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

Generate All Combinations Sum K

📖 Scenario: You are working on a shopping app where customers can select different items with prices. You want to find all possible combinations of items that add up exactly to a gift card value.

🎯 Goal: Build a program that finds all combinations of numbers from a given list that sum up to a target value k.

📋 What You'll Learn

Create an array called numbers with the exact values [2, 3, 6, 7].

Create a variable called target and set it to 7.

Write a function called findCombinations that uses recursion to find all combinations of numbers that sum to target.

Print the result array called result which contains all valid combinations.

💡 Why This Matters

🌍 Real World

Finding combinations of items that fit a budget or target sum is common in shopping apps, budgeting tools, and game design.

💼 Career

Understanding recursion and backtracking is important for solving complex algorithm problems in software engineering roles.

1

Create the numbers array

Create an array called numbers with these exact values: [2, 3, 6, 7].

DSA Javascript

# Create the array numbers with values [2, 3, 6, 7]
// Your code here

Hint

Use const numbers = [2, 3, 6, 7]; to create the array.

2

Set the target sum

Create a variable called target and set it to the number 7.

DSA Javascript

const numbers = [2, 3, 6, 7];
// Create the variable target and set it to 7
// Your code here

Hint

Use const target = 7; to set the target sum.

3

Write the recursive function to find combinations

Write a function called findCombinations that takes start, currentSum, and currentCombo as parameters. Use recursion to find all combinations of numbers from numbers starting at index start that sum to target. Store valid combinations in an array called result.

DSA Javascript

const numbers = [2, 3, 6, 7];
const target = 7;

const result = [];

// Write the recursive function findCombinations(start, currentSum, currentCombo) here
// Your code here

Hint

Use a for loop starting from start to try each number. Add the number to currentCombo, call findCombinations recursively, then remove the number to backtrack.

4

Print the result array

Print the result array to display all combinations that sum to target.

DSA Javascript

const numbers = [2, 3, 6, 7];
const target = 7;

const result = [];

function findCombinations(start, currentSum, currentCombo) {
    if (currentSum === target) {
        result.push([...currentCombo]);
        return;
    }
    if (currentSum > target) {
        return;
    }
    for (let i = start; i < numbers.length; i++) {
        currentCombo.push(numbers[i]);
        findCombinations(i, currentSum + numbers[i], currentCombo);
        currentCombo.pop();
    }
}

findCombinations(0, 0, []);

// Print the result array
// Your code here

Hint

Use console.log(result); to print the array of 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 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