[Solved] You are given a set of coin denominations and a target amount.... Which algorithmic pattern best fits this problem? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Number of Ways to Make Change

You are given a set of coin denominations and a target amount. You want to find how many distinct combinations of coins can sum up to the target, where each coin can be used unlimited times and order does not matter. Which algorithmic pattern best fits this problem?

AUnbounded Knapsack dynamic programming counting combinations

BGreedy algorithm for minimum coin count

CLongest Common Subsequence dynamic programming

DTopological sorting on a graph

Step-by-Step Solution

Solution:

Step 1: Identify problem characteristics
The problem involves counting combinations with unlimited use of items (coins) to reach a target sum.
Step 2: Match to known patterns
This matches the unbounded knapsack pattern where order does not matter and we count ways, not optimize.
Final Answer:
Option A -> Option A
Quick Check:
Counting combinations with unlimited items -> unbounded knapsack DP [OK]

Quick Trick: Unlimited items + count combos -> unbounded knapsack [OK]

Common Mistakes:

MISTAKES

Confusing with greedy minimum coin problem
Thinking order matters (permutations)
Using LCS which is unrelated

Trap Explanation:

PITFALL

Candidates often confuse counting combinations with optimization or sequence problems, leading to wrong pattern choice.

Interviewer Note:

CONTEXT

Tests candidate's ability to recognize DP pattern from problem description.

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More Dynamic Programming: Knapsack Quizzes

Which algorithmic pattern best fits this problem?

Step 1: Identify problem characteristics

Step 2: Match to known patterns

Final Answer:

Quick Check:

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