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

Recall & Review

beginner

What is the 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

In the Coin Change Minimum Coins problem, what does a dynamic programming array usually represent?

Each position in the array represents the minimum number of coins needed to make that amount.

intermediate

Why do we initialize the DP array with a large number (like Infinity) except for the 0th position?

Because initially, we assume amounts are not reachable except 0, which requires 0 coins.

intermediate

What is the time complexity of the typical dynamic programming solution for Coin Change Minimum Coins with n coins and amount m?

O(n * m), where n is the number of coin types and m is the amount.

beginner

What does it mean if the DP array value for the target amount remains Infinity after processing?

It means the amount cannot be formed with the given coins.

What initial value is commonly used in the DP array for amounts other than zero?

A Negative one

B Zero

C Infinity or a very large number

D One

We use Infinity to represent that the amount is initially unreachable.

If you have coins [1, 3, 4] and amount 6, what is the minimum number of coins needed?

A 2

B 3

C 1

D 4

6 can be made with 3 + 3 (2 coins) or 4 + 1 + 1 (3 coins), so minimum is 2.

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

A Dynamic Programming

B Greedy Algorithm

C Brute Force without memoization

D Sorting coins only

Dynamic Programming efficiently finds minimum coins by building solutions for smaller amounts.

What does dp[0] equal in the DP array for Coin Change Minimum Coins?

A 1

B -1

C Infinity

D 0

Zero coins are needed to make amount zero.

If no combination of coins can make the amount, what should the function return?

A Infinity

B -1

C 0

D Amount itself

Returning -1 indicates no solution exists.

Explain how dynamic programming is used to solve the Coin Change Minimum Coins problem.

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

Describe what the DP array represents and how it changes during the Coin Change Minimum Coins algorithm.

Focus on the meaning of each position in the DP array.