Day 003/365: Solving Problems with Arrays – Count Elements with Greater Counterparts

Welcome to Day 03 of Project 365, where we continue our journey to master coding concepts through daily challenges. Today, we tackle a practical problem related to arrays: Counting the elements in an array that have at least one greater element.

This article provides a comprehensive explanation of the problem, its solution, and insights to deepen your understanding. Let's get started!

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Problem Statement

Given an integer array of size (N), count the number of elements that have at least one other element greater than themselves.

Example Input and Output

• Input: [-3, -2, 6, 8, 4, 8, 6]

• Output: 5

Explanation

In the array [-3, -2, 6, 8, 4, 8, 6]:

• Elements -3, -2, 6, 4, and 6 have a greater element (8).

• The largest elements, 8 and 8, do not have any greater elements.

• Count of elements with a greater element: 5.

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Approach to Solve

To solve this problem, we can break it down into the following steps:

1. Find the Maximum Element:
   Identify the largest value in the array, as no elements can be greater than this.

2. Count Smaller Elements:
   Iterate through the array and count all elements smaller than the maximum.

3. Return the Count:
   The count represents the number of elements with at least one greater element.

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C# Implementation

Here’s how you can implement this solution in C#:

using System;

class Program
{
    static void Main()
    {
        int[] array = { -3, -2, 6, 8, 4, 8, 6 };
        int result = CountElementsWithGreater(array);
        Console.WriteLine($"Count: {result}");
    }

    static int CountElementsWithGreater(int[] nums)
    {
        int maxElement = int.MinValue;
        foreach (int num in nums)
        {
            if (num > maxElement)
            {
                maxElement = num;
            }
        }

        int count = 0;
        foreach (int num in nums)
        {
            if (num < maxElement)
            {
                count++;
            }
        }

        return count;
    }
}

Complexity Analysis

• Time Complexity: O(N)O(N)O(N)

  • Finding the maximum element: O(N)O(N)O(N).

  • Counting elements smaller than the maximum: O(N)O(N)O(N).

• Space Complexity: O(1)O(1)O(1)

  • No additional space is used.

Sample Inputs and Outputs

Input Array : [5, 2, 9, 1, 5]

Output : 4

Explanation : Elements 5, 2, 1, and 5 have a greater element (9).

Input Array : [10, 10, 10]

Output : 0

Explanation : All elements are the largest; no element has a greater one.

Input Array : [-3, -2, 6, 8, 4, 8, 6]

Output : 5

Explanation : elements -3, -2, 6, 4, and 6 have a greater element (8).

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Edge Cases

1. Single Element Array:

   • Input: [5]

   • Output: 0

   • Explanation: No other elements to compare.

2. All Elements Are the Same:

   • Input: [4, 4, 4]

   • Output: 0

   • Explanation: No element has a greater counterpart.

3. Array with Negatives:

   • Input: [-1, -2, -3, 0]

   • Output: 3

   • Explanation: Elements -1, -2, and -3 have a greater element (0).

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Key Takeaways

• Arrays are a fundamental data structure that offer a variety of problem-solving opportunities.

• Efficient iteration and attention to edge cases are crucial in developing robust solutions.

• Solving practical problems strengthens your intuition for coding challenges.

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Call to Action

Challenge yourself by solving similar problems! Share your solutions and insights with the community. Stay tuned for Day 04 as we continue exploring the exciting world of programming with Project 365.
Let’s master coding, one day at a time. 🚀