2657. find the prefix common array of two arrays

General
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  1. find the prefix common array of two arrays
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Understanding the Prefix Common Array of Two Arrays

To find the prefix common array of two arrays, we first need to understand what a prefix common array is. A prefix common array essentially contains the count of common elements that the two given arrays share from the start up to each position (index) when traversed.

Suppose we have two arrays, A and B. A prefix common array P can be constructed such that for each index i, P[i] gives the count of common elements in the sub-arrays A[0:i] and B[0:i].

Let’s break this task down into a step-by-step approach to construct the prefix common array.

Step-by-Step Approach

  1. Initialize Variables and Data Structures:

    • Create an empty list P to store the prefix common count at each index.
    • Use two dictionaries or hash maps to track elements and their counts in the sub-arrays of A and B up to the current index.

  2. Iterate Through Each Index:

    • For each index i in the arrays:
      • Update the count of the current element in both dictionaries (for array A and array B).
      • Calculate the number of common elements by comparing the counts in both dictionaries.
      • Store the count of common elements up to the current index in the prefix common array P.

  3. Return Result:

    • The resulting array P is the prefix common array of A and B.

Example

Consider the following illustration:

Given Arrays:

  • Array A: [1, 2, 3, 4, 5]
  • Array B: [3, 2, 5, 4, 1]

Algorithm to Find Prefix Common Array

Let’s implement the detailed algorithm:

def prefix_common_array(A, B):
    # Initialize the prefix common array
    P = []

    # Dictionaries to track the occurrence of elements in A and B
    dict_A = {}
    dict_B = {}

    # Iterate over each index
    for i in range(len(A)):
        # Update dictionaries with current elements from A and B
        if A[i] in dict_A:
            dict_A[A[i]] += 1
        else:
            dict_A[A[i]] = 1
        
        if B[i] in dict_B:
            dict_B[B[i]] += 1
        else:
            dict_B[B[i]] = 1
        
        # Count common elements by finding the minimum frequency of each element present in both dictionaries
        common_count = 0
        for key in dict_A:
            if key in dict_B:
                common_count += min(dict_A[key], dict_B[key])
        
        # Append the common element count to the prefix array
        P.append(common_count)

    return P

# Example usage
A = [1, 2, 3, 4, 5]
B = [3, 2, 5, 4, 1]
result = prefix_common_array(A, B)
print("Prefix Common Array: ", result)

Output Explained

Using our example:

  • i = 0: A[0] = 1, B[0] = 3. Common elements = 0 (P[0] = 0)
  • i = 1: A[0:2] = [1, 2], B[0:2] = [3, 2]. Common elements = 1 (P[1] = 1)
  • i = 2: A[0:3] = [1, 2, 3], B[0:3] = [3, 2, 5]. Common elements = 2 (P[2] = 2)
  • i = 3: A[0:4] = [1, 2, 3, 4], B[0:4] = [3, 2, 5, 4]. Common elements = 3 (P[3] = 3)
  • i = 4: A[0:5] = [1, 2, 3, 4, 5], B[0:5] = [3, 2, 5, 4, 1]. Common elements = 5 (P[4] = 5)

Thus, the prefix common array P is [0, 1, 2, 3, 5].

This methodology can be adapted to any pair of arrays to find their prefix common array. Feel free to use the code above with different arrays to see how they work with this approach.