Count Pairs

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Unit 4 Session 2 (Click for link to problem statements)

U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• How does the function handle the scenario where all elements are greater than or equal to the target?
  • If all elements in the list, when summed with any other, exceed the target, the function should return 0 as no valid pairs meet the condition.
• What happens if the list is empty or contains only one element?
  • In cases where the list is empty or contains only one element, the function should return 0 as there are no possible pairs.

P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Sort the list to facilitate the use of a two-pointer technique where one pointer starts from each element and the other searches for the upper limit where their sum is less than the target.

1) Sort the list of numbers to allow ordered comparisons.
2) Initialize a counter to track the number of valid pairs.
3) Iterate through the list with a pointer `left` starting from the first element.
4) For each element at `left`, initiate a second pointer `right` from `left + 1`.
5) Use a while loop to move `right` while `nums[left] + nums[right]` is less than the target.
6) After exiting the loop for each `left`, calculate the number of valid pairs by subtracting `left + 1` from `right` and add to the count.
7) Return the total count of pairs.

⚠️ Common Mistakes

• Incorrect loop condition or incorrect update of the right pointer could lead to missing valid pairs or counting invalid pairs.
• Miscounting the number of valid pairs by not adjusting for the indices properly.

I-mplement

def count_pairs(nums, target):
    nums.sort()  # Sort the array to use two pointers
    count = 0
    n = len(nums)

    for left in range(n):
        right = left + 1
        while right < n and nums[left] + nums[right] < target:
            right += 1
        count += right - left - 1  # Add the number of valid pairs with nums[left]

    return count