Coin Change Total Number of Ways in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the 'Coin Change Total Number of Ways' problem ask you to find?

It asks for the total number of different ways to make a target amount using given coin denominations, where coins can be used unlimited times.

beginner

In the Coin Change problem, why do we use dynamic programming?

Because it helps us build the solution step-by-step by storing results of smaller amounts to avoid repeated calculations, making the process efficient.

beginner

What does the dp array represent in the Coin Change Total Number of Ways solution?

Each index in the dp array represents the number of ways to make that amount using the given coins.

intermediate

Why do we iterate over coins first, then amounts, in the Coin Change solution?

Iterating coins first ensures combinations are counted without duplicates, as each coin is considered in order to build up amounts.

beginner

What is the base case for the dp array in the Coin Change Total Number of Ways problem?

dp[0] = 1, meaning there is exactly one way to make amount zero — by choosing no coins.

What does dp[i] represent in the Coin Change Total Number of Ways problem?

A Number of ways to make amount i

B Minimum coins needed to make amount i

C Maximum coins used to make amount i

D Number of coins available

dp[i] stores the total number of ways to make amount i using the given coins.

Why is dp[0] initialized to 1 in the Coin Change problem?

A Because amount zero can be made in one way: using no coins

B Because zero coins are available

C Because zero is the smallest coin

D Because dp arrays start with 1 by default

There is exactly one way to make amount zero: by choosing no coins.

In the Coin Change problem, which loop order avoids counting duplicate combinations?

A Loop over amounts first, then coins

B Loop over coins first, then amounts

C Loop over coins twice

D Loop over amounts twice

Looping over coins first ensures combinations are counted uniquely without duplicates.

If coins = [1, 2] and amount = 3, how many ways are there to make 3?

A 3

B 4

C 1

D 2

Ways: (1+1+1), (1+2). Since order does not matter, total unique combinations are 2 ways: (1+1+1) and (1+2).

What is the time complexity of the Coin Change Total Number of Ways dynamic programming solution?

A O(n^2)

B O(amount^2)

C O(n * amount), where n is number of coins

D O(n + amount)

The solution uses nested loops over coins and amounts, resulting in O(n * amount) time.

Explain how to use dynamic programming to find the total number of ways to make a target amount with given coins.

Think about building solutions from smaller amounts to bigger amounts.

Describe why the order of loops matters in the Coin Change Total Number of Ways problem.

Consider how counting changes if you swap loops.