2176. Count Equal and Divisible Pairs in an Array

2176. Count Equal and Divisible Pairs in an Array Difficulty: Easy Topics: Array Given a 0-indexed integer array nums of length n and an integer k, return the number of pairs (i, j) where 0

Apr 17, 2025 - 06:04

Difficulty: Easy

Topics: Array

Given a 0-indexed integer array nums of length n and an integer k, return the number of pairs (i, j) where 0 <= i < j < n, such that nums[i] == nums[j] and (i * j) is divisible by k.

Example 1:

Input: nums = [3,1,2,2,2,1,3], k = 2
Output: 4
Explanation: There are 4 pairs that meet all the requirements:
- nums[0] == nums[6], and 0 * 6 == 0, which is divisible by 2.
- nums[2] == nums[3], and 2 * 3 == 6, which is divisible by 2.
- nums[2] == nums[4], and 2 * 4 == 8, which is divisible by 2.
- nums[3] == nums[4], and 3 * 4 == 12, which is divisible by 2.

Example 2:

Input: nums = [1,2,3,4], k = 1
Output: 0
Explanation: Since no value in nums is repeated, there are no pairs (i,j) that meet all the requirements.

Constraints:

1 <= nums.length <= 100
1 <= nums[i], k <= 100

Hint:

For every possible pair of indices (i, j) where i < j, check if it satisfies the given conditions.

Solution:

We need to count the number of pairs (i, j) in a given array such that the elements at these indices are equal and the product of their indices is divisible by a given integer k.

Approach

The approach involves iterating through all possible pairs of indices (i, j) where i < j. For each pair, we check two conditions:

The elements at indices i and j are equal.
The product of i and j is divisible by k.

Given the constraints that the array length is at most 100, a brute-force approach is feasible. This approach involves checking each pair directly, which is manageable due to the small size of the input.

Let's implement this solution in PHP: 2176. Count Equal and Divisible Pairs in an Array


/**
 * @param Integer[] $nums
 * @param Integer $k
 * @return Integer
 */
function countPairs($nums, $k) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Example 1:
$nums1 = array(3, 1, 2, 2, 2, 1, 3);
$k1 = 2;
echo "Output: " . countPairs($nums1, $k1) . "\n"; // Output: 4

// Example 2:
$nums2 = array(1, 2, 3, 4);
$k2 = 1;
echo "Output: " . countPairs($nums2, $k2) . "\n"; // Output: 0
?>

Explanation:

Initialization: We start by initializing a counter to keep track of valid pairs.
Nested Loops: We use two nested loops to generate all possible pairs (i, j) where i < j. The outer loop runs from 0 to n-2, and the inner loop runs from i+1 to n-1.
Condition Check: For each pair (i, j), we check if the elements at these indices are equal and if their product modulo k is zero. If both conditions are met, we increment the counter.
Return Result: Finally, we return the count of valid pairs.

This approach ensures that we check all possible pairs efficiently within the constraints, providing the correct result with a time complexity of O(n^2), which is acceptable given the input size.

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