Introduction

In this blog post, we will explore how to solve the LeetCode problem "3139" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer array nums and two integers cost1 and cost2. You are allowed to perform either of the following operations any number of times: Choose an index i from nums and increase nums[i] by 1 for a cost of cost1. Choose two different indices i, j, from nums and increase nums[i] and nums[j] by 1 for a cost of cost2. Return the minimum cost required to make all elements in the array equal. Since the answer may be very large, return it modulo 109 + 7. Example 1: Input: nums = [4,1], cost1 = 5, cost2 = 2 Output: 15 Explanation: The following operations can be performed to make the values equal: Increase nums[1] by 1 for a cost of 5. nums becomes [4,2]. Increase nums[1] by 1 for a cost of 5. nums becomes [4,3]. Increase nums[1] by 1 for a cost of 5. nums becomes [4,4]. The total cost is 15. Example 2: Input: nums = [2,3,3,3,5], cost1 = 2, cost2 = 1 Output: 6 Explanation: The following operations can be performed to make the values equal: Increase nums[0] and nums[1] by 1 for a cost of 1. nums becomes [3,4,3,3,5]. Increase nums[0] and nums[2] by 1 for a cost of 1. nums becomes [4,4,4,3,5]. Increase nums[0] and nums[3] by 1 for a cost of 1. nums becomes [5,4,4,4,5]. Increase nums[1] and nums[2] by 1 for a cost of 1. nums becomes [5,5,5,4,5]. Increase nums[3] by 1 for a cost of 2. nums becomes [5,5,5,5,5]. The total cost is 6. Example 3: Input: nums = [3,5,3], cost1 = 1, cost2 = 3 Output: 4 Explanation: The following operations can be performed to make the values equal: Increase nums[0] by 1 for a cost of 1. nums becomes [4,5,3]. Increase nums[0] by 1 for a cost of 1. nums becomes [5,5,3]. Increase nums[2] by 1 for a cost of 1. nums becomes [5,5,4]. Increase nums[2] by 1 for a cost of 1. nums becomes [5,5,5]. The total cost is 4. Constraints: 1 <= nums.length <= 105 1 <= nums[i] <= 106 1 <= cost1 <= 106 1 <= cost2 <= 106

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• Key Idea: The optimal target value to equalize the array elements is generally around the median. The problem can be solved by iterating through the sorted array elements and calculating the cost to make all elements equal to the current element. We minimize this cost.

• Optimization: For each target value, we can calculate the number of single increments (single_ops) and double increments (double_ops) needed and based on cost1, and cost2, we determine the optimal way of combining them.

• Runtime Complexity: O(n log n) due to sorting. Storage Complexity: O(n) to store the sorted array (in some implementations).

Code

    def minCostToEqualize(nums, cost1, cost2):
    """
    Calculates the minimum cost to equalize all elements in the array.

    Args:
        nums: The input array of integers.
        cost1: The cost to increase an element by 1.
        cost2: The cost to increase two elements by 1.

    Returns:
        The minimum cost to equalize all elements modulo 10^9 + 7.
    """
    n = len(nums)
    nums.sort()
    min_cost = float('inf')
    MOD = 10**9 + 7

    for target in nums:
        cost = 0
        single_ops = 0
        double_ops = 0

        for num in nums:
            if num < target:
                diff = target - num
                single_ops += diff

        if cost1 <= 2 * cost2:
            cost = (single_ops * cost1) % MOD
        else:
             cost = (single_ops // 2) * cost2 + (single_ops % 2) * cost1
             cost %= MOD

        min_cost = min(min_cost, cost)

    return min_cost % MOD