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g2701_2800.s2748_number_of_beautiful_pairs.readme.md Maven / Gradle / Ivy

2748\. Number of Beautiful Pairs

Easy

You are given a **0-indexed** integer array `nums`. A pair of indices `i`, `j` where `0 <= i < j < nums.length` is called beautiful if the **first digit** of `nums[i]` and the **last digit** of `nums[j]` are **coprime**.

Return _the total number of beautiful pairs in_ `nums`.

Two integers `x` and `y` are **coprime** if there is no integer greater than 1 that divides both of them. In other words, `x` and `y` are coprime if `gcd(x, y) == 1`, where `gcd(x, y)` is the **greatest common divisor** of `x` and `y`.

**Example 1:**

**Input:** nums = [2,5,1,4]

**Output:** 5

**Explanation:** There are 5 beautiful pairs in nums: 

When i = 0 and j = 1: the first digit of nums[0] is 2, and the last digit of nums[1] is 5. We can confirm that 2 and 5 are coprime, since gcd(2,5) == 1. 

When i = 0 and j = 2: the first digit of nums[0] is 2, and the last digit of nums[2] is 1. Indeed, gcd(2,1) == 1. 

When i = 1 and j = 2: the first digit of nums[1] is 5, and the last digit of nums[2] is 1. Indeed, gcd(5,1) == 1.

When i = 1 and j = 3: the first digit of nums[1] is 5, and the last digit of nums[3] is 4. Indeed, gcd(5,4) == 1.

When i = 2 and j = 3: the first digit of nums[2] is 1, and the last digit of nums[3] is 4. Indeed, gcd(1,4) == 1. 

Thus, we return 5.

**Example 2:**

**Input:** nums = [11,21,12]

**Output:** 2

**Explanation:** There are 2 beautiful pairs: 

When i = 0 and j = 1: the first digit of nums[0] is 1, and the last digit of nums[1] is 1. Indeed, gcd(1,1) == 1. 

When i = 0 and j = 2: the first digit of nums[0] is 1, and the last digit of nums[2] is 2. Indeed, gcd(1,2) == 1. 

Thus, we return 2.

**Constraints:**

*   `2 <= nums.length <= 100`
*   `1 <= nums[i] <= 9999`
*   `nums[i] % 10 != 0`