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.

Practice

1. What does the "Coin Change Minimum Coins" problem ask you to find?

easy

A. The maximum amount of money you can make with given coins

B. The total number of different coins available

C. The least number of coins needed to make a given amount

D. The sum of all coin values

Solution

1. Step 1: Understand the problem goal

   The problem asks for the minimum number of coins needed to make a specific amount.

2. Step 2: Differentiate from other coin problems

   It is not about counting coins or maximum amount, but minimizing coin count for exact amount.

3. Final Answer:

   The least number of coins needed to make a given amount -> Option C

4. Quick Check:

   Minimum coins = least number needed [OK]

Hint: Focus on minimum coins to form amount, not total coins [OK]

Common Mistakes:

• Confusing minimum coins with total coin types
• Thinking problem asks for maximum amount
• Ignoring the exact amount requirement

2. Which of the following is the correct TypeScript function signature for a coin change minimum coins function?

easy

A. function minCoins(coins: number[], amount: number): number

B. function minCoins(amount: number, coins: number[]): void

C. function minCoins(coins: number, amount: number[]): number[]

D. function minCoins(coins: string[], amount: string): number

Solution

1. Step 1: Check parameter types and order

   The function should take an array of coin values (number[]) and an amount (number).

2. Step 2: Check return type

   The function returns a number representing minimum coins needed.

3. Final Answer:

   function minCoins(coins: number[], amount: number): number -> Option A

4. Quick Check:

   Correct types and return number [OK]

Hint: Coins array first, amount second, returns number [OK]

Common Mistakes:

• Swapping parameter order
• Using wrong types like string instead of number
• Returning void or array instead of number

3. What is the output of the following TypeScript code?

function minCoins(coins: number[], amount: number): number {
  const dp = Array(amount + 1).fill(amount + 1);
  dp[0] = 0;
  for (let i = 1; i <= amount; i++) {
    for (const coin of coins) {
      if (coin <= i) {
        dp[i] = Math.min(dp[i], dp[i - coin] + 1);
      }
    }
  }
  return dp[amount] > amount ? -1 : dp[amount];
}

console.log(minCoins([1, 2, 5], 11));

medium

A. 2

B. 3

C. -1

D. 5

Solution

1. Step 1: Understand dp array initialization

   dp array size is 12 (0 to 11), initialized with 12 (amount+1), dp[0] = 0.

2. Step 2: Calculate dp values for amount 11

   Using coins 1,2,5, minimum coins for 11 is 3 (5+5+1).

3. Final Answer:

   3 -> Option B

4. Quick Check:

   Minimum coins for 11 with [1,2,5] = 3 [OK]

Hint: Use dp array to track min coins for each amount [OK]

Common Mistakes:

• Returning dp[amount] without checking if > amount
• Misunderstanding dp initialization
• Confusing coin values and indices

4. Identify the bug in this TypeScript code for minimum coins:

function minCoins(coins: number[], amount: number): number {
  const dp = new Array(amount + 1).fill(0);
  dp[0] = 0;
  for (let i = 1; i <= amount; i++) {
    dp[i] = Infinity;
    for (const coin of coins) {
      if (coin < i) {
        dp[i] = Math.min(dp[i], dp[i - coin] + 1);
      }
    }
  }
  return dp[amount] === Infinity ? -1 : dp[amount];
}

medium

A. The condition should be coin <= i, not coin < i

B. dp array should be initialized with Infinity, not 0

C. dp[0] should be Infinity, not 0

D. Return statement should check dp[amount] > Infinity

Solution

1. Step 1: Check coin usage condition

   The condition 'coin < i' skips cases where coin equals i, missing exact matches.

2. Step 2: Correct condition to include equal coins

   Change condition to 'coin <= i' to allow using coin equal to current amount.

3. Final Answer:

   The condition should be coin <= i, not coin < i -> Option A

4. Quick Check:

   Include coin equal to amount [OK]

Hint: Use <= to include exact coin matches [OK]

Common Mistakes:

• Using < instead of <= in coin check
• Initializing dp array incorrectly
• Wrong return condition check

5. Given coins = [2, 3, 7] and amount = 13, what is the minimum number of coins needed? Use the coin change minimum coins approach.

hard

A. -1

B. 4

C. 2

D. 3

Solution

1. Step 1: Try combinations to form 13

   Possible combos: 7+3+3 = 3 coins, 2+2+2+7 = 4 coins, etc.

2. Step 2: Identify minimum coins

   Minimum coins is 3 using 7, 3, and 3.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   7+3+3 = 13 with 3 coins [OK]

Hint: Try largest coins first to minimize count [OK]

Common Mistakes:

• Assuming no solution (-1) without checking combos
• Counting coins incorrectly
• Ignoring combinations with repeated coins