In this problem, you are given an array of ages and need to count the number of valid friend requests. A friend request is valid if both people meet specific age-related conditions. Using binary search over the valid answer space, you can efficiently calculate the number of valid requests, which is a key focus in this problem.
Problem Statement
You are given an array of integers, ages, representing the ages of individuals on a social media platform. A person x will not send a friend request to a person y if any of the following conditions are true: y's age is less than 0.5 * x's age + 7 or y's age is greater than x's age, or y's age is greater than 100 and x's age is less than 100. Otherwise, a valid friend request can be made.
Your task is to count how many friend requests can be made within the given array of ages by ensuring each pair of individuals satisfies the conditions outlined. The goal is to compute this efficiently, especially given the constraints on the number of people (up to 20,000).
Examples
Example 1
Input: ages = [16,16]
Output: 2
2 people friend request each other.
Example 2
Input: ages = [16,17,18]
Output: 2
Friend requests are made 17 -> 16, 18 -> 17.
Example 3
Input: ages = [20,30,100,110,120]
Output: 3
Friend requests are made 110 -> 100, 120 -> 110, 120 -> 100.
Constraints
- n == ages.length
- 1 <= n <= 2 * 104
- 1 <= ages[i] <= 120
Solution Approach
Sort and Binary Search
The first step in the solution is to sort the array of ages. Once sorted, we can use binary search to efficiently determine the valid range of friend requests for each person. This significantly reduces the number of comparisons required compared to a brute force approach.
Two Pointers for Counting
After sorting the array, we use a two-pointer technique. For each person x, we can find the range of people whose ages allow them to send a request to x using the binary search results. The two-pointer method helps to count valid pairs efficiently.
Final Calculation of Requests
For each person in the array, once we have the valid range of ages that can send requests to them, we simply multiply the number of people within that range by the number of people to whom they can send requests. This allows us to count the total number of valid friend requests.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity of this solution is O(n log n) due to the sorting step, followed by O(n log n) for binary searches, leading to an overall time complexity of O(n log n). The space complexity is O(n) due to the storage requirements for the sorted array and the auxiliary space used by the binary search.
What Interviewers Usually Probe
- Candidate demonstrates understanding of binary search and two-pointer techniques.
- Candidate suggests sorting as a first step for optimization.
- Candidate efficiently calculates the number of valid requests without resorting to brute force.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to handle edge cases, such as when people have very young or very old ages.
- Incorrectly calculating the valid age range for friend requests, especially when ages are close to boundaries.
- Attempting to brute force the solution without leveraging sorting and binary search for optimization.
Follow-up variants
- Implement a solution without sorting the array, using only binary search to determine valid pairs.
- Modify the problem to allow for weighted age differences when determining valid requests.
- Adapt the problem for real-time computations with streaming data, requiring constant updates to the array of ages.
How GhostInterview Helps
- GhostInterview breaks down the problem into manageable steps, guiding you through sorting, binary search, and counting using two pointers.
- With GhostInterview's targeted hints, you can identify common pitfalls and avoid time-consuming mistakes in the interview setting.
- GhostInterview provides practical advice for optimizing both time and space complexity while ensuring the solution meets constraints.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How can binary search be used in Friends Of Appropriate Ages?
Binary search helps by efficiently finding the range of ages that can send a friend request to a given person. This reduces the number of comparisons needed, speeding up the solution.
Why is sorting necessary in Friends Of Appropriate Ages?
Sorting helps arrange the ages in increasing order, making it easier to apply binary search and use two pointers to efficiently count valid pairs.
What are common mistakes in solving Friends Of Appropriate Ages?
Common mistakes include neglecting to handle edge cases, making incorrect age comparisons, and failing to optimize the solution with sorting and binary search.
How does GhostInterview optimize the solving process?
GhostInterview helps by providing focused guidance on sorting, binary search, and two-pointer techniques, allowing you to quickly implement an efficient solution.
Can the problem be solved without sorting the array?
While it is possible to solve the problem without sorting, using sorting and binary search is the most efficient approach for this problem, reducing time complexity.
Need direct help with Friends Of Appropriate Ages instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Friends Of Appropriate Ages from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Assign workers to jobs maximizing total profit using difficulty, profit, and worker arrays efficiently with binary search pattern.
Open problem page#786 K-th Smallest Prime FractionFind the k-th smallest fraction from a sorted array of unique primes using a binary search over the answer space.
Open problem page#719 Find K-th Smallest Pair DistanceSolve Find K-th Smallest Pair Distance by sorting nums, then binary searching the distance and counting valid pairs with two pointers.
Open problem page