[Solved] You want to count the number of ways to make change for a target amount using given coin... Which of the following changes is necessary compared to the unlimited coin usage DP approach? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Number of Ways to Make Change

You want to count the number of ways to make change for a target amount using given coin denominations, but each coin can be used at most once. Which of the following changes is necessary compared to the unlimited coin usage DP approach?

AChange the inner loop to iterate backwards over amounts to avoid counting duplicates

BInitialize dp array with zeros except dp[amount] = 1

CSort the coins in descending order before processing

DUse a recursive approach without memoization

Step-by-Step Solution

Solution:

Step 1: Understand difference in usage constraints
Unlimited usage allows forward iteration; single-use requires backward iteration to prevent reuse in the same iteration.
Step 2: Identify necessary DP modification
Iterating backwards ensures each coin is counted only once per amount.
Final Answer:
Option A -> Option A
Quick Check:
Backward iteration prevents multiple counting of same coin [OK]

Quick Trick: Use backward iteration for single-use coin constraints [OK]

Common Mistakes:

MISTAKES

Using forward iteration leading to overcounting
Incorrect dp initialization
Assuming sorting coins affects counting

Trap Explanation:

PITFALL

Forward iteration causes counting same coin multiple times

Interviewer Note:

CONTEXT

Tests knowledge of DP modifications for single-use coin change problem

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More Dynamic Programming: Knapsack Quizzes

Which of the following changes is necessary compared to the unlimited coin usage DP approach?

Step 1: Understand difference in usage constraints

Step 2: Identify necessary DP modification

Final Answer:

Quick Check:

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