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Divide Array Into Equal Pairs

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Arrays

You are given an integer array nums consisting of 2 * n integers.

You need to divide nums into n pairs such that:

Each element belongs to exactly one pair.
The elements present in a pair are equal.

Return true if nums can be divided into n pairs, otherwise return false.

Example 1:

Input: nums = [3,2,3,2,2,2]
Output: true
Explanation: 
There are 6 elements in nums, so they should be divided into 6 / 2 = 3 pairs.
If nums is divided into the pairs (2, 2), (3, 3), and (2, 2), it will satisfy all the conditions.

Example 2:

Input: nums = [1,2,3,4]
Output: false
Explanation: 
There is no way to divide nums into 4 / 2 = 2 pairs such that the pairs satisfy every condition.

Constraints:

nums.length == 2 * n
1 <= n <= 500
1 <= nums[i] <= 500

Try coding it in LeetCode

Divide Array Into Equal Pairs

Easy

Asked by:

63 views

Topics:

Arrays

You are given an integer array nums consisting of 2 * n integers.

You need to divide nums into n pairs such that:

Each element belongs to exactly one pair.
The elements present in a pair are equal.

Return true if nums can be divided into n pairs, otherwise return false.

Example 1:

Input: nums = [3,2,3,2,2,2]
Output: true
Explanation: 
There are 6 elements in nums, so they should be divided into 6 / 2 = 3 pairs.
If nums is divided into the pairs (2, 2), (3, 3), and (2, 2), it will satisfy all the conditions.

Example 2:

Input: nums = [1,2,3,4]
Output: false
Explanation: 
There is no way to divide nums into 4 / 2 = 2 pairs such that the pairs satisfy every condition.

Constraints:

nums.length == 2 * n
1 <= n <= 500
1 <= nums[i] <= 500

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the expected return value if the input array cannot be divided into equal pairs?
Can the input array contain negative numbers?
What is the range of values for the integers within the array?
Is the input array guaranteed to have an even number of elements?
Are we concerned about potential integer overflow if the numbers are very large?

Brute Force Solution

Approach

The brute force approach to pairing elements in the array involves checking every single possible combination of pairs. Think of it as trying every imaginable pairing to see if it works. If we find a working set of pairs, we know we have found the solution.

Here's how the algorithm would work step-by-step:

Pick the first number in the array.
Search the rest of the array for a number that is identical to it.
If you find a match, mark both numbers as paired and remove them from consideration.
If you don't find a match for the first number, it's impossible to make pairs, and you can stop.
Repeat this process for the next unpaired number in the array until all numbers have been processed.
If all the numbers could be paired successfully, then you have found a way to divide the array into equal pairs; otherwise, it is not possible.

Code Implementation

def divide_array_into_equal_pairs(numbers):
    numbers_list = numbers.copy()

    while numbers_list:
        first_number = numbers_list[0]

        # Find a match for the first number
        found_match = False
        for index in range(1, len(numbers_list)):
            if numbers_list[index] == first_number:
                second_number_index = index
                found_match = True
                break

        # If no match is found, return False.
        if not found_match:
            return False

        # Remove the paired numbers
        numbers_list.pop(second_number_index)
        numbers_list.pop(0)

    # If all numbers are paired, return True
    return True

Big(O) Analysis

Time Complexity

O(n²) – The algorithm iterates through the array of size n. For each element, it searches for a matching element in the remaining portion of the array. In the worst case, for the first element, we might scan almost the entire array (n-1 elements). For the next unpaired element, we might scan up to (n-3) elements, and so on. This implies roughly n * (n/2) operations, which in Big O notation simplifies to O(n²).

Space Complexity

O(1) – The plain English solution describes iterating through the array and marking/removing elements. Without a specific data structure mentioned for marking or removing, the most straightforward interpretation involves in-place modification. In this case, no additional data structures that scale with the input size N are explicitly created. Therefore, the auxiliary space used is constant, regardless of the size of the input array, N.

Optimal Solution

Approach

The core idea is to count how many times each number appears. If we can successfully pair all the numbers, each number should show up an even number of times.

Here's how the algorithm would work step-by-step:

First, take a piece of paper and keep track of how many times each number shows up.
Then, go through your list. If every number shows up an even number of times (like 2, 4, 6, etc.), you can make equal pairs from the numbers.
If even one number shows up an odd number of times, then you won't be able to make equal pairs.

Code Implementation

def divide_array_into_equal_pairs(numbers) -> bool:
    number_counts = {}
    for number in numbers:
        if number in number_counts:
            number_counts[number] += 1
        else:
            number_counts[number] = 1

    # Iterate through the counts to check for odd occurrences.
    for number in number_counts:
        # If any number appears an odd number of times, return false.
        if number_counts[number] % 2 != 0:
            return False

    # If all numbers appear an even number of times, return true.
    return True

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input array of size n once to count the frequency of each number using a hash map (or similar data structure). After counting, it iterates through the unique numbers in the hash map, which in the worst case could also be n. Both loops are independent and take linear time with respect to the input size. Therefore, the overall time complexity is O(n).

Space Complexity

O(N) – The provided plain English explanation outlines a process of counting the frequency of each number in the input array. This implies the use of a data structure, such as a hash map or an array, to store these counts. In the worst-case scenario, where all N numbers in the input array are distinct, the space required to store the counts will be proportional to N. Therefore, the auxiliary space complexity is O(N).

Edge Cases

Case	How to Handle
Null or undefined input array	Throw an IllegalArgumentException or return an appropriate error value like null or an empty array, depending on the requirements.
Empty array (length 0)	Return true (or an empty list of pairs), as vacuously true; an empty array is divisible into equal pairs.
Array with odd number of elements	Return false immediately because it cannot be divided into equal pairs.
Array with a large number of elements (close to maximum integer size)	Consider space complexity of data structures used (e.g., hash map) to ensure it doesn't exceed memory limits.
Array contains negative numbers	The hash map (or sorting-based approach) will work correctly with negative numbers.
Array contains zero values	The solution should correctly handle zero values like any other number.
Array where elements cannot be paired	The hash map or sorting approach will result in an unmatched element, leading to a return of false.
Integer overflow during calculations (if applicable)	Ensure calculations are done using data types that can accommodate the potential range of values, or implement checks to prevent overflow.

Null or undefined input array

How to Handle:

Throw an IllegalArgumentException or return an appropriate error value like null or an empty array, depending on the requirements.

Empty array (length 0)

How to Handle:

Return true (or an empty list of pairs), as vacuously true; an empty array is divisible into equal pairs.

Array with odd number of elements

How to Handle:

Return false immediately because it cannot be divided into equal pairs.

Array with a large number of elements (close to maximum integer size)

How to Handle:

Consider space complexity of data structures used (e.g., hash map) to ensure it doesn't exceed memory limits.

Array contains negative numbers

How to Handle:

The hash map (or sorting-based approach) will work correctly with negative numbers.

Array contains zero values

How to Handle:

The solution should correctly handle zero values like any other number.

Array where elements cannot be paired

How to Handle:

The hash map or sorting approach will result in an unmatched element, leading to a return of false.

Integer overflow during calculations (if applicable)

How to Handle:

Ensure calculations are done using data types that can accommodate the potential range of values, or implement checks to prevent overflow.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the expected return value if the input array cannot be divided into equal pairs?
Can the input array contain negative numbers?
What is the range of values for the integers within the array?
Is the input array guaranteed to have an even number of elements?
Are we concerned about potential integer overflow if the numbers are very large?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Pick the first number in the array.
Search the rest of the array for a number that is identical to it.
If you find a match, mark both numbers as paired and remove them from consideration.
If you don't find a match for the first number, it's impossible to make pairs, and you can stop.
Repeat this process for the next unpaired number in the array until all numbers have been processed.
If all the numbers could be paired successfully, then you have found a way to divide the array into equal pairs; otherwise, it is not possible.

Code Implementation

def divide_array_into_equal_pairs(numbers):
    numbers_list = numbers.copy()

    while numbers_list:
        first_number = numbers_list[0]

        # Find a match for the first number
        found_match = False
        for index in range(1, len(numbers_list)):
            if numbers_list[index] == first_number:
                second_number_index = index
                found_match = True
                break

        # If no match is found, return False.
        if not found_match:
            return False

        # Remove the paired numbers
        numbers_list.pop(second_number_index)
        numbers_list.pop(0)

    # If all numbers are paired, return True
    return True

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

The core idea is to count how many times each number appears. If we can successfully pair all the numbers, each number should show up an even number of times.

Here's how the algorithm would work step-by-step:

First, take a piece of paper and keep track of how many times each number shows up.
Then, go through your list. If every number shows up an even number of times (like 2, 4, 6, etc.), you can make equal pairs from the numbers.
If even one number shows up an odd number of times, then you won't be able to make equal pairs.

Code Implementation

def divide_array_into_equal_pairs(numbers) -> bool:
    number_counts = {}
    for number in numbers:
        if number in number_counts:
            number_counts[number] += 1
        else:
            number_counts[number] = 1

    # Iterate through the counts to check for odd occurrences.
    for number in number_counts:
        # If any number appears an odd number of times, return false.
        if number_counts[number] % 2 != 0:
            return False

    # If all numbers appear an even number of times, return true.
    return True

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or undefined input array	Throw an IllegalArgumentException or return an appropriate error value like null or an empty array, depending on the requirements.
Empty array (length 0)	Return true (or an empty list of pairs), as vacuously true; an empty array is divisible into equal pairs.
Array with odd number of elements	Return false immediately because it cannot be divided into equal pairs.
Array with a large number of elements (close to maximum integer size)	Consider space complexity of data structures used (e.g., hash map) to ensure it doesn't exceed memory limits.
Array contains negative numbers	The hash map (or sorting-based approach) will work correctly with negative numbers.
Array contains zero values	The solution should correctly handle zero values like any other number.
Array where elements cannot be paired	The hash map or sorting approach will result in an unmatched element, leading to a return of false.
Integer overflow during calculations (if applicable)	Ensure calculations are done using data types that can accommodate the potential range of values, or implement checks to prevent overflow.

Null or undefined input array

How to Handle:

Throw an IllegalArgumentException or return an appropriate error value like null or an empty array, depending on the requirements.

Empty array (length 0)

How to Handle:

Return true (or an empty list of pairs), as vacuously true; an empty array is divisible into equal pairs.

Array with odd number of elements

How to Handle:

Return false immediately because it cannot be divided into equal pairs.

Array with a large number of elements (close to maximum integer size)

How to Handle:

Consider space complexity of data structures used (e.g., hash map) to ensure it doesn't exceed memory limits.

Array contains negative numbers

How to Handle:

The hash map (or sorting-based approach) will work correctly with negative numbers.

Array contains zero values

How to Handle:

The solution should correctly handle zero values like any other number.

Array where elements cannot be paired

How to Handle:

The hash map or sorting approach will result in an unmatched element, leading to a return of false.

Integer overflow during calculations (if applicable)

How to Handle:

Ensure calculations are done using data types that can accommodate the potential range of values, or implement checks to prevent overflow.