ret
+    }
+}
+```

Problemset/2523-Closest Prime Numbers in Range/README_CN.md

@@ -0,0 +1,76 @@
+# 2523. 范围内最接近的两个质数
+给你两个正整数 `left` 和 `right` ，请你找到两个整数 `num1` 和 `num2` ，它们满足：
+
+* `left <= nums1 < nums2 <= right`  。
+* `nums1` 和 `nums2` 都是 **质数** 。
+* `nums2 - nums1` 是满足上述条件的质数对中的 **最小值** 。
+
+请你返回正整数数组 `ans = [nums1, nums2]` 。如果有多个整数对满足上述条件，请你返回 `nums1` 最小的质数对。如果不存在符合题意的质数对，请你返回 `[-1, -1]` 。
+
+如果一个整数大于 `1` ，且只能被 `1` 和它自己整除，那么它是一个质数。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> left = 10, right = 19
+<strong>输出:</strong> [11,13]
+<strong>解释:</strong> 10 到 19 之间的质数为 11 ，13 ，17 和 19 。
+质数对的最小差值是 2 ，[11,13] 和 [17,19] 都可以得到最小差值。
+由于 11 比 17 小，我们返回第一个质数对。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> left = 4, right = 6
+<strong>输出:</strong> [-1,-1]
+<strong>解释:</strong> 给定范围内只有一个质数，所以题目条件无法被满足。
+</pre>
+
+#### 提示:
+* <code>1 <= left <= right <= 10<sup>6</sup></code>
+
+## 题解 (Rust)
+
+### 1. 题解
+```Rust
+impl Solution {
+    pub fn closest_primes(left: i32, right: i32) -> Vec<i32> {
+        let mut is_prime = vec![true; right as usize + 1];
+        let mut primes = vec![];
+        let mut ret = vec![-1, i32::MAX - 1];
+
+        for nums2 in 2..=right {
+            if ret[1] - ret[0] < 3 {
+                break;
+            }
+
+            if is_prime[nums2 as usize] {
+                if let Some(&nums1) = primes.last() {
+                    if nums1 >= left && nums2 - nums1 < ret[1] - ret[0] {
+                        ret = vec![nums1, nums2];
+                    }
+                }
+
+                primes.push(nums2);
+            }
+
+            for prime in &primes {
+                if prime * nums2 > right {
+                    break;
+                }
+
+                is_prime[(prime * nums2) as usize] = false;
+
+                if nums2 % prime == 0 {
+                    break;
+                }
+            }
+        }
+
+        if ret[0] == -1 {
+            ret[1] = -1;
+        }
+
+        ret
+    }
+}
+```

Problemset/2523-Closest Prime Numbers in Range/Solution.rs

@@ -0,0 +1,41 @@
+impl Solution {
+    pub fn closest_primes(left: i32, right: i32) -> Vec<i32> {
+        let mut is_prime = vec![true; right as usize + 1];
+        let mut primes = vec![];
+        let mut ret = vec![-1, i32::MAX - 1];
+
+        for nums2 in 2..=right {
+            if ret[1] - ret[0] < 3 {
+                break;
+            }
+
+            if is_prime[nums2 as usize] {
+                if let Some(&nums1) = primes.last() {
+                    if nums1 >= left && nums2 - nums1 < ret[1] - ret[0] {
+                        ret = vec![nums1, nums2];
+                    }
+                }
+
+                primes.push(nums2);
+            }
+
+            for prime in &primes {
+                if prime * nums2 > right {
+                    break;
+                }
+
+                is_prime[(prime * nums2) as usize] = false;
+
+                if nums2 % prime == 0 {
+                    break;
+                }
+            }
+        }
+
+        if ret[0] == -1 {
+            ret[1] = -1;
+        }
+
+        ret
+    }
+}

README.md

@@ -1206,6 +1206,7 @@
 [2515][2515l]|[Shortest Distance to Target String in a Circular Array][2515]                        |![rs]
 [2520][2520l]|[Count the Digits That Divide a Number][2520]                                         |![rs]
 [2521][2521l]|[Distinct Prime Factors of Product of Array][2521]                                    |![rs]
+[2523][2523l]|[Closest Prime Numbers in Range][2523]                                                |![rs]
 [2525][2525l]|[Categorize Box According to Criteria][2525]                                          |![rs]
 [2526][2526l]|[Find Consecutive Integers from a Data Stream][2526]                                  |![rs]
 [2529][2529l]|[Maximum Count of Positive Integer and Negative Integer][2529]                        |![py]
@@ -2449,6 +2450,7 @@
 [2515]:Problemset/2515-Shortest%20Distance%20to%20Target%20String%20in%20a%20Circular%20Array/README.md#2515-shortest-distance-to-target-string-in-a-circular-array
 [2520]:Problemset/2520-Count%20the%20Digits%20That%20Divide%20a%20Number/README.md#2520-count-the-digits-that-divide-a-number
 [2521]:Problemset/2521-Distinct%20Prime%20Factors%20of%20Product%20of%20Array/README.md#2521-distinct-prime-factors-of-product-of-array
+[2523]:Problemset/2523-Closest%20Prime%20Numbers%20in%20Range/README.md#2523-closest-prime-numbers-in-range
 [2525]:Problemset/2525-Categorize%20Box%20According%20to%20Criteria/README.md#2525-categorize-box-according-to-criteria
 [2526]:Problemset/2526-Find%20Consecutive%20Integers%20from%20a%20Data%20Stream/README.md#2526-find-consecutive-integers-from-a-data-stream
 [2529]:Problemset/2529-Maximum%20Count%20of%20Positive%20Integer%20and%20Negative%20Integer/README.md#2529-maximum-count-of-positive-integer-and-negative-integer
@@ -3695,6 +3697,7 @@
 [2515l]:https://leetcode.com/problems/shortest-distance-to-target-string-in-a-circular-array/
 [2520l]:https://leetcode.com/problems/count-the-digits-that-divide-a-number/
 [2521l]:https://leetcode.com/problems/distinct-prime-factors-of-product-of-array/
+[2523l]:https://leetcode.com/problems/closest-prime-numbers-in-range/
 [2525l]:https://leetcode.com/problems/categorize-box-according-to-criteria/
 [2526l]:https://leetcode.com/problems/find-consecutive-integers-from-a-data-stream/
 [2529l]:https://leetcode.com/problems/maximum-count-of-positive-integer-and-negative-integer/

README_CN.md

@@ -1206,6 +1206,7 @@
 [2515][2515l]|[到目标字符串的最短距离][2515]                            |![rs]
 [2520][2520l]|[统计能整除数字的位数][2520]                              |![rs]
 [2521][2521l]|[数组乘积中的不同质因数数目][2521]                        |![rs]
+[2523][2523l]|[范围内最接近的两个质数][2523]                            |![rs]
 [2525][2525l]|[根据规则将箱子分类][2525]                                |![rs]
 [2526][2526l]|[找到数据流中的连续整数][2526]                            |![rs]
 [2529][2529l]|[正整数和负整数的最大计数][2529]                          |![py]
@@ -2449,6 +2450,7 @@
 [2515]:Problemset/2515-Shortest%20Distance%20to%20Target%20String%20in%20a%20Circular%20Array/README_CN.md#2515-到目标字符串的最短距离
 [2520]:Problemset/2520-Count%20the%20Digits%20That%20Divide%20a%20Number/README_CN.md#2520-统计能整除数字的位数
 [2521]:Problemset/2521-Distinct%20Prime%20Factors%20of%20Product%20of%20Array/README_CN.md#2521-数组乘积中的不同质因数数目
+[2523]:Problemset/2523-Closest%20Prime%20Numbers%20in%20Range/README_CN.md#2523-范围内最接近的两个质数
 [2525]:Problemset/2525-Categorize%20Box%20According%20to%20Criteria/README_CN.md#2525-根据规则将箱子分类
 [2526]:Problemset/2526-Find%20Consecutive%20Integers%20from%20a%20Data%20Stream/README_CN.md#2526-找到数据流中的连续整数
 [2529]:Problemset/2529-Maximum%20Count%20of%20Positive%20Integer%20and%20Negative%20Integer/README_CN.md#2529-正整数和负整数的最大计数
@@ -3695,6 +3697,7 @@
 [2515l]:https://leetcode.cn/problems/shortest-distance-to-target-string-in-a-circular-array/
 [2520l]:https://leetcode.cn/problems/count-the-digits-that-divide-a-number/
 [2521l]:https://leetcode.cn/problems/distinct-prime-factors-of-product-of-array/
+[2523l]:https://leetcode.cn/problems/closest-prime-numbers-in-range/
 [2525l]:https://leetcode.cn/problems/categorize-box-according-to-criteria/
 [2526l]:https://leetcode.cn/problems/find-consecutive-integers-from-a-data-stream/
 [2529l]:https://leetcode.cn/problems/maximum-count-of-positive-integer-and-negative-integer/