Prune Backtracking Combination Sum With Constraints

Combination-sum problems feel manageable until constraints appear: max picks, sorted inputs, or limited counts. This article shows how to prune backtracking cleanly so you keep recursion trees small and interview explanations clear.

TL;DR

• Pruning cuts branches that cannot yield valid sums, shrinking recursion trees and runtime.
• Interviewers value pruning because it shows you reason about feasibility instead of brute-forcing every path.
• Core steps: sort candidates, choose/skip with updated remaining target, stop early when remaining < 0 or depth exceeds a limit.
• Beginners often forget to backtrack state, allow duplicates after sorting, or prune only after doing expensive recursion.
• You'll see a TypeScript snippet, visual tree sketch, practice drills, and pitfalls, with light mention of tools like LeetCopilot for guided checks.

Beginner-Friendly Explanations

Why Pruning Works

If the smallest remaining candidate already exceeds the remaining target, no deeper path can succeed. Cutting the branch now saves time.

Constraints That Matter

Common twists: fixed combination length, limited usage per number, or sorted candidates. Naming each constraint aloud helps you wire it into the recursion.

The Role of Sorting

Sorting lets you stop as soon as candidates[i] > remaining, a standard trick highlighted in the sliding window learning path.

Step-by-Step Learning Guidance

1) Restate Inputs With Constraints

Write: candidates (sorted?), target, max picks (if any), duplicates allowed? This checklist keeps your recursion aligned with the prompt.

2) Build the Recursive Frame

Function signature dfs(start, remaining, path). start avoids reusing prior indices when combinations must be non-decreasing.

3) Add Early Exits

• If remaining === 0, record the path.
• If remaining < 0 or path.length > maxLen, return immediately.
• If candidates[i] > remaining, break the loop.

4) Choose and Recurse

Push candidates[i], recurse with updated remaining - candidates[i], optionally i (reuse allowed) or i + 1 (no reuse).

5) Backtrack State

Pop the last element before the next iteration. Say it out loud as you would in a mock interview routine.

Visualizable Example: Pruned Combination Sum in TypeScript

function combinationSumLimited(
  candidates: number[],
  target: number,
  maxLen = Infinity,
): number[][] {
  const results: number[][] = [];
  candidates.sort((a, b) => a - b);

  function dfs(start: number, remaining: number, path: number[]): void {
    if (remaining === 0) {
      results.push([...path]);
      return;
    }
    if (remaining < 0 || path.length >= maxLen) return;

    for (let i = start; i < candidates.length; i++) {
      const num = candidates[i];
      if (num > remaining) break; // prune larger candidates
      if (i > start && candidates[i] === candidates[i - 1]) continue; // skip duplicates

      path.push(num);
      dfs(i, remaining - num, path); // reuse allowed; use i+1 if not
      path.pop();
    }
  }

  dfs(0, target, []);
  return results;
}

Sketch the recursion tree with remaining values at each node. Draw X over branches cut by num > remaining or depth limits so you see pruning impact.

Practical Preparation Strategies

Narrate Pruning Conditions

Say "stop because remaining < 0" or "break because current > remaining" aloud. This shows intention during interviews and mirrors interview communication guide advice.

Test Edge Cases First

Run small cases: empty candidates, single candidate equal to target, and target smaller than smallest number. Verify pruning exits immediately.

Time Yourself

Practice generating solutions within a two-minute explanation window. Keeping narration tight signals confidence to interviewers.

Alternate Reuse Rules

Solve once with unlimited reuse, once with single-use numbers. Observe how dfs signature or loop index changes.

Tools like LeetCopilot can supply gentle hints when a pruning condition is missing, helping you fix logic without spoiling the solution.

Common Mistakes to Avoid

Forgetting to Sort Before Pruning

Without sorting, num > remaining is meaningless and branches stay larger than needed.

Using Return Instead of Continue on Duplicates

A mistaken return exits the whole call; prefer continue to skip only the repeated candidate.

Over-Pruning With Depth Limits

If maxLen is optional, set a sensible default (e.g., Infinity) to avoid cutting valid answers.

Mutating Shared Arrays Without Backtracking

Always pop after recursion. Leaving values behind pollutes sibling branches.

FAQ

How do I know a pruning rule is correct?
Check whether any future number could fix the violation. If not, the rule is safe.

What should I learn before this?
Basic recursion flow and array iteration. Understanding sorted order helps a lot.

Is pruning always necessary?
For small inputs, maybe not, but interviews reward demonstrating it because it proves you think about efficiency.

How can I practice?
Rotate through 2–3 combination prompts daily. Quick hints from LeetCopilot can confirm pruning conditions without giving away full answers.

Conclusion

When you prune backtracking combination sum with constraints, recursion feels controlled rather than chaotic. Sorting inputs, adding clear early exits, and rehearsing backtracking steps prepare you to explain solutions confidently under interview pressure.