Introduction

Combination Problems means:

  • selecting elements
  • to form valid combinations

Unlike permutations:

  • order does NOT matter

Example:

Input:Candidates = [2,3,6,7]
Target = 7

Output:
[2,2,3]
[7]

Explanation:

Different combinations can produce the target value.

This problem is one of the most important applications of:

Backtracking

Constraints

1 <= Array Size <= 20

Approach : Backtracking Solution

Explanations:

Explanation:

The idea is:

  • recursively try combinations
  • track remaining target

Steps:

  1. Choose current element.
  2. Add to combination.
  3. Reduce target value.
  4. Recurse further.
  5. Backtrack and remove element.

Stopping Conditions:

  • target becomes 0 → valid answer
  • target becomes negative → stop recursion

This approach:

  • explores valid combinations
  • prunes invalid paths

Dry Run

Candidates:2 3 6 7

Target:
7

Choose 2:
[2]

Choose 2:
[2,2]

Choose 3:
[2,2,3]

Target becomes 0.
Valid combination found.

Practice :

Complexity Analysis :

Time Complexity:- Exponential
Explanation :
Many recursive combination paths are explored.

Space Complexity:- O(n)
Explanation :
Recursion stack and combination storage are used.

Why This Problem is Important

This problem builds the foundation for:

  • Backtracking
  • Recursive exploration
  • Constraint satisfaction
  • Search-space pruning
  • Combination generation

Real-World Applications

Combination concepts are used in:

  • Recommendation systems
  • Scheduling systems
  • Resource allocation
  • Search algorithms
  • Optimization problems

Common Beginner Mistakes

  • Forgetting backtracking step
  • Wrong target handling
  • Infinite recursion
  • Incorrect recursion index
  • Duplicate combinations

Interview Tip

Interviewers often expect:

  • backtracking understanding
  • pruning explanation
  • recursive exploration logic
  • complexity analysis

Always explain:

  • target reduction
  • pruning invalid paths
  • backtracking flow

Related Questions

  • Subsets
  • Permutations
  • Combination Sum II
  • N-Queens
  • Backtracking Basics

Final Takeaway

The Combination Problems pattern is one of the most important beginner backtracking concepts.

It teaches:

  • backtracking
  • recursive exploration
  • pruning
  • combination generation

Understanding this problem builds a strong foundation for:

  • advanced backtracking problems
  • recursion optimization
  • interview-level algorithms.