What is the optimal time complexity of solving Can all numbers of array be made equal?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Can all numbers of array be made equal?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Can all numbers of array be made equal?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Can all numbers of array be made equal?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Can all numbers of array be made equal

Learn how to solve the 'Can all numbers of array be made equal' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function can_make_equal(arr) that determines if all elements of the array can be made equal by repeatedly adding or subtracting any element from another. This is possible if and only if the total sum of the array is divisible by the length of the array (i.e., the mean is an integer). Return True if possible, False otherwise. Note: a simpler interpretation — if we can redistribute values freely, we can always make them equal when the sum is divisible by length.

Constraints

•1 <= len(arr) <= 10^5
•-10^6 <= arr[i] <= 10^6

Examples

Example 1

Input

arr = [1, 1, 1]

Output

True

Explanation

All elements are already equal.

Example 2

Input

arr = [1, 2, 3]

Output

True

Explanation

Sum = 6, length = 3. 6/3 = 2. We can make all elements 2.

Example 3

Input

arr = [1, 2, 4]

Output

False

Explanation

Sum = 7, length = 3. 7/3 is not an integer, so we cannot make all equal.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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