Generate All Combinations Sum K in DSA Python - 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 algorithmic 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 early.

intermediate

Why do we sort the input list before generating combinations for sum K?

Sorting helps to stop early when the current number exceeds the remaining sum and avoids duplicate combinations by skipping repeated numbers.

intermediate

In backtracking for sum K, what is the purpose of the 'start' index parameter?

It ensures combinations are built in order and prevents reusing elements before the current position, avoiding duplicates.

beginner

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

The base case is when the remaining sum is zero, meaning a valid combination is found and should be recorded.

What should you do if the current number is greater than the remaining sum in combination sum problem?

A Stop exploring this path further

B Add the number anyway

C Skip to the next number without stopping

D Restart the entire process

If the current number is greater than the remaining sum, no further numbers will fit because the list is sorted, so stop exploring this path.

Why do we skip duplicate numbers in the input list during backtracking?

A To reduce the size of the input list

B To avoid duplicate combinations in the result

C To increase the number of combinations

D To sort the list

Skipping duplicates prevents generating the same combination multiple times.

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

A Stack

B Queue

C List or array

D Hash map

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

When do you add a combination to the final result list?

A When the sum is greater than K

B When the combination is empty

C When the sum is less than K

D When the sum of the combination equals the target K

Only combinations that sum exactly to K are added to the results.

What is the role of recursion in generating all combinations that sum to K?

A To explore all possible combinations by trying each number

B To sort the input list

C To remove duplicates

D To calculate the sum directly

Recursion helps explore all possible combinations by trying each number and backtracking when needed.

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

Think about exploring paths and undoing choices.

Describe the steps to avoid duplicate combinations when generating all combinations that sum to K.

Focus on sorting and skipping duplicates.

Practice

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

easy

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

B. The largest number less than K

C. The count of numbers equal to K

D. The smallest number greater than K

Solution

1. Step 1: Understand the problem goal

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

2. Step 2: Clarify uniqueness and sum condition

   Each combination must add up to K without duplicates in the result.

3. Final Answer:

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

4. Quick Check:

   Combinations sum to K = All unique combinations of numbers that add up to K [OK]

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

Common Mistakes:

• Confusing combinations with permutations
• Looking for single numbers equal to K
• Ignoring the sum condition

2. Which of the following Python function signatures is correct to start solving "Generate All Combinations Sum K"?

easy

A. def combinationSumK(nums, k): return int

B. def combination_sum_k(k: int, nums: list[int]) -> list[int]:

C. def combination_sum_k(nums: int, k: int) -> list[int]:

D. def combination_sum_k(nums: list[int], k: int) -> list[list[int]]:

Solution

1. Step 1: Check parameter types and return type

   The function should take a list of integers and an integer k, returning a list of lists of integers.

2. Step 2: Match signature to problem needs

   def combination_sum_k(nums: list[int], k: int) -> list[list[int]]: matches the expected input and output types correctly.

3. Final Answer:

   def combination_sum_k(nums: list[int], k: int) -> list[list[int]]: -> Option D

4. Quick Check:

   Correct signature with list inputs and list of lists output [OK]

Hint: Use list[int] for input and list[list[int]] for output [OK]

Common Mistakes:

• Wrong parameter types
• Incorrect return type
• Swapping parameter order

3. What is the output of the following code?

def comb_sum(nums, k):
    result = []
    def backtrack(start, path, total):
        if total == k:
            result.append(path[:])
            return
        if total > k:
            return
        for i in range(start, len(nums)):
            path.append(nums[i])
            backtrack(i + 1, path, total + nums[i])
            path.pop()
    backtrack(0, [], 0)
    return result

print(comb_sum([2,3,6,7], 7))

medium

A. [[2, 2, 3]]

B. [[2, 3, 6]]

C. [[7]]

D. [[3, 7]]

Solution

1. Step 1: Trace backtracking with input [2,3,6,7] and target 7

   Check combinations starting from index 0, adding numbers without repetition.

2. Step 2: Identify valid combinations summing to 7

   Only [7] sums exactly to 7 without exceeding or repeating indices.

3. Final Answer:

   [[7]] -> Option C

4. Quick Check:

   Only [7] sums to 7 in given list [OK]

Hint: Backtrack with index increment to avoid duplicates [OK]

Common Mistakes:

• Allowing repeated elements
• Not stopping when total > k
• Appending path without copying

4. Find the error in this code snippet for generating combinations summing to k:

def comb_sum(nums, k):
    result = []
    def backtrack(start, path, total):
        if total == k:
            result.append(path[:])
            return
        if total > k:
            return
        for i in range(start, len(nums)):
            path.append(nums[i])
            backtrack(i, path, total + nums[i])
            path.pop()
    backtrack(0, [], 0)
    return result

medium

A. Appending path without copying causes all results to be the same

B. Using backtrack(i, ...) allows repeated elements incorrectly

C. Missing base case for total < k

D. Not initializing result as a global variable

Solution

1. Step 1: Analyze recursive call backtrack(i, ...)

   Using i instead of i+1 allows reuse of the same element multiple times.

2. Step 2: Understand problem requires unique combinations without repeats

   To avoid duplicates, index must increase to i+1 in recursive calls.

3. Final Answer:

   Using backtrack(i, path, total + nums[i]) allows repeated elements incorrectly -> Option B

4. Quick Check:

   Index must increase to avoid repeats [OK]

Hint: Increment index in recursion to prevent repeats [OK]

Common Mistakes:

• Not copying path when appending
• Allowing repeated elements by wrong index
• Ignoring base cases

5. Given the list [1, 2, 3, 4, 5] and target sum 5, which of the following is the correct set of all unique combinations that sum to 5?

hard

A. [[1, 4], [2, 3], [5]]

B. [[1, 2, 2], [5]]

C. [[1, 1, 3], [2, 3]]

D. [[5, 0], [2, 3]]

Solution

1. Step 1: List all combinations of numbers from [1,2,3,4,5] that sum to 5

   Possible sums: 1+4=5, 2+3=5, 5=5.

2. Step 2: Verify uniqueness and validity

   Combinations like [1,2,2] or [1,1,3] are invalid as 2 or 1 repeated without duplicates allowed.

3. Final Answer:

   [[1, 4], [2, 3], [5]] -> Option A

4. Quick Check:

   Unique combos summing to 5 = [[1, 4], [2, 3], [5]] [OK]

Hint: Sum unique sets without repeating elements [OK]

Common Mistakes:

• Including repeated elements not in input
• Adding zero which is not in list
• Ignoring uniqueness of combinations