[Solved] You need to find all unique combinations of exac... Which algorithmic approach guarantees finding all valid combinations efficiently by exploring partial solutions and pruning impossible paths early? | Subsets & Combinations

Subsets & Combinations - Combination Sum III (K Numbers to N)

You need to find all unique combinations of exactly k distinct numbers from 1 to 9 that add up to a target sum n. Which algorithmic approach guarantees finding all valid combinations efficiently by exploring partial solutions and pruning impossible paths early?

AGreedy algorithm that picks the largest numbers first until the sum is reached or exceeded

BBacktracking with pruning based on current sum and remaining numbers' possible sums

CDynamic programming that counts combinations without generating them explicitly

DSorting the numbers and using two pointers to find pairs that sum to n

Step-by-Step Solution

Step 1: Understand problem constraints
The problem requires all unique combinations of size k from numbers 1 to 9 summing to n, which suggests exploring subsets.
Step 2: Identify suitable algorithm
Backtracking with pruning efficiently explores partial combinations and stops early when sums cannot reach n, guaranteeing correctness and efficiency.
Final Answer:
Option B -> Option B
Quick Check:
Backtracking with pruning is standard for combination sum problems [OK]

Quick Trick: Backtracking with pruning finds all valid combos efficiently [OK]

Common Mistakes:

MISTAKES

Thinking greedy or two pointers can find all combinations
Confusing counting with generating combinations

Trap Explanation:

PITFALL

Greedy or two pointers fail because they don't explore all subsets; DP counts but doesn't generate combinations.

Interviewer Note:

CONTEXT

Tests if candidate recognizes backtracking with pruning as the correct pattern for combination sum problems.

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Which algorithmic approach guarantees finding all valid combinations efficiently by exploring partial solutions and pruning impossible paths early?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithm

Final Answer:

Quick Check:

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