Coin Change Total Number of Ways in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the ways vector with 1 at index 0.

DSA Rust

let mut ways = vec![0; amount + 1];
ways[1] = 1;

Drag options to blanks, or click blank then click option'

A[amount]

B[1]

C[0]

D[amount + 1]

Attempts:

3 left

💡 Hint

Common Mistakes

Setting ways[amount] = 1 instead of ways[0] = 1

Forgetting to initialize ways[0]

Using an index out of range

The ways vector should have 1 way to make amount 0, so ways[0] = 1.

2fill in blank

medium

Complete the code to iterate over each coin in the coins vector.

DSA Rust

for [1] in coins.iter() {

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Acoin

Bcoins

Ci

Damount

Attempts:

3 left

💡 Hint

Common Mistakes

Using the plural 'coins' instead of singular 'coin'

Using an index variable instead of iter()

Using an undefined variable

We iterate over each coin by using coin as the variable name for each element.

3fill in blank

hard

Fix the error in the inner loop to update ways correctly.

DSA Rust

for x in [1]..=amount {
    ways[x] += ways[x - *coin];
}

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A0

B1

Ccoin

D*coin

Attempts:

3 left

💡 Hint

Common Mistakes

Starting loop from 0 causing negative index

Using 1 instead of coin as start

Using multiplication instead of coin value

The loop should start from the coin value to avoid negative indexing.

4fill in blank

hard

Fill both blanks to complete the function signature and return statement.

DSA Rust

fn count_ways(coins: Vec<usize>, [1]: usize) -> [2] {
    // function body
}

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Aamount

Busize

CVec<usize>

Di32

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter name

Returning Vec instead of usize

Using signed integer types

The function takes amount as usize and returns usize representing number of ways.

5fill in blank

hard

Fill all three blanks to complete the main logic of updating ways.

DSA Rust

for [1] in coins.iter() {
    for x in [2]..=[3] {
        ways[x] += ways[x - *coin];
    }
}

Drag options to blanks, or click blank then click option'

Acoin

B*coin

Camount

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using coins instead of coin in loop

Starting inner loop from 0 instead of *coin

Using wrong upper bound

We iterate over coins as coin, start inner loop from *coin to amount.

Practice

1. What does the "Coin Change Total Number of Ways" problem ask you to find?

easy

A. The minimum number of coins needed to make a target amount.

B. The total number of ways to make a target amount using given coin denominations.

C. The maximum value of coins that can be used without exceeding the target.

D. The total sum of all coin denominations.

Solution

1. Step 1: Understand the problem goal

   The problem asks for counting all possible combinations of coins that sum up to the target amount.

2. Step 2: Differentiate from similar problems

   Unlike minimum coins problem, here we count ways, not minimize coins.

3. Final Answer:

   The total number of ways to make a target amount using given coin denominations. -> Option B

4. Quick Check:

   Count ways, not minimum coins [OK]

Hint: Count combinations, not minimum coins [OK]

Common Mistakes:

• Confusing total ways with minimum coins needed
• Thinking about maximum coin value instead of count
• Ignoring that order of coins does not matter

2. Which of the following Rust code snippets correctly initializes a vector to store ways to make amounts up to `target` with 0 ways initially except for 0 amount which has 1 way?

easy

A. let mut ways = vec![0; target + 1]; ways[0] = 1;

B. let mut ways = vec![1; target]; ways[0] = 0;

C. let mut ways = vec![0; target]; ways[0] = 1;

D. let mut ways = vec![1; target + 1]; ways[0] = 0;

Solution

1. Step 1: Initialize vector size correctly

   Vector size must be target + 1 to include amount 0 to target.

2. Step 2: Set base case for amount 0

   ways[0] = 1 means one way to make amount 0 (using no coins).

3. Final Answer:

   let mut ways = vec![0; target + 1]; ways[0] = 1; -> Option A

4. Quick Check:

   Vector size = target+1, ways[0] = 1 [OK]

Hint: ways vector size = target+1, ways[0] = 1 [OK]

Common Mistakes:

• Using vector size target instead of target+1
• Setting ways[0] to 0 instead of 1
• Initializing all elements to 1 incorrectly

3. What is the output of the following Rust code snippet for coins = [1, 2] and target = 3?

let coins = vec![1usize, 2usize];
let target: usize = 3;
let mut ways = vec![0; target + 1];
ways[0] = 1;
for &coin in &coins {
    for amount in coin..=target {
        ways[amount] += ways[amount - coin];
    }
}
println!("{}", ways[target]);

medium

A. 4

B. 1

C. 2

D. 3

Solution

1. Step 1: Calculate ways using coin 1

   ways after coin 1: ways[0]=1, ways[1]=1, ways[2]=1, ways[3]=1

2. Step 2: Update ways using coin 2

   ways[2] += ways[0] => 1+1=2; ways[3] += ways[1] => 1+1=2; final ways = [1,1,2,2]

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Ways to make 3 with [1,2] = 2 [OK]

Hint: Add ways for each coin incrementally [OK]

Common Mistakes:

• Not updating ways correctly for each coin
• Confusing ways count with minimum coins
• Off-by-one errors in loops

4. Identify the bug in this Rust code snippet for coin change ways calculation:

let coins = vec![1usize, 2usize, 3usize];
let target: usize = 4;
let mut ways = vec![0; target + 1];
ways[0] = 1;
for &coin in &coins {
    for amount in 1usize..=target {
        if amount >= coin {
            ways[amount] += ways[amount - coin];
        }
    }
}
println!("{}", ways[target]);

medium

A. The inner loop should start from coin, not 1.

B. ways[0] should be initialized to 0.

C. coins vector should be mutable.

D. The outer loop should iterate over amounts, not coins.

Solution

1. Step 1: Check inner loop range

   Starting inner loop from 1 causes unnecessary checks; it should start from coin value to avoid redundant iterations.

2. Step 2: Confirm initialization and loops

   ways[0] = 1 is correct; coins vector does not need to be mutable; outer loop over coins is correct.

3. Final Answer:

   The inner loop should start from coin, not 1. -> Option A

4. Quick Check:

   Inner loop start = coin [OK]

Hint: Inner loop starts at coin value to optimize [OK]

Common Mistakes:

• Starting inner loop from 1 instead of coin
• Incorrect initialization of ways[0]
• Misunderstanding loop roles

5. Given coins = [1, 3, 5] and target = 7, how many total ways are there to make the target amount? Use the coin change total number of ways approach.

hard

A. 6

B. 5

C. 7

D. 4

Solution

1. Step 1: Initialize ways vector

   ways = [1,0,0,0,0,0,0,0] for amounts 0 to 7.

2. Step 2: Update ways with coin 1

   ways after coin 1: ways[i] = 1 for all i from 0 to 7 (only using 1s).

3. Step 3: Update ways with coin 3

   ways[3]+=ways[0]=1, ways[4]+=ways[1]=1, ways[5]+=ways[2]=1, ways[6]+=ways[3]=2, ways[7]+=ways[4]=2; ways now: [1,1,1,2,2,2,3,3]

4. Step 4: Update ways with coin 5

   ways[5] += ways[0] => 2 + 1 = 3; ways[6] += ways[1] => 3 + 1 = 4; ways[7] += ways[2] => 3 + 1 = 4; final ways: [1,1,1,2,2,3,4,4]

5. Final Answer:

   4 -> Option D

6. Quick Check:

   Count ways with coins [1,3,5] for 7 = 4 [OK]

Hint: Add ways incrementally for each coin [OK]

Common Mistakes:

• Not updating ways correctly for each coin
• Forgetting to include ways[0] = 1
• Mixing up order of loops