[Solved] Identify the bug in the following code snippet for counting ways to make change using 1D DP: def count_ways_bug(coins, amount): dp = [0] * (amount + 1) dp[0] = 0 for coin in coins:... | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Number of Ways to Make Change

Identify the bug in the following code snippet for counting ways to make change using 1D DP:

def count_ways_bug(coins, amount):
    dp = [0] * (amount + 1)
    dp[0] = 0
    for coin in coins:
        for w in range(amount, coin - 1, -1):
            dp[w] += dp[w - coin]
    return dp[amount]

What is the bug?

Adp[0] should be initialized to 1, not 0

BThe inner loop should iterate forwards from coin to amount, not backwards

CThe dp array size should be amount, not amount + 1

DThe return statement should return dp[0] instead of dp[amount]

Step-by-Step Solution

Solution:

Step 1: Check base case initialization
dp[0] represents ways to make amount 0, which must be 1 (empty combination), but here it is set to 0, causing all dp values to remain 0.
Step 2: Verify loop direction
Though iterating backwards is incorrect for unlimited coin usage, the critical bug causing zero results is dp[0] initialization.
Final Answer:
Option A -> Option A
Quick Check:
Correct base case dp[0]=1 is essential for counting ways [OK]

Quick Trick: dp[0] must be 1 to count empty combination [OK]

Common Mistakes:

MISTAKES

Initializing dp[0] to 0 misses base case
Iterating amounts backwards in 1D DP misses combinations
Incorrect dp array size causes index errors

Trap Explanation:

PITFALL

Though backwards iteration is a bug, the base case initialization is the root cause of zero counts.

Interviewer Note:

CONTEXT

Tests if candidate spots subtle base case bugs that break DP correctness.

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More Dynamic Programming: Knapsack Quizzes

Identify the bug in the following code snippet for counting ways to make change using 1D DP:

Step 1: Check base case initialization

Step 2: Verify loop direction

Final Answer:

Quick Check:

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