How do you solve Detect Squares on LeetCode?

Detect Squares (LeetCode #2013) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using a frequency map allows for quick access to point counts, making the solution efficient.

What is the brute force solution for Detect Squares?

The brute force approach for Detect Squares is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we will check every combination of three points in the data structure to see if they can form a square with the query point. This is straightforward but inefficient as the number of points increases. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Detect Squares?

Detect Squares uses the following concepts: Array, Hash Table, Design, Counting, Data Stream. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Detect Squares?

Clarify the problem requirements and constraints before jumping into coding. Think about data structures that can optimize your solution, like HashMaps for counting. Practice explaining your thought process as you code; it helps solidify your understanding.

What are common mistakes when solving Detect Squares?

Failing to account for duplicate points in the frequency map. Not considering all potential square corners when counting.

#2013

Detect Squares

Medium

ArrayHash TableDesignCountingData StreamHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

In the optimal solution, we maintain a frequency map of points to quickly access how many points exist at specific coordinates. This allows us to count potential squares efficiently without checking every combination.

⚙️

Algorithm

3 steps

1Step 1: Use a HashMap to store the frequency of each point.
2Step 2: For each query point, find points with the same y-coordinate and calculate the potential coordinates for the other two corners of the square.
3Step 3: Use the frequency map to count how many of these potential points exist and calculate the total combinations.

solution.py18 lines

1from collections import defaultdict
2
3class DetectSquares:
4    def __init__(self):
5        self.point_count = defaultdict(int)
6
7    def add(self, point):
8        self.point_count[tuple(point)] += 1
9
10    def count(self, point):
11        count = 0
12        xq, yq = point
13        for (x, y), freq in self.point_count.items():
14            if y == yq:
15                side_length = abs(x - xq)
16                count += freq * self.point_count[(x, yq + side_length)] * self.point_count[(xq, yq + side_length)]
17                count += freq * self.point_count[(x, yq - side_length)] * self.point_count[(xq, yq - side_length)]
18        return count

ℹ

Complexity note: This complexity is linear because we only traverse the points once to build the frequency map and then check potential squares in constant time for each point.

1Using a frequency map allows for quick access to point counts, making the solution efficient.
2Identifying points with the same y-coordinate is crucial for forming squares.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.