Which algorithmic approach guarantees an optimal solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Dynamic Programming: Knapsack - Subset Sum
You are given a list of positive integers and a target sum. You need to determine if there exists a subset of these integers that sums exactly to the target. Which algorithmic approach guarantees an optimal solution for this problem?
AA greedy algorithm that picks the largest numbers first until the sum is reached or exceeded.
BA dynamic programming approach that builds a boolean table tracking achievable sums up to the target.
CA depth-first search that tries all subsets without memoization.
DA sorting-based two-pointer technique to find pairs that sum to the target.
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires checking if any subset sums exactly to a target, which is a classic subset sum problem.
Step 2: Identify algorithm that guarantees correctness
Greedy and two-pointer approaches fail because they do not consider all subsets. DFS without memoization is correct but inefficient. Dynamic programming builds a table of achievable sums, ensuring all subsets are considered efficiently.
Final Answer:
Option B -> Option B
Quick Check:
DP tracks all sums up to target -> correct [OK]
Quick Trick:Subset sum requires DP to track achievable sums [OK]
Common Mistakes:
MISTAKES
Thinking greedy or sorting solves subset sum optimally
Trap Explanation:
PITFALL
Greedy and two-pointer methods seem simpler but fail on subsets that skip large numbers.
Interviewer Note:
CONTEXT
Tests if candidate recognizes subset sum pattern beyond textbook names.
Master "Subset Sum" in Dynamic Programming: Knapsack
3 interactive learning modes - each teaches the same concept differently
