explanation.md

Smallest Distance Pair - Step-by-Step Explanation

This section provides a detailed explanation of how to find the k-th smallest distance pair in a given array using C++, Java, JavaScript, Python, and Go. The problem involves using a combination of sorting, two-pointer technique, and binary search to achieve the desired result.

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C++ Implementation

1. Sorting the Array:

   • The first step involves sorting the array to facilitate the two-pointer technique for finding pairs with the smallest distances.

2. Binary Search Setup:

   • The search range for the smallest distance is initialized, with low as the smallest possible distance (0) and high as the largest possible distance (difference between the maximum and minimum elements in the array).

3. Counting Valid Pairs:

   • For a given midpoint (mid) in the binary search, count how many pairs in the array have a distance less than or equal to mid.
   • This involves iterating through the array and using a second pointer to find valid pairs that meet the condition.

4. Binary Search Execution:

   • Adjust the search range based on the count of valid pairs found.
   • If the count is greater than or equal to k, search the lower half; otherwise, search the upper half.

5. Result:

   • After binary search completes, the low value will represent the k-th smallest distance.

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Java Implementation

1. Sorting the Array:

   • The array is sorted to allow efficient pair counting with the two-pointer technique.

2. Binary Search Initialization:

   • Set up the binary search range with low as 0 and high as the difference between the maximum and minimum elements in the array.

3. Counting Pairs with Two Pointers:

   • For each midpoint (mid), count the number of pairs with a difference less than or equal to mid.
   • Use two pointers to iterate through the array, counting valid pairs.

4. Binary Search Logic:

   • Adjust the binary search range based on whether the count of valid pairs is greater than or equal to k.

5. Final Result:

   • The value of low after binary search will be the k-th smallest distance.

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JavaScript Implementation

1. Sorting the Array:

   • Begin by sorting the array to facilitate pair counting with two pointers.

2. Binary Search Preparation:

   • Initialize the search range with low as the smallest possible distance (0) and high as the maximum possible distance.

3. Counting Pairs:

   • For a given midpoint (mid), count the number of pairs with a difference less than or equal to mid using two pointers.

4. Binary Search Execution:

   • Based on the count of valid pairs, adjust the search range: search the lower half if the count is greater than or equal to k, otherwise search the upper half.

5. Final Value:

   • After completing the binary search, low will hold the k-th smallest distance.

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Python Implementation

1. Sorting the Array:

   • The array is sorted to enable efficient pair counting.

2. Binary Search Setup:

   • Set up the search range with low as 0 and high as the difference between the maximum and minimum elements in the array.

3. Counting Valid Pairs:

   • For each midpoint (mid), use a two-pointer technique to count pairs with a difference less than or equal to mid.

4. Binary Search Progression:

   • Adjust the search range based on the count of valid pairs. If the count is greater than or equal to k, search the lower half; otherwise, search the upper half.

5. Conclusion:

   • The value of low after binary search will be the k-th smallest distance.

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Go Implementation

1. Array Sorting:

   • Sort the array to prepare for pair counting using two pointers.

2. Binary Search Initialization:

   • Set up the binary search range, with low as 0 and high as the difference between the maximum and minimum elements in the array.

3. Counting Pairs:

   • For each midpoint (mid), count the number of pairs with a distance less than or equal to mid.

4. Binary Search Execution:

   • Adjust the binary search range based on the count of valid pairs. If the count is sufficient, search the lower half; otherwise, search the upper half.

5. Final Output:

   • After binary search, low will contain the k-th smallest distance.