Generate All Combinations Sum K in DSA Python - Build from Scratch

Generate All Combinations Sum K

📖 Scenario: You are helping a chef who wants to create special dishes by combining ingredients. Each ingredient has a unique number representing its flavor strength. The chef wants to find all possible combinations of ingredients that add up to a specific flavor strength K.

🎯 Goal: Build a program that finds all unique combinations of numbers from a given list that sum exactly to K. Each number can be used only once in each combination.

📋 What You'll Learn

💡 Why This Matters

🌍 Real World

Finding combinations that meet a target sum is useful in recipe creation, budgeting, and resource allocation.

💼 Career

Backtracking and combination generation are common in coding interviews and algorithm design roles.

1

Create the ingredients list

Create a list called ingredients with these exact values: [2, 3, 6, 7].

DSA Python

# Create the ingredients list
# Your code here

Hint

Use square brackets to create a list and separate numbers with commas.

2

Set the target sum K

Create a variable called K and set it to the integer 7.

DSA Python

ingredients = [2, 3, 6, 7]
# Set the target sum K
# Your code here

Hint

Use the assignment operator = to set K to 7.

3

Write the function to find combinations

Write a function called find_combinations that takes ingredients and K as parameters and returns a list of all unique combinations where the sum is exactly K. Use a helper function with backtracking to explore combinations. Each ingredient can be used only once per combination.

DSA Python

ingredients = [2, 3, 6, 7]
K = 7

# Write the find_combinations function below
# Your code here

Hint

Use a helper function inside find_combinations to try adding each ingredient starting from the current index. Stop when the sum matches or exceeds K.

4

Print all combinations found

Call the function find_combinations with ingredients and K, and print the returned list of combinations.

DSA Python

ingredients = [2, 3, 6, 7]
K = 7

def find_combinations(ingredients, target):
    result = []
    ingredients.sort()
    def backtrack(start, path, total):
        if total == target:
            result.append(path[:])
            return
        if total > target:
            return
        for i in range(start, len(ingredients)):
            if i > start and ingredients[i] == ingredients[i-1]:
                continue
            path.append(ingredients[i])
            backtrack(i + 1, path, total + ingredients[i])
            path.pop()
    backtrack(0, [], 0)
    return result

# Print the combinations
# Your code here

Hint

Call the function and print the result to see all combinations.

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