Generate All Combinations Sum K in DSA C# - Build from Scratch

Generate All Combinations Sum K

📖 Scenario: You are helping a chef prepare special ingredient combinations for a recipe. The chef wants to find all unique combinations of ingredients where the total quantity equals a specific target amount.

🎯 Goal: Build a program that finds all unique combinations of numbers from a given list that add up exactly to a target sum k.

📋 What You'll Learn

Create a list of integers called ingredients with the values 2, 3, 6, 7.

Create an integer variable called targetSum and set it to 7.

Write a method called FindCombinations that takes the list ingredients, the targetSum, a starting index, a temporary list for the current combination, and a list to store all valid combinations.

Use recursion and backtracking inside FindCombinations to find all unique combinations where the sum equals targetSum.

Print all the combinations found in the format: [2, 2, 3].

💡 Why This Matters

🌍 Real World

Finding combinations of ingredients or items that meet a specific total is useful in cooking, budgeting, and resource allocation.

💼 Career

This problem teaches recursion and backtracking, important for software engineers working on search algorithms, optimization, and combinatorial problems.

1

Create the list of ingredients

Create a list of integers called ingredients with the exact values 2, 3, 6, and 7.

DSA C#

# Create the list of ingredients
// Your code here

Hint

Use List<int> and initialize it with the values inside curly braces.

2

Set the target sum

Create an integer variable called targetSum and set it to 7.

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List ingredients = new List { 2, 3, 6, 7 };
        // Create targetSum variable
        // Your code here
    }
}

Hint

Use int targetSum = 7; inside the Main method.

3

Write the recursive method to find combinations

Write a method called FindCombinations that takes parameters: List<int> ingredients, int targetSum, int start, List<int> current, and List<List<int>> result. Use recursion and backtracking to find all unique combinations where the sum equals targetSum.

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List ingredients = new List { 2, 3, 6, 7 };
        int targetSum = 7;
    }

    // Write FindCombinations method here
    // Your code here
}

Hint

Use recursion with backtracking: add ingredient, recurse with reduced target, then remove ingredient.

4

Call the method and print all combinations

In the Main method, create a list of lists called result to store combinations. Call FindCombinations with ingredients, targetSum, 0, an empty list, and result. Then print each combination in result in the format [2, 2, 3].

DSA C#

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        List ingredients = new List { 2, 3, 6, 7 };
        int targetSum = 7;
        // Create result list and call FindCombinations
        // Print all combinations
        // Your code here
    }

    static void FindCombinations(List ingredients, int targetSum, int start, List current, List> result)
    {
        if (targetSum == 0)
        {
            result.Add(new List(current));
            return;
        }
        if (targetSum < 0)
        {
            return;
        }

        for (int i = start; i < ingredients.Count; i++)
        {
            current.Add(ingredients[i]);
            FindCombinations(ingredients, targetSum - ingredients[i], i, current, result);
            current.RemoveAt(current.Count - 1);
        }
    }
}

Hint

Initialize result as a list of lists. Call FindCombinations with an empty list for current combination. Print each combination using string.Join.

Practice

1. What does the problem "Generate All Combinations Sum K" ask you to find?

easy

A. The largest number less than K

B. The sum of all numbers from 1 to K

C. All unique combinations of numbers that add up to K

D. The product of all numbers that divide K

Solution

1. Step 1: Understand the problem goal

   The problem asks to find all unique sets of numbers that add exactly to K.

2. Step 2: Identify the correct description

   All unique combinations of numbers that add up to K correctly describes finding all unique combinations summing to K.

3. Final Answer:

   All unique combinations of numbers that add up to K -> Option C

4. Quick Check:

   Combinations sum K = all sets adding to K [OK]

Hint: Look for options describing sets adding exactly to K [OK]

Common Mistakes:

• Confusing sum with product
• Thinking about single numbers instead of combinations
• Choosing options about divisors or ranges

2. Which of the following is the correct C# syntax to start a recursive method named FindCombinations that takes a list of integers and a target sum?

easy

A. void FindCombinations(List nums, int target) { }

B. void FindCombinations(List<int> nums, int target) { }

C. void FindCombinations(int nums[], int target) { }

D. void FindCombinations(List<int> nums; int target) { }

Solution

1. Step 1: Check parameter types and syntax

   In C#, a list of integers is declared as List<int>. The method parameters must be separated by commas.

2. Step 2: Identify correct syntax

   void FindCombinations(List<int> nums, int target) { } uses List<int> and comma-separated parameters correctly. Others have syntax errors or wrong types.

3. Final Answer:

   void FindCombinations(List<int> nums, int target) { } -> Option B

4. Quick Check:

   Correct C# method syntax = void FindCombinations(List<int> nums, int target) { } [OK]

Hint: Remember C# uses List<int> and commas between parameters [OK]

Common Mistakes:

• Using array syntax int nums[] in method parameters
• Missing commas between parameters
• Using untyped List without <int>

3. What is the output of the following C# code snippet that generates all combinations of numbers from 1 to 3 that sum to 3?

void Generate(int start, int target, List<int> current, List result) {
  if (target == 0) {
    result.Add(new List<int>(current));
    return;
  }
  for (int i = start; i <= 3; i++) {
    if (i <= target) {
      current.Add(i);
      Generate(i + 1, target - i, current, result);
      current.RemoveAt(current.Count - 1);
    }
  }
}

var result = new List();
Generate(1, 3, new List<int>(), result);
foreach(var combo in result) {
  Console.WriteLine(string.Join(",", combo));
}

medium

A. 3
2,1

B. 1,1,1
3

C. 1,2
2,1
3

D. 1,2
3

Solution

1. Step 1: Trace recursive calls and combinations

   The code tries numbers from start to 3, adding to current if <= target. It avoids repeats by increasing start each call.

2. Step 2: Identify valid combinations summing to 3

   Possible combinations are [1,2] and [3]. The code prints these two lines: "1,2" and "3".

3. Final Answer:

   1,2 3 -> Option D

4. Quick Check:

   Unique combos summing 3 = 1,2 and 3 [OK]

Hint: Check recursion start index to avoid duplicates [OK]

Common Mistakes:

• Expecting repeated numbers like 1,1,1
• Confusing order of output lines
• Including reversed duplicates like 2,1

4. The following code is intended to generate all combinations of numbers from 1 to 4 that sum to 5. What is the main error causing it to miss some combinations?

void Generate(int start, int target, List<int> current, List result) {
  if (target == 0) {
    result.Add(new List<int>(current));
    return;
  }
  for (int i = start; i < 4; i++) {
    if (i <= target) {
      current.Add(i);
      Generate(i + 1, target - i, current, result);
      current.RemoveAt(current.Count - 1);
    }
  }
}

medium

A. The loop condition should be <= 4, not < 4

B. The recursive call should use i, not i + 1

C. The target check should be target < i, not i <= target

D. The current list should not be copied when adding to result

Solution

1. Step 1: Analyze the for loop range

   The loop runs from start to i < 4, so it stops at i=3, missing i=4.

2. Step 2: Identify impact on combinations

   Because 4 is excluded, combinations including 4 are missed. Changing to i <= 4 fixes this.

3. Final Answer:

   The loop condition should be <= 4, not < 4 -> Option A

4. Quick Check:

   Loop range excludes 4, missing combos [OK]

Hint: Check loop boundaries carefully for inclusive ranges [OK]

Common Mistakes:

• Using wrong loop end condition
• Changing recursion start incorrectly
• Not copying list before adding to result

5. You want to generate all combinations of numbers from 1 to 7 that sum to 7, but each number can be used multiple times. Which change to the recursive call in this C# code will allow repeated numbers?

void Generate(int start, int target, List<int> current, List result) {
  if (target == 0) {
    result.Add(new List<int>(current));
    return;
  }
  for (int i = start; i <= 7; i++) {
    if (i <= target) {
      current.Add(i);
      Generate(??? , target - i, current, result);
      current.RemoveAt(current.Count - 1);
    }
  }
}

hard

A. Use i to allow repeats

B. Use start to allow repeats

C. Use i + 1 to avoid repeats

D. Use 1 to restart from beginning

Solution

1. Step 1: Understand how recursion controls repeats

   Using i + 1 moves start forward, preventing repeats. Using i keeps start same, allowing repeats.

2. Step 2: Choose correct recursive call argument

   To allow repeated numbers, pass i as start in recursive call.

3. Final Answer:

   Use i to allow repeats -> Option A

4. Quick Check:

   Passing i keeps current number available [OK]

Hint: Pass current index to allow repeats, increment to avoid [OK]

Common Mistakes:

• Using i + 1 disables repeats
• Using start (unchanged) may cause infinite loops
• Restarting from 1 causes duplicates and inefficiency