Generate All Combinations Sum K in DSA Javascript - 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 by building candidates step-by-step and abandoning those that exceed the target sum.

intermediate

Why do we sort the input array before generating combinations in this problem?

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

beginner

In backtracking for this problem, what does it mean to 'backtrack'?

Backtracking means removing the last added number from the current combination to try other possibilities after exploring one path.

intermediate

How do you avoid duplicate combinations when the input array contains repeated numbers?

By skipping numbers that are the same as the previous one at the same recursion level, you avoid generating duplicate combinations.

What is the main goal in the 'Generate All Combinations Sum K' problem?

A Find all combinations that sum to K

B Find the largest number less than K

C Sort the array in ascending order

D Count the total numbers in the array

The problem asks to find all unique combinations of numbers that add up exactly to the target sum K.

Which technique helps explore all possible combinations efficiently?

A Binary Search

B Greedy Algorithm

C Dynamic Programming

D Backtracking

Backtracking tries all possible combinations and abandons paths that exceed the target sum.

Why do we sort the input array before starting the combination search?

A To reverse the array

B To stop early when sum exceeds target and avoid duplicates

C To find the maximum number

D To count duplicates

Sorting helps to stop exploring when the current number is too large and to skip duplicates.

What does 'backtracking' do when a path does not lead to a solution?

A Removes the last number and tries another

B Adds more numbers

C Stops the entire process

D Sorts the array again

Backtracking removes the last added number to explore other possible combinations.

How do you avoid duplicate combinations when input has repeated numbers?

A Sort in descending order

B Use all numbers regardless

C Skip numbers equal to the previous at the same recursion level

D Add duplicates multiple times

Skipping repeated numbers at the same recursion level prevents duplicate combinations.

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

Think about building combinations and undoing choices.

Describe how sorting and skipping duplicates improve the solution for generating combinations summing to K.

Consider efficiency and uniqueness.

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 greater than K

D. The product of all numbers up to 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 what combinations mean

   Combinations mean groups of numbers without regard to order, all adding to K.

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 sums equal to K, not counts or products [OK]

Common Mistakes:

• Confusing combinations with permutations
• Looking for counts instead of actual combinations
• Trying to find products instead of sums

2. Which of the following is the correct way to start a recursive function in JavaScript to generate combinations summing to K?

easy

A. function findCombos() { return; }

B. function findCombos(nums, target) { return nums + target; }

C. function findCombos(nums, target, start, path, result) { ... }

D. function findCombos(nums) { console.log(target); }

Solution

1. Step 1: Identify correct recursive function signature

   The function needs parameters for numbers, target sum, start index, current path, and result storage.

2. Step 2: Check options for these parameters

   Only function findCombos(nums, target, start, path, result) { ... } includes all necessary parameters for recursion and backtracking.

3. Final Answer:

   function findCombos(nums, target, start, path, result) { ... } -> Option C

4. Quick Check:

   Recursive function with all params = function findCombos(nums, target, start, path, result) { ... } [OK]

Hint: Include start index and path for backtracking recursion [OK]

Common Mistakes:

• Missing parameters needed for recursion
• Returning wrong values instead of building combinations
• Not including start index to avoid duplicates

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

function combinationSum(nums, target) {
  const result = [];
  function backtrack(start, path, sum) {
    if (sum === target) {
      result.push([...path]);
      return;
    }
    if (sum > target) return;
    for (let i = start; i < nums.length; i++) {
      path.push(nums[i]);
      backtrack(i + 1, path, sum + nums[i]);
      path.pop();
    }
  }
  backtrack(0, [], 0);
  return result;
}

console.log(combinationSum([2,3,6,7], 7));

medium

A. [[7]]

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

C. [[2,3,7]]

D. [[2,2,3]]

Solution

1. Step 1: Understand the code logic

   The function finds combinations of numbers from the array that sum to 7 without reuse (i + 1).

2. Step 2: Trace the combinations

   Only 7 alone sums to 7; others like 2+3=5, 2+3+6=11 exceed or don't match target.

3. Final Answer:

   [[7]] -> Option A

4. Quick Check:

   Only [7] sums to 7 without repeats = [[7]] [OK]

Hint: Check sum and index increment to avoid reuse [OK]

Common Mistakes:

• Assuming numbers can be reused multiple times
• Including combinations that exceed target
• Not copying path array before pushing

4. Identify the bug in this code snippet for generating combinations summing to K:

function findCombos(nums, target) {
  const result = [];
  function backtrack(start, path, sum) {
    if (sum === target) {
      result.push(path);
      return;
    }
    if (sum > target) return;
    for (let i = start; i < nums.length; i++) {
      path.push(nums[i]);
      backtrack(i + 1, path, sum + nums[i]);
      path.pop();
    }
  }
  backtrack(0, [], 0);
  return result;
}

medium

A. The base case sum === target is missing

B. The path array is pushed directly without copying, causing reference issues

C. The loop should start from 0 instead of start

D. The function does not return any result

Solution

1. Step 1: Check how results are stored

   The code pushes 'path' directly, which is a reference and will change later.

2. Step 2: Identify correct way to store combinations

   Must push a copy of path (e.g., [...path]) to save current state.

3. Final Answer:

   The path array is pushed directly without copying, causing reference issues -> Option B

4. Quick Check:

   Push copy of path, not reference = The path array is pushed directly without copying, causing reference issues [OK]

Hint: Always push a copy of path array to result [OK]

Common Mistakes:

• Pushing path reference instead of copy
• Incorrect loop start index causing duplicates
• Missing base case for sum equal to target

5. Given the array [1, 2, 3, 4] and target sum 5, which of the following is the correct set of all unique combinations that sum to 5, assuming numbers can be used only once?

hard

A. [[1,2,2]]

B. [[1,1,3],[2,3]]

C. [[5]]

D. [[1,4],[2,3]]

Solution

1. Step 1: List all combinations without reuse that sum to 5

   Possible pairs: 1+4=5, 2+3=5; triples or singles don't sum to 5 without reuse.

2. Step 2: Verify options against these combinations

   [[1,4],[2,3]] matches these pairs exactly; others include duplicates or invalid sums.

3. Final Answer:

   [[1,4],[2,3]] -> Option D

4. Quick Check:

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

Hint: Sum pairs without reuse to find valid combos [OK]

Common Mistakes:

• Including repeated numbers when only single use allowed
• Assuming single number 5 exists in array
• Counting invalid sums or duplicates