C# Coding Test Course, Finding the Sum of Remainders

Solution Process

1. Problem Analysis

This problem uniquely asks to obtain target through the addition of two elements followed by a modulo operation.
In other words, if the two numbers we are looking for are x and y, it must hold that
(x + y) % target == target. It is essential to understand the implications of the addition and modulo conditions.

2. Algorithm Design

To solve this problem, we will traverse the array only once and calculate the remainder for each element to match the target condition.
One method involves using a hash set to store previous values and check the condition by calculating the remainder with the current value.
The reason for using a hash set is to maintain an average time complexity of O(1).

3. Code Implementation

Now, let’s implement this algorithm in C#. Below is the solution code.

using System;
using System.Collections.Generic;

public class Solution
{
    public int[] FindTwoElementsWithTargetModulo(int[] numbers, int target)
    {
        // Dictionary to store the index of elements
        Dictionary valueToIndex = new Dictionary();
        
        for (int i = 0; i < numbers.Length; i++)
        {
            // Calculate the remainder for the current element
            int requiredValue = (target - numbers[i]) % target;

            // Check if the remainder exists in the dictionary
            if (valueToIndex.ContainsKey(requiredValue))
            {
                return new int[] { valueToIndex[requiredValue], i };
            }

            // Record the current element in the dictionary
            if (!valueToIndex.ContainsKey(numbers[i]))
            {
                valueToIndex[numbers[i]] = i;
            }
        }
        
        // If no two elements satisfy the condition
        return new int[] { -1 };
    }
}
        

4. Time Complexity

The time complexity of this algorithm is O(n). We can find the result with a single traversal of the array.
Additionally, the extra space complexity is O(n) due to the storage of values in the hash set.

5. Test Cases

Let’s write various test cases to verify the functionality.

public class Program
{
    public static void Main()
    {
        Solution solution = new Solution();

        // Test case 1
        int[] numbers1 = { 1, 2, 3, 4, 5 };
        int target1 = 5;
        int[] result1 = solution.FindTwoElementsWithTargetModulo(numbers1, target1);
        Console.WriteLine(string.Join(", ", result1)); // Expected output: 0, 4

        // Test case 2
        int[] numbers2 = { 1, 2, 3, 7 };
        int target2 = 5;
        int[] result2 = solution.FindTwoElementsWithTargetModulo(numbers2, target2);
        Console.WriteLine(string.Join(", ", result2)); // Expected output: 0, 2

        // Test case 3
        int[] numbers3 = { 3, 8, 12, 5 };
        int target3 = 10;
        int[] result3 = solution.FindTwoElementsWithTargetModulo(numbers3, target3);
        Console.WriteLine(string.Join(", ", result3)); // Expected output: -1
    }
}
        

6. Conclusion

In this lecture, we learned how to optimize space and time by using a hash set to solve the problem of finding the sum modulo.
This approach is very useful for solving various problems that may appear in coding tests.
I hope you gain confidence by solving more algorithm problems.