Generate All Combinations Sum K in DSA Go - 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 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 K, why do we skip numbers that make the sum exceed K?

Because continuing would never reach the target sum K, so skipping saves time by pruning the search space.

intermediate

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

It ensures combinations are built without repeating previous elements, avoiding duplicate combinations.

advanced

How do you handle duplicates in the input list when generating all combinations that sum to K?

Sort the input and skip over duplicate numbers during recursion to avoid repeated combinations.

What is the main purpose of backtracking in generating combinations that sum to K?

A To explore all possible combinations and discard invalid ones early

B To sort the input list

C To multiply numbers to reach K

D To find the maximum number in the list

Backtracking explores all combinations and stops exploring paths that exceed the target sum.

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

A Sorting is not needed

B To reverse the order of numbers

C To find the smallest number only

D To easily skip duplicates and optimize pruning

Sorting helps skip duplicates and stop early when sums exceed K.

In the recursive function, what does the 'start index' control?

A The total number of combinations

B The target sum K

C Which numbers can be chosen next to avoid duplicates

D The maximum sum allowed

The start index ensures we only pick numbers from the current position forward to avoid duplicates.

What should you do if the current sum exceeds K during recursion?

A Continue adding numbers

B Stop exploring this path and backtrack

C Reset the sum to zero

D Add negative numbers

If sum exceeds K, no need to continue; backtrack to try other combinations.

Which data structure is best to store the current combination during recursion?

A A slice (dynamic array)

B A map

C A queue

D A stack

A slice is used to store the current combination and can be easily appended or removed.

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

Think about how you try numbers one by one and back up when you go too far.

Describe how to avoid duplicate combinations when the input list has repeated numbers.

Sorting helps you spot duplicates easily.

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 sum of all numbers from 1 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 the target sum K.

2. Step 2: Clarify what combinations mean

   Combinations mean groups of numbers where order does not matter, and each number can be used once or multiple times depending on problem rules.

3. Final Answer:

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

4. Quick Check:

   Combinations sum K = unique sets adding to K [OK]

Hint: Focus on sums that exactly equal K, ignoring order [OK]

Common Mistakes:

• Confusing combinations with permutations
• Looking for a single sum instead of all combinations
• Ignoring the target sum K

2. Which of the following Go function signatures is correct for a function that generates all combinations summing to K from a slice of integers?

easy

A. func combinationSum(nums []int, target int) int

B. func combinationSum(nums int, target []int) []int

C. func combinationSum(nums []int, target int) []int

D. func combinationSum(nums []int, target int) [][]int

Solution

1. Step 1: Identify input parameters

   The function should take a slice of integers and a target integer sum.

2. Step 2: Identify return type

   It should return a slice of slices of integers, representing all combinations.

3. Final Answer:

   func combinationSum(nums []int, target int) [][]int -> Option D

4. Quick Check:

   Input slice and target int, output slice of int slices [OK]

Hint: Return type must hold multiple combinations ([][]int) [OK]

Common Mistakes:

• Swapping parameter types
• Returning a single slice instead of slice of slices
• Returning an int instead of combinations

3. What is the output of the following Go code snippet?

func main() {
    nums := []int{2, 3, 6, 7}
    target := 7
    result := combinationSum(nums, target)
    fmt.Println(result)
}

func combinationSum(nums []int, target int) [][]int {
    var res [][]int
    var backtrack func(start, target int, path []int)
    backtrack = func(start, target int, path []int) {
        if target == 0 {
            temp := make([]int, len(path))
            copy(temp, path)
            res = append(res, temp)
            return
        }
        for i := start; i < len(nums); i++ {
            if nums[i] > target {
                continue
            }
            backtrack(i, target-nums[i], append(path, nums[i]))
        }
    }
    backtrack(0, target, []int{})
    return res
}

medium

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

B. [[2 3 6] [7]]

C. [[3 3 3] [7]]

D. [[2 2 2 3] [7]]

Solution

1. Step 1: Understand backtracking logic

   The function tries combinations starting from each index, allowing reuse of numbers, and collects paths summing to target.

2. Step 2: Trace combinations for target 7

   Possible sums are [2,2,2,3] and [7] because 2+2+2+3=9 is incorrect, so check carefully: 2+2+2+3=9 (too big), so that is invalid. The actual combinations are [2,2,3] (2+2+3=7) and [7].

3. Step 3: Verify options

   [[2 2 2 3] [7]] shows [2 2 2 3] which sums to 9, invalid. [[2 2 3] [7]] shows [2 2 3] and [7], which is correct.

4. Final Answer:

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

5. Quick Check:

   Backtracking finds [2 2 3] and [7] sums [OK]

Hint: Look for combinations that sum exactly to 7 using given nums [OK]

Common Mistakes:

• Including invalid sums like [2 3 6]
• Ignoring reuse of numbers
• Confusing order of elements

4. Identify the bug in this Go function for generating combinations summing to K:

func combinationSum(nums []int, target int) [][]int {
    var res [][]int
    var backtrack func(start, target int, path []int)
    backtrack = func(start, target int, path []int) {
        if target == 0 {
            res = append(res, path)
            return
        }
        for i := start; i < len(nums); i++ {
            if nums[i] > target {
                continue
            }
            backtrack(i, target-nums[i], append(path, nums[i]))
        }
    }
    backtrack(0, target, []int{})
    return res
}

medium

A. The target check should be target < 0 instead of target == 0

B. The loop should start from 0 every time, not from start

C. Appending path directly causes shared slice reference issues

D. The function should return a single slice, not slice of slices

Solution

1. Step 1: Check how path is appended to result

   Appending path directly stores the reference, causing all results to point to the same underlying array.

2. Step 2: Fix by copying path before appending

   Make a copy of path slice before appending to res to avoid shared references.

3. Final Answer:

   Appending path directly causes shared slice reference issues -> Option C

4. Quick Check:

   Copy path before append to avoid shared slice bugs [OK]

Hint: Always copy slices before appending to result [OK]

Common Mistakes:

• Appending slice references directly
• Incorrect loop start index
• Wrong base case condition

5. Given a list of integers with duplicates, how would you modify the combination sum algorithm to generate all unique combinations summing to K without duplicates? Choose the best approach.

hard

A. Use a map to store sums and ignore duplicates after generation

B. Sort the list and skip duplicate numbers during recursion

C. Allow duplicates freely and filter results at the end

D. Increase target by 1 to avoid duplicates

Solution

1. Step 1: Sort the input list

   Sorting helps group duplicates together so they can be skipped during recursion.

2. Step 2: Skip duplicates in recursion

   When iterating, skip numbers equal to the previous one at the same recursion level to avoid duplicate combinations.

3. Final Answer:

   Sort the list and skip duplicate numbers during recursion -> Option B

4. Quick Check:

   Sorting + skipping duplicates = unique combinations [OK]

Hint: Sort input and skip duplicates while recursing [OK]

Common Mistakes:

• Filtering duplicates after generating all combinations
• Not sorting input before recursion
• Changing target incorrectly