14_Find_the_Prefix_Common_Array_of_Two_Arrays.cpp

// 2657. Find the Prefix Common Array of Two Arrays

// You are given two 0-indexed integer permutations A and B of length n.

// A prefix common array of A and B is an array C such that C[i] is equal to the count of numbers that are present at or before the index i in both A and B.

// Return the prefix common array of A and B.

// A sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.

 

// Example 1:

// Input: A = [1,3,2,4], B = [3,1,2,4]
// Output: [0,2,3,4]
// Explanation: At i = 0: no number is common, so C[0] = 0.
// At i = 1: 1 and 3 are common in A and B, so C[1] = 2.
// At i = 2: 1, 2, and 3 are common in A and B, so C[2] = 3.
// At i = 3: 1, 2, 3, and 4 are common in A and B, so C[3] = 4.
// Example 2:

// Input: A = [2,3,1], B = [3,1,2]
// Output: [0,1,3]
// Explanation: At i = 0: no number is common, so C[0] = 0.
// At i = 1: only 3 is common in A and B, so C[1] = 1.
// At i = 2: 1, 2, and 3 are common in A and B, so C[2] = 3.
 

// Constraints:

// 1 <= A.length == B.length == n <= 50
// 1 <= A[i], B[i] <= n
// It is guaranteed that A and B are both a permutation of n integers.

class Solution
{
public:
    vector<int> findThePrefixCommonArray(vector<int> &A, vector<int> &B)
    {
        int n = A.size();
        vector<int> freq(n + 1, 0);
        vector<int> result;
        int common = 0;
        for (int i = 0; i < n; i++)
        {
            if (++freq[A[i]] == 2)
                common++;
            if (++freq[B[i]] == 2)
                common++;
            result.push_back(common);
        }

        return result;
    }
};

/*
This code finds the prefix common array of two permutations A and B:
1. It creates a frequency array 'freq' to track occurrences of numbers
2. For each index i, it:
   - Increments frequency count for A[i] and B[i]
   - When any number's frequency becomes 2, it means that number is common in both arrays
   - Keeps track of total common numbers in 'common' variable
   - Stores current count of common numbers in result array
3. Finally returns the result array containing prefix common counts
Time Complexity: O(n), Space Complexity: O(n)
*/