Finding Non-Common Index Pairs in Large Integer Sets Using C#

Introduction

Hello, coding enthusiast! On our journey to master coding and problem-solving, we've arrived at an interesting challenge today. We're going to focus heavily on combinatorial problems . Specifically, we're examining combinatorial problems that involve working with large datasets and multiple pairs of numbers. We'll learn how to solve significant problems efficiently by implementing smart use of data structures like dictionaries and sidestepping expensive operations, such as iterating over large arrays. Are you ready? Let's dive in!

Task Statement

i \ne j

Understanding the Solution: The Idea

n \cdot (n - 1) / 2

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using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        // (The rest of the code will be added in subsequent steps)
        return totalPairs; // Temporary return to avoid error
    }

    static void Main(string[] args)
    {
        Console.WriteLine(NonCommonPairs(new int[][] { })); // Example usage, to be updated later
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        // (The rest of the code will be added in the next step)
        return totalPairs; // Temporary return to avoid error
    }

    static void Main(string[] args)
    {
        Console.WriteLine(NonCommonPairs(new int[][] { })); // Example usage, to be updated later
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        // (The rest of the code will be added in the next step)
        return totalPairs; // Temporary return to avoid error
    }

    static void Main(string[] args)
    {
        Console.WriteLine(NonCommonPairs(new int[][] { })); // Example usage, to be updated later
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        int commonPairs = 0;
        foreach (var entry in indices)
        {
            int size = entry.Value.Count;
            commonPairs += size * (size - 1) / 2;
        }

        return totalPairs - commonPairs;
    }

    static void Main(string[] args)
    {
        int[][] testArr = {
            new int[] { 2, 5 },
            new int[] { 1, 6 },
            new int[] { 3, 2 },
            new int[] { 4, 2 },
            new int[] { 5, 1 },
            new int[] { 6, 3 }
        };
        Console.WriteLine("Count of non-common pairs: " + NonCommonPairs(testArr)); // Output: Count of non-common pairs: 8
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        int commonPairs = 0;
        foreach (var entry in indices)
        {
            int size = entry.Value.Count;
            commonPairs += size * (size - 1) / 2;
        }

        return totalPairs - commonPairs;
    }

    static void Main(string[] args)
    {
        int[][] testArr = {
            new int[] { 2, 5 },
            new int[] { 1, 6 },
            new int[] { 3, 2 },
            new int[] { 4, 2 },
            new int[] { 5, 1 },
            new int[] { 6, 3 }
        };
        Console.WriteLine("Count of non-common pairs: " + NonCommonPairs(testArr)); // Output: Count of non-common pairs: 8
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        // (The rest of the code will be added in subsequent steps)
        return totalPairs; // Temporary return to avoid error
    }

    static void Main(string[] args)
    {
        Console.WriteLine(NonCommonPairs(new int[][] { })); // Example usage, to be updated later
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        // (The rest of the code will be added in the next step)
        return totalPairs; // Temporary return to avoid error
    }

    static void Main(string[] args)
    {
        Console.WriteLine(NonCommonPairs(new int[][] { })); // Example usage, to be updated later
    }
}

using System;
using System.Collections.Generic;

class Program
{
    public static int NonCommonPairs(int[][] arr)
    {
        var indices = new Dictionary<int, List<int>>();
        int totalPairs = arr.Length * (arr.Length - 1) / 2;

        for (int idx = 0; idx < arr.Length; idx++)
        {
            foreach (var num in arr[idx])
            {
                if (!indices.ContainsKey(num))
                {
                    indices[num] = new List<int>();
                }
                indices[num].Add(idx);
            }
        }

        int commonPairs = 0;
        foreach (var entry in indices)
        {
            int size = entry.Value.Count;
            commonPairs += size * (size - 1) / 2;
        }

        return totalPairs - commonPairs;
    }

    static void Main(string[] args)
    {
        int[][] testArr = {
            new int[] { 2, 5 },
            new int[] { 1, 6 },
            new int[] { 3, 2 },
            new int[] { 4, 2 },
            new int[] { 5, 1 },
            new int[] { 6, 3 }
        };
        Console.WriteLine("Count of non-common pairs: " + NonCommonPairs(testArr)); // Output: Count of non-common pairs: 8
    }
}