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

Recall & Review

beginner

What does 'Generate All Combinations Sum K' mean?

It means finding all groups of numbers from a list that add up exactly to a target number K.

beginner

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

Backtracking is used to explore all possible number combinations and pick those that sum to K.

intermediate

In backtracking for sum K, why do we sort the input list first?

Sorting helps to stop early when the sum exceeds K and avoid duplicate combinations.

beginner

What is the base case in the recursive backtracking for sum K?

When the current sum equals K, we save the current combination as a valid answer.

intermediate

How do we avoid using the same element multiple times in combinations?

By moving the start index forward in recursion, we ensure each element is used once per combination.

What is the main goal of 'Generate All Combinations Sum K'?

A Sort numbers in ascending order

B Find the largest number less than K

C Find all number groups that add up to K

D Count numbers greater than K

The goal is to find all combinations of numbers that sum exactly to K.

Which method helps explore all possible combinations efficiently?

A Backtracking

B Binary Search

C Dynamic Programming

D Sorting

Backtracking tries all combinations and backtracks when sum exceeds K.

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

A Because no further numbers can reduce the sum

B Because sum can become negative

C Because we want the smallest sum

D Because sum equals zero

Once sum is bigger than K, adding more numbers only increases it, so we stop.

How do we avoid duplicate combinations in the result?

A By using only even numbers

B By using a hash map

C By reversing the list

D By sorting and skipping duplicates

Sorting helps detect duplicates and skip them during backtracking.

What happens when the current sum equals K during recursion?

A We reset the sum

B We save the current combination

C We continue adding numbers

D We discard the combination

When sum equals K, the current combination is a valid answer to save.

Explain how backtracking helps find all combinations that sum to K.

Think of exploring paths and going back when a path is not valid.

Describe how sorting the input list improves the combination sum algorithm.

Sorting organizes numbers to make decisions easier.

Practice

1. What is the main goal of the Generate All Combinations Sum K problem?

easy

A. Count the total number of elements in an array

B. Sort an array of numbers in ascending order

C. Find the maximum number in an array

D. Find all unique combinations of numbers that add up to a target sum K

Solution

1. Step 1: Understand the problem statement

   The problem asks to find all unique sets of numbers that add up exactly to a given sum K.

2. Step 2: Identify the goal

   The goal is to generate all possible combinations, not just one or count elements.

3. Final Answer:

   Find all unique combinations of numbers that add up to a target sum K -> Option D

4. Quick Check:

   Combination sum = find all sets adding to K [OK]

Hint: Focus on combinations that sum exactly to K [OK]

Common Mistakes:

• Confusing combination sum with sorting
• Looking for maximum instead of combinations
• Counting elements instead of sums

2. Which of the following is the correct way to start a recursive function header in C for generating combinations that sum to K from an array arr of size n?

easy

A. void generate(int arr[], int n, int target, int start, int currentSum, int combination[], int combSize)

B. int generate(int arr, int n, int target, int start, int currentSum, int combination[], int combSize)

C. void generate(int arr, int n, int target, int start, int currentSum, int combination[], int combSize)

D. int generate(int arr[], int n, int target, int start, int currentSum, int combination[], int combSize)

Solution

1. Step 1: Check parameter types for array and function return

   In C, arrays are passed as int arr[] and recursive functions for generating combinations usually return void.

2. Step 2: Verify function signature correctness

   void generate(int arr[], int n, int target, int start, int currentSum, int combination[], int combSize) correctly uses void return type and int arr[] for the array parameter.

3. Final Answer:

   void generate(int arr[], int n, int target, int start, int currentSum, int combination[], int combSize) -> Option A

4. Quick Check:

   Correct C syntax for recursive combination function [OK]

Hint: Use void return and array as int arr[] in C [OK]

Common Mistakes:

• Using int instead of int[] for array parameter
• Returning int instead of void for recursive function
• Missing array brackets in parameter

3. What will be the output combinations for the array [2, 3, 6, 7] and target sum 7 using combination sum logic?

medium

A. [[7], [2, 2, 3]]

B. [[7], [3, 4]]

C. [[2, 3, 6], [7]]

D. [[2, 2, 3], [6, 1]]

Solution

1. Step 1: Identify valid combinations summing to 7

   From the array, 7 alone is valid. Also, 2+2+3 = 7 is valid. 3+4 is invalid as 4 is not in array. 6+1 invalid as 1 not in array.

2. Step 2: Confirm combinations

   Valid combinations are [7] and [2, 2, 3].

3. Final Answer:

   [[7], [2, 2, 3]] -> Option A

4. Quick Check:

   Sum 7 from array = [7], [2,2,3] [OK]

Hint: Check sums only from given array elements [OK]

Common Mistakes:

• Including numbers not in the array
• Ignoring repeated elements allowed
• Mixing invalid sums

4. Given the following snippet, what is the bug that prevents correct generation of combinations summing to K?

void generate(int arr[], int n, int target, int start, int currentSum, int combination[], int combSize) {
    if (currentSum == target) {
        // print combination
        return;
    }
    for (int i = start; i < n; i++) {
        if (currentSum + arr[i] <= target) {
            combination[combSize] = arr[i];
            generate(arr, n, target, i, currentSum + arr[i], combination, combSize + 1);
        }
    }
}

medium

A. Incorrect base case condition for currentSum == target

B. Loop should start from 0 instead of start

C. Missing backtracking step to remove last element after recursion

D. Function should return int instead of void

Solution

1. Step 1: Analyze recursion and combination building

   The function adds elements to combination but never removes them after recursion, causing incorrect combinations.

2. Step 2: Identify missing backtracking

   Backtracking requires removing last added element after recursive call to explore other paths.

3. Final Answer:

   Missing backtracking step to remove last element after recursion -> Option C

4. Quick Check:

   Backtracking needs element removal after recursion [OK]

Hint: Always remove last element after recursive call [OK]

Common Mistakes:

• Not removing last element after recursion
• Wrong base case check
• Loop starting index error

5. You want to generate all unique combinations from array [1, 2, 3] that sum to 4. Which of the following modifications ensures no duplicate combinations appear when numbers can be reused multiple times?

hard

A. Sort the array and skip duplicates by checking if current element equals previous

B. In recursive calls, pass i as start index to allow reuse and avoid duplicates

C. In recursive calls, always pass 0 as start index to restart from beginning

D. Use a global visited array to mark elements used

Solution

1. Step 1: Understand reuse and duplicates in combinations

   Allowing reuse means next recursion starts from current index i, not 0, to avoid duplicate sets in different orders.

2. Step 2: Identify correct start index usage

   Passing i as start index allows reuse and prevents duplicates by not revisiting earlier elements.

3. Final Answer:

   In recursive calls, pass i as start index to allow reuse and avoid duplicates -> Option B

4. Quick Check:

   Start index = i to reuse and avoid duplicates [OK]

Hint: Pass current index as start to reuse elements [OK]

Common Mistakes:

• Restarting from 0 causing duplicates
• Using visited array unnecessarily
• Not sorting or skipping duplicates properly