Introduction

In this blog post, we will explore how to solve the LeetCode problem "3301" 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 array maximumHeight, where maximumHeight[i] denotes the maximum height the ith tower can be assigned. Your task is to assign a height to each tower so that: The height of the ith tower is a positive integer and does not exceed maximumHeight[i]. No two towers have the same height. Return the maximum possible total sum of the tower heights. If it's not possible to assign heights, return -1. Example 1: Input: maximumHeight = [2,3,4,3] Output: 10 Explanation: We can assign heights in the following way: [1, 2, 4, 3]. Example 2: Input: maximumHeight = [15,10] Output: 25 Explanation: We can assign heights in the following way: [15, 10]. Example 3: Input: maximumHeight = [2,2,1] Output: -1 Explanation: It's impossible to assign positive heights to each index so that no two towers have the same height. Constraints: 1 <= maximumHeight.length <= 105 1 <= maximumHeight[i] <= 109

Explanation

Here's the breakdown of the solution:

• Sort and Iterate: Sort the maximumHeight array. Then, iterate through the sorted array, assigning heights from 1 up to n (the number of towers), ensuring each assigned height doesn't exceed the corresponding maximumHeight value.
• Check for Infeasibility: If at any point the required height i+1 (since we're assigning from 1) exceeds the maximumHeight[i], it's impossible to assign distinct heights, so return -1.

• Calculate Sum: Accumulate the assigned heights to get the maximum possible sum.

• Runtime Complexity: O(n log n) due to sorting. Storage Complexity: O(n) in the worst-case due to Python's sorted() function creating a copy. In-place sorting algorithms exist but might not be Python's default sorted().

Code

    def maximum_tower_height_sum(maximumHeight):
    """
    Calculates the maximum possible sum of tower heights under the given constraints.

    Args:
        maximumHeight: A list of integers representing the maximum height of each tower.

    Returns:
        The maximum possible total sum of the tower heights, or -1 if it's impossible to assign heights.
    """
    n = len(maximumHeight)
    sorted_heights = sorted(maximumHeight)
    total_sum = 0
    for i in range(n):
        required_height = i + 1
        if required_height > sorted_heights[i]:
            return -1
        total_sum += required_height
    return total_sum