Why Generate All Combinations Sum K in DSA Go?

The Big Idea

Discover how to find every perfect group of numbers adding to your target without missing a single one!

The Scenario

Imagine you have a box of different colored beads, and you want to find all the ways to pick some beads so that their total count is exactly 5. Doing this by trying every possible group by hand would take forever!

The Problem

Manually listing all groups that add up to a number is slow and confusing. You might miss some groups or repeat others. It's easy to make mistakes and waste a lot of time.

The Solution

Using a method called "Generate All Combinations Sum K," a computer can quickly find every group of numbers that add up to the target sum. It tries adding numbers step-by-step and backtracks when the sum is too big, so it never wastes time on wrong groups.

Before vs After

✗ Before

var results [][]int
// Manually check each combination by hand
for i := 1; i <= 9; i++ {
  for j := i+1; j <= 9; j++ {
    if i+j == 5 {
      results = append(results, []int{i, j})
    }
  }
}

✓ After

func backtrack(start, k, target int, current []int, results *[][]int) {
  if target == 0 && len(current) == k {
    *results = append(*results, append([]int{}, current...))
    return
  }
  for i := start; i <= 9; i++ {
    if i > target {
      break
    }
    backtrack(i+1, k, target-i, append(current, i), results)
  }
}

What It Enables

This lets you quickly find all possible groups of numbers that add up to a target, which is useful in puzzles, games, and planning tasks.

Real Life Example

Suppose you want to pick a team of 3 players whose skill levels add up to exactly 15. This method helps find all such teams without missing any or repeating.

Key Takeaways

Manual checking is slow and error-prone.

Backtracking finds all combinations efficiently.

Useful for puzzles, planning, and selection problems.

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