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Assign Elements to Groups with Constraints

Difficulty: Medium

Problem Description

You are given an integer array groups, where groups[i] represents the size of the i-th group. You are also given an integer array elements. Your task is to assign one element to each group based on the following rules:

  • An element at index j can be assigned to a group i if groups[i] is divisible by elements[j].
  • If there are multiple elements that can be assigned, assign the element with the smallest index j.
  • If no element satisfies the condition for a group, assign -1 to that group.

Return an integer array assigned, where assigned[i] is the index of the element chosen for group i, or -1 if no suitable element exists.

Key Insights

  • Each group size must be checked against all elements to find a suitable assignment.
  • The assignment must prioritize the smallest index of the element that can satisfy the divisibility condition.
  • A proper iteration through the elements for each group allows for the correct assignment or determination of -1.

Space and Time Complexity

Time Complexity: O(n * m), where n is the number of groups and m is the number of elements. Space Complexity: O(n), where n is the size of the assigned array.

Solution

To solve this problem, we will use a straightforward approach:

  1. Iterate through each group in the groups array.
  2. For each group, iterate through the elements array to check for divisibility.
  3. If an element divides the group size, record its index if it is the first valid element found.
  4. If no valid element is found for a group, assign -1 to that group.
  5. Return the array of assigned indices.

We can utilize a simple list to store the results for the assigned indices.

Code Solutions

def assign_elements(groups, elements):
    assigned = [-1] * len(groups)  # Initialize the result array with -1
    for i in range(len(groups)):  # Iterate over each group
        for j in range(len(elements)):  # Iterate over each element
            if groups[i] % elements[j] == 0:  # Check divisibility
                assigned[i] = j  # Assign the index of the element
                break  # Stop searching after the first valid element
    return assigned
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