Rod Cutting Problem in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the maximum revenue array for rod lengths.

DSA C#

int[] maxRevenue = new int[[1] + 1];

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

An

Bn * 2

Cn - 1

Dn + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using array size n instead of n+1 causes index out of range errors.

Using n-1 misses the last rod length.

We need an array of size n+1 to store maximum revenues for all lengths from 0 to n.

2fill in blank

medium

Complete the code to iterate over all rod lengths from 1 to n.

DSA C#

for (int i = 1; i <= [1]; i++)

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

An - 1

BmaxRevenue.Length - 1

Cn

DmaxRevenue.Length

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of maxRevenue.Length - 1 causes confusion about array size.

Using maxRevenue.Length causes index out of range.

The loop should run from 1 to maxRevenue.Length - 1 to cover all rod lengths.

3fill in blank

hard

Fix the error in the inner loop to iterate over possible first cut lengths.

DSA C#

for (int j = 1; j <= [1]; j++)

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

Ai

BmaxRevenue.Length - 1

CmaxRevenue.Length

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of i causes incorrect iteration beyond current rod length.

Using maxRevenue.Length causes index errors.

The inner loop must run from 1 to i, the current rod length being considered.

4fill in blank

hard

Fill both blanks to update maxRevenue[i] with the maximum revenue possible.

DSA C#

maxRevenue[i] = Math.Max(maxRevenue[i], [1][j - 1] + [2][i - j]);

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

Aprices

BmaxRevenue

CpricesList

Dprice

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong variable names like pricesList or price causes errors.

Mixing up indices leads to wrong revenue calculation.

We use prices[j - 1] for the price of the first cut and maxRevenue[i - j] for the remaining length.

5fill in blank

hard

Fill all three blanks to return the maximum revenue for rod length n.

DSA C#

return [1][[2]]; // max revenue for length [3]

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

AmaxRevenue

Bprices

Cn

DmaxRevenue.Length - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning prices instead of maxRevenue returns wrong value.

Using n instead of maxRevenue.Length - 1 causes confusion about array size.

maxRevenue[maxRevenue.Length - 1] holds the max revenue for rod length n.

Practice

1. What is the main goal of the Rod Cutting Problem in algorithms?

easy

A. To count the total number of ways to cut the rod

B. To maximize the total profit by cutting the rod into pieces

C. To find the shortest rod length possible

D. To minimize the number of cuts made on the rod

Solution

1. Step 1: Understand the problem objective

   The rod cutting problem aims to cut a rod into pieces to get the highest total price from selling those pieces.

2. Step 2: Identify the goal

   The goal is to maximize profit, not minimize cuts or count ways.

3. Final Answer:

   To maximize the total profit by cutting the rod into pieces -> Option B

4. Quick Check:

   Maximize profit = To maximize the total profit by cutting the rod into pieces [OK]

Hint: Focus on maximizing profit from pieces, not cuts or counts [OK]

Common Mistakes:

• Thinking the goal is to minimize cuts
• Confusing with counting ways to cut
• Assuming shortest rod length is the goal

2. Which of the following is the correct C# method signature for a function solving the rod cutting problem recursively?

easy

A. int CutRod(int prices, int[] n)

B. void CutRod(int prices[], int n)

C. int CutRod(int[] prices, int n)

D. int CutRod(int[] prices, int[] lengths)

Solution

1. Step 1: Check parameter types and order

   The function should take an array of prices and an integer length n.

2. Step 2: Verify return type

   The function returns an integer representing maximum profit.

3. Final Answer:

   int CutRod(int[] prices, int n) -> Option C

4. Quick Check:

   Correct signature returns int and takes int[] and int [OK]

Hint: Return int max profit; input array prices and int length [OK]

Common Mistakes:

• Using void instead of int return type
• Swapping parameter types
• Passing arrays incorrectly

3. What is the output of the following C# code snippet for rod cutting?

int[] prices = {1, 5, 8, 9};
int n = 4;
int result = CutRod(prices, n);
Console.WriteLine(result);

int CutRod(int[] price, int length) {
    if (length == 0) return 0;
    int max_val = int.MinValue;
    for (int i = 1; i <= length; i++) {
        max_val = Math.Max(max_val, price[i - 1] + CutRod(price, length - i));
    }
    return max_val;
}

medium

A. 10

B. 9

C. 8

D. 5

Solution

1. Step 1: Understand recursive calls and prices

   Prices: length 1=1, 2=5, 3=8, 4=9. The function tries all cuts and sums prices recursively.

2. Step 2: Calculate max profit for length 4

   Possible cuts: - 1 + CutRod(3) = 1 + 8 = 9 - 5 + CutRod(2) = 5 + 5 = 10 - 8 + CutRod(1) = 8 + 1 = 9 - 9 + CutRod(0) = 9 + 0 = 9 Max is 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Max profit for length 4 = 10 [OK]

Hint: Try all cuts, pick max sum of price + recursive result [OK]

Common Mistakes:

• Ignoring recursive calls
• Choosing first price only
• Misindexing price array

4. Identify the bug in this C# code for rod cutting and select the fix:

int CutRod(int[] price, int length) {
    if (length == 0) return 0;
    int max_val = 0;
    for (int i = 1; i <= length; i++) {
        max_val = Math.Max(max_val, price[i] + CutRod(price, length - i));
    }
    return max_val;
}

medium

A. Change 'price[i]' to 'price[i - 1]' to fix array index out of bounds

B. Initialize max_val to int.MinValue instead of 0

C. Change loop to 'for (int i = 0; i < length; i++)' to fix indexing

D. Add base case for length == 1 to return price[0]

Solution

1. Step 1: Check array indexing in loop

   Loop uses i from 1 to length, but price array is zero-indexed. Accessing price[i] causes out of bounds when i == length.

2. Step 2: Fix indexing by subtracting 1

   Change price[i] to price[i - 1] to access correct element safely.

3. Final Answer:

   Change 'price[i]' to 'price[i - 1]' to fix array index out of bounds -> Option A

4. Quick Check:

   Index fix = Change 'price[i]' to 'price[i - 1]' to fix array index out of bounds [OK]

Hint: Array index starts at 0, loop starts at 1, adjust index [OK]

Common Mistakes:

• Using price[i] directly causing runtime error
• Changing loop incorrectly breaking logic
• Ignoring base case

5. Given a rod of length 5 and prices int[] prices = {2, 5, 7, 8, 10};, what is the maximum profit using dynamic programming bottom-up approach?

hard

A. 10

B. 12

C. 15

D. 14

Solution

1. Step 1: Initialize dp array for lengths 0 to 5

   dp[0]=0. Calculate dp[i] for i=1 to 5 using max of price[j-1]+dp[i-j].

2. Step 2: Calculate dp values step-by-step

   dp[1]=2 dp[2]=max(5,2+2)=5 dp[3]=max(7,5+2,2+5)=7 dp[4]=max(8,7+2,5+5,2+7)=10 dp[5]=max(10,8+2,7+5,5+7,2+10)=14

3. Final Answer:

   14 -> Option D

4. Quick Check:

   Bottom-up dp max profit = 14 [OK]

Hint: Build dp array from length 1 to n, pick max at each step [OK]

Common Mistakes:

• Not using dp array, causing repeated calculations
• Incorrect max calculation in loop
• Ignoring smaller cuts combinations