[Solved] You are given an array of integers and a target integer. You want to assign either a plus or minus... Which algorithmic approach guarantees finding the total number of such assignments efficiently? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Target Sum

You are given an array of integers and a target integer. You want to assign either a plus or minus sign to each integer such that the resulting sum equals the target. Which algorithmic approach guarantees finding the total number of such assignments efficiently?

ASorting the array and using two pointers to find pairs that sum to the target

BGreedy algorithm that picks signs based on local sum minimization

CDynamic programming using a 0/1 knapsack-like approach with state representing achievable sums

DDivide and conquer by splitting the array and combining results without memoization

Step-by-Step Solution

Step 1: Understand problem constraints
The problem requires counting all sign assignments to reach a target sum, which involves exploring exponential combinations.
Step 2: Identify suitable algorithmic pattern
Greedy and two-pointer approaches fail because they do not consider all combinations. Divide and conquer without memoization is exponential. DP with states representing achievable sums efficiently counts all valid assignments.
Final Answer:
Option C -> Option C
Quick Check:
DP handles overlapping subproblems and sums efficiently [OK]

Quick Trick: Counting sign assignments requires DP over sums [OK]

Common Mistakes:

MISTAKES

Thinking greedy or sorting solves counting sign assignments

Trap Explanation:

PITFALL

Greedy and two-pointer approaches seem simpler but fail to explore all sign combinations.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the problem as a variant of 0/1 knapsack DP pattern.

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More Dynamic Programming: Knapsack Quizzes

Which algorithmic approach guarantees finding the total number of such assignments efficiently?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithmic pattern

Final Answer:

Quick Check:

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