Generate All Combinations Sum K in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the problem 'Generate All Combinations Sum K' ask you to find?

It asks to find all unique combinations of numbers from a given list that add up exactly to a target sum K.

beginner

Which algorithm technique is commonly used to solve 'Generate All Combinations Sum K'?

Backtracking is commonly used because it explores all possible combinations and abandons paths that exceed the target sum.

intermediate

In backtracking for combinations sum, why do we sort the input array first?

Sorting helps to stop early when the current number exceeds the remaining sum and to avoid duplicate combinations.

intermediate

What is the role of the 'start index' in the recursive backtracking function for combinations sum?

It ensures that combinations are built without reusing previous elements and avoids duplicates by moving forward in the list.

advanced

How do you avoid duplicate combinations when the input list contains repeated numbers?

By skipping over numbers that are the same as the previous one at the same recursion level during iteration.

What is the base case in backtracking for generating combinations that sum to K?

A When the current sum is less than K

B When the current sum equals K

C When the current sum is greater than K

D When all elements are used

The base case is when the sum of the current combination equals the target K, meaning a valid combination is found.

Why do we stop exploring a path if the current sum exceeds K?

A Because continuing will never reach K

B Because we want to find smaller sums

C Because the input is sorted

D Because duplicates are not allowed

If the sum exceeds K, adding more numbers will only increase the sum, so no valid combination can be found along this path.

How do you ensure combinations are unique when input has duplicates?

A By using a hash set to store combinations

B By allowing repeated elements

C By sorting and skipping duplicates during iteration

D By ignoring duplicates

Sorting the input and skipping duplicate numbers at the same recursion level prevents generating duplicate combinations.

What data structure is typically used to store the current combination during backtracking?

A List or array

B Queue

C Stack

D Dictionary

A list or array is used to keep track of the current numbers chosen in the combination.

In C#, which method signature best fits the recursive backtracking function for this problem?

A bool Backtrack(int[] nums, int target, int index)

B int Backtrack(int[] nums, int target)

C List<int> Backtrack(int[] nums, int target)

D void Backtrack(int[] nums, int target, int start, List<int> current, List<List<int>> result)

The method takes the input array, target sum, start index, current combination list, and result list to build all combinations.

Explain step-by-step how backtracking finds all combinations that sum to K.

Think about how you build combinations and when you stop or save them.

Describe how to handle duplicate numbers in the input to avoid duplicate combinations.

Sorting helps to detect duplicates easily.

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