How do you solve Find the Prefix Common Array of Two Arrays on LeetCode?

Find the Prefix Common Array of Two Arrays (LeetCode #2657) 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: Both arrays are permutations, so every number from 1 to n appears exactly once.

What is the brute force solution for Find the Prefix Common Array of Two Arrays?

The brute force approach for Find the Prefix Common Array of Two Arrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks each index of the arrays A and B and counts how many numbers are common up to that index. It’s straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Prefix Common Array of Two Arrays?

Find the Prefix Common Array of Two Arrays uses the following concepts: Array, Hash Table, Bit Manipulation. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Prefix Common Array of Two Arrays?

Always clarify the constraints and properties of the input data. Think about how to reduce the number of iterations needed to solve the problem. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Find the Prefix Common Array of Two Arrays?

Not recognizing that both arrays are permutations, leading to unnecessary checks. Overcomplicating the counting process instead of using a frequency array.

#2657

Find the Prefix Common Array of Two Arrays

Medium

ArrayHash TableBit ManipulationHash 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)

The optimal solution uses a frequency array to track the occurrences of numbers seen so far in both arrays. This allows us to count common elements efficiently without nested loops.

⚙️

Algorithm

5 steps

1Step 1: Initialize an empty array C of the same length as A and B.
2Step 2: Initialize a frequency array of size n+1 to count occurrences of numbers in A and B.
3Step 3: For each index i from 0 to n-1, increment the frequency of A[i] and B[i].
4Step 4: Count how many numbers have been seen in both arrays up to index i and store that in C[i].
5Step 5: Return the array C.

solution.py14 lines

1# Full working Python code
2
3def findPrefixCommonArray(A, B):
4    n = len(A)
5    C = [0] * n
6    freq = [0] * (n + 1)
7    for i in range(n):
8        freq[A[i]] += 1
9        freq[B[i]] += 1
10        C[i] = sum(1 for count in freq if count > 1)
11    return C
12
13# Example usage
14print(findPrefixCommonArray([1,3,2,4], [3,1,2,4]))

ℹ

Complexity note: The time complexity is O(n) because we iterate through the arrays once, and the space complexity is O(n) due to the frequency array used to track occurrences.

1Both arrays are permutations, so every number from 1 to n appears exactly once.
2Counting occurrences efficiently allows us to determine common elements without nested loops.

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