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Assign Elements to Groups with Constraints

Number: 3760

Difficulty: Medium

Paid? No

Companies: N/A

Problem Description

Given two arrays, groups and elements, assign a single element (identified by its index) to each group such that the group size is divisible by the element’s value. If multiple suitable elements exist, choose the one with the smallest index. If no such element exists for a group, assign -1.

Key Insights

  • Preprocess the elements array to record, for each distinct element value, the smallest index at which it appears.
  • For each group value, determine its divisors by scanning from 1 to sqrt(group value). For each divisor, check if it (or its complementary divisor) exists in the preprocessed mapping.
  • By comparing candidates from all valid divisors, select the element with the smallest index.
  • An element may be used for multiple groups.

Space and Time Complexity

Time Complexity: O(n * sqrt(m)) where n is the length of groups and m is the maximum group value (up to 10^5).
Space Complexity: O(k) where k is the number of distinct values in elements (at most 10^5).

Solution

We first build a dictionary mapping each distinct element value in the elements array to its smallest index. Then for each group value, we compute its divisors by iterating from 1 up to the square root of the group value. For each divisor d, if d divides the group value, we check if d is present in our mapping; similarly, we check for the complementary divisor (group value divided by d). We then select the candidate with the smallest index. If no candidate is found, we assign -1 to that group.

Code Solutions

# Python solution with line-by-line comments

def assignElements(groups, elements):
    # Preprocess elements: map each element value to its smallest index.
    value_to_index = {}
    for idx, value in enumerate(elements):
        # Only record the first occurrence (smallest index) for each value.
        if value not in value_to_index:
            value_to_index[value] = idx
    
    # Prepare the answer array.
    assigned = []
    
    # Process each group.
    for group in groups:
        best_index = float('inf')  # Use infinity as an initial high value.
        # Iterate through possible divisors up to sqrt(group)
        d = 1
        while d * d <= group:
            if group % d == 0:
                # First potential divisor is "d".
                if d in value_to_index:
                    best_index = min(best_index, value_to_index[d])
                # Second potential divisor is group // d.
                other = group // d
                if other != d and other in value_to_index:
                    best_index = min(best_index, value_to_index[other])
            d += 1
        
        # If no valid candidate was found, assign -1.
        assigned.append(best_index if best_index != float('inf') else -1)
    
    return assigned

# Example usage:
groups = [8,4,3,2,4]
elements = [4,2]
print(assignElements(groups, elements))  # Output: [0, 0, -1, 1, 0]
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