Generate All Combinations Sum K in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to start the backtracking with an empty combination.

DSA Python

def combination_sum_k(n, k):
    result = []
    def backtrack(start, path, target):
        if target == 0:
            result.append(path[:])
            return
        for i in range(start, n + 1):
            if i > target:
                break
            path.append(i)
            backtrack(i + 1, path, target - i)
            path.pop()
    backtrack(1, [1], k)
    return result

Drag options to blanks, or click blank then click option'

A[1]

B[k]

C[0]

D[]

Attempts:

3 left

💡 Hint

Common Mistakes

Starting with a non-empty list causes wrong combinations.

Passing None or a number instead of a list causes errors.

We start with an empty list to build combinations.

2fill in blank

medium

Complete the code to stop exploring when the current number exceeds the remaining target.

DSA Python

def combination_sum_k(n, k):
    result = []
    def backtrack(start, path, target):
        if target == 0:
            result.append(path[:])
            return
        for i in range(start, n + 1):
            if [1]:
                break
            path.append(i)
            backtrack(i + 1, path, target - i)
            path.pop()
    backtrack(1, [], k)
    return result

Drag options to blanks, or click blank then click option'

Ai < target

Btarget < 0

Ci > target

Di == target

Attempts:

3 left

💡 Hint

Common Mistakes

Using i < target causes skipping valid numbers.

Checking target < 0 is unnecessary here.

If the current number is greater than the target, no need to continue.

3fill in blank

hard

Fix the error in the recursive call to correctly reduce the target.

DSA Python

def combination_sum_k(n, k):
    result = []
    def backtrack(start, path, target):
        if target == 0:
            result.append(path[:])
            return
        for i in range(start, n + 1):
            if i > target:
                break
            path.append(i)
            backtrack(i + 1, path, [1])
            path.pop()
    backtrack(1, [], k)
    return result

Drag options to blanks, or click blank then click option'

Atarget + i

Btarget - i

Ctarget * i

Dtarget / i

Attempts:

3 left

💡 Hint

Common Mistakes

Adding instead of subtracting increases target incorrectly.

Multiplying or dividing target causes wrong calculations.

We subtract the chosen number from the target to track remaining sum.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps numbers to their squares for numbers less than 5.

DSA Python

squares = [1]: [2] for x in range(1, 10) if x < 5

Drag options to blanks, or click blank then click option'

Ax

Bx**2

Cx*2

Dx+2

Attempts:

3 left

💡 Hint

Common Mistakes

Using x*2 instead of x**2 gives wrong values.

Swapping keys and values reverses the dictionary.

The keys are numbers x and values are squares x**2 for x less than 5.

5fill in blank

hard

Fill all three blanks to create a list comprehension that filters even numbers and squares them.

DSA Python

[x[1]2 for x in range(1, 11) if x [2] 2 == 0 and x > [3]]

Drag options to blanks, or click blank then click option'

A**

B%

C<

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of ** for squaring.

Using < instead of > for filtering.

We square x with **2, check even with %2, and filter x > 5.

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