Coin Change Minimum Coins in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Coin Change Minimum Coins problem?

To find the smallest number of coins needed to make a given amount using available coin denominations.

beginner

Which data structure is commonly used to store intermediate results in the Coin Change Minimum Coins problem?

An array (or list) where each index represents an amount and stores the minimum coins needed to make that amount.

intermediate

Why do we initialize the DP array with a large number (like amount+1) in the Coin Change Minimum Coins problem?

Because it represents an impossible high number of coins, so any real solution will be smaller and can replace it.

beginner

What does dp[0] = 0 represent in the Coin Change Minimum Coins problem?

It means zero coins are needed to make the amount zero.

intermediate

How do you update the dp array when considering a coin of value c for amount i?

If i >= c, update dp[i] = min(dp[i], dp[i - c] + 1), meaning either keep current or use one more coin c.

What does dp[i] represent in the Coin Change Minimum Coins problem?

A Number of coin types available

B Maximum coins needed to make amount i

C Total value of coins used

D Minimum coins needed to make amount i

dp[i] stores the minimum number of coins needed to make the amount i.

What is the base case value for dp[0] in the Coin Change Minimum Coins problem?

A 0

B 1

C amount

D -1

Zero coins are needed to make amount zero, so dp[0] = 0.

If no combination of coins can make the amount, what should the result be?

A -1

B 0

C amount

D Infinity

Return -1 to indicate no solution exists.

Which approach is commonly used to solve the Coin Change Minimum Coins problem efficiently?

A Greedy algorithm

B Dynamic programming

C Brute force recursion without memoization

D Sorting coins only

Dynamic programming efficiently stores intermediate results to avoid repeated work.

When updating dp[i], why do we add 1 to dp[i - coin]?

A Because we reset the count

B Because we remove one coin

C Because we use one more coin of the current denomination

D Because we double the coins

Adding 1 accounts for using one coin of the current denomination.

Explain how dynamic programming solves the Coin Change Minimum Coins problem step-by-step.

Think about building the solution from smaller amounts to larger amounts.

Describe what the dp array looks like after processing coins for amount 5 with coins [1, 3, 4].

Build dp array incrementally considering each coin.