Introduction

In this blog post, we will explore how to solve the LeetCode problem "2860" 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 a 0-indexed integer array nums of length n where n is the total number of students in the class. The class teacher tries to select a group of students so that all the students remain happy. The ith student will become happy if one of these two conditions is met: The student is selected and the total number of selected students is strictly greater than nums[i]. The student is not selected and the total number of selected students is strictly less than nums[i]. Return the number of ways to select a group of students so that everyone remains happy. Example 1: Input: nums = [1,1] Output: 2 Explanation: The two possible ways are: The class teacher selects no student. The class teacher selects both students to form the group. If the class teacher selects just one student to form a group then the both students will not be happy. Therefore, there are only two possible ways. Example 2: Input: nums = [6,0,3,3,6,7,2,7] Output: 3 Explanation: The three possible ways are: The class teacher selects the student with index = 1 to form the group. The class teacher selects the students with index = 1, 2, 3, 6 to form the group. The class teacher selects all the students to form the group. Constraints: 1 <= nums.length <= 105 0 <= nums[i] < nums.length

Explanation

Here's the breakdown of the solution:

• Sorting: Sort the input array nums in non-decreasing order. This allows us to efficiently find ranges of students who can be selected based on the condition selected > nums[i].
• Iteration and Counting: Iterate through the sorted array. For each possible number of selected students k, check if there's a valid range of indices i such that selecting students from 0 to k-1 makes everyone happy. This involves verifying that k > nums[k-1] (if k>0) and k < nums[k] (if k < n).

• Counting Valid Combinations: Keep track of the number of valid combinations.

• Runtime Complexity: O(n log n) due to sorting.

• Storage Complexity: O(1) excluding the space used to store the input (can be O(n) if sorting algorithm like mergesort are used)

Code

    def count_ways(nums):
    """
    Counts the number of ways to select a group of students so that everyone remains happy.

    Args:
        nums: A list of integers representing the nums values for each student.

    Returns:
        The number of ways to select a group of students so that everyone remains happy.
    """

    n = len(nums)
    nums.sort()
    count = 0

    # Case: Select no students
    valid_no_selection = True
    for i in range(n):
        if 0 >= nums[i]:
            valid_no_selection = False
            break

    if valid_no_selection:
        count += 1

    # Case: Select some students
    for k in range(1, n + 1):
        valid_selection = True

        # Check condition for selected students
        if k > 0:
            if k <= nums[k - 1]:
                valid_selection = False
                continue

        # Check condition for unselected students
        if k < n:
            if k >= nums[k]:
                valid_selection = False
                continue

        if valid_selection:
            count += 1

    return count