Rod Cutting Problem in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Rod Cutting Maximum Revenue Calculation

What is the output of the following C# code that calculates the maximum revenue for a rod of length 4?

DSA C#

using System;

class RodCutting {
    public static int MaxRevenue(int[] prices, int length) {
        int[] dp = new int[length + 1];
        dp[0] = 0;
        for (int i = 1; i <= length; i++) {
            int max_val = int.MinValue;
            for (int j = 1; j <= i; j++) {
                max_val = Math.Max(max_val, prices[j - 1] + dp[i - j]);
            }
            dp[i] = max_val;
        }
        return dp[length];
    }

    static void Main() {
        int[] prices = {1, 5, 8, 9, 10};
        int length = 4;
        Console.WriteLine(MaxRevenue(prices, length));
    }
}

A 5

B 9

C 8

D 10

💡 Hint

Think about all possible ways to cut the rod and sum prices.

The maximum revenue for length 4 is 10, achieved by cutting the rod into two pieces of length 2 each (5 + 5).

❓ Predict Output

intermediate

Output of Rod Cutting with Different Prices

What is the output of this C# code for maximum revenue when rod length is 5?

DSA C#

using System;

class RodCutting {
    public static int MaxRevenue(int[] prices, int length) {
        int[] dp = new int[length + 1];
        dp[0] = 0;
        for (int i = 1; i <= length; i++) {
            int max_val = int.MinValue;
            for (int j = 1; j <= i; j++) {
                max_val = Math.Max(max_val, prices[j - 1] + dp[i - j]);
            }
            dp[i] = max_val;
        }
        return dp[length];
    }

    static void Main() {
        int[] prices = {2, 5, 7, 8, 10};
        int length = 5;
        Console.WriteLine(MaxRevenue(prices, length));
    }
}

A 12

B 15

C 14

D 10

💡 Hint

Try cutting the rod into pieces of length 2 and 3.

The maximum revenue for length 5 is 12, achieved by cutting into lengths 2 and 3 (5 + 7).

🔧 Debug

advanced

Identify the Error in Rod Cutting Code

What error does the following C# code produce when run?

DSA C#

using System;

class RodCutting {
    public static int MaxRevenue(int[] prices, int length) {
        int[] dp = new int[length];
        dp[0] = 0;
        for (int i = 1; i <= length; i++) {
            int max_val = int.MinValue;
            for (int j = 1; j <= i; j++) {
                max_val = Math.Max(max_val, prices[j - 1] + dp[i - j]);
            }
            dp[i] = max_val;
        }
        return dp[length];
    }

    static void Main() {
        int[] prices = {1, 5, 8, 9, 10};
        int length = 4;
        Console.WriteLine(MaxRevenue(prices, length));
    }
}

A IndexOutOfRangeException

B NullReferenceException

C Compilation error

D No error, outputs 10

💡 Hint

Check array size and indexing carefully.

The dp array is declared with size 'length' but accessed at dp[length], causing IndexOutOfRangeException.

🧠 Conceptual

advanced

Time Complexity of Rod Cutting Dynamic Programming

What is the time complexity of the dynamic programming solution for the rod cutting problem with rod length n?

A O(n log n)

B O(n^2)

C O(n)

D O(2^n)

💡 Hint

Consider nested loops over length and cut positions.

The solution uses two nested loops: outer loop runs n times, inner loop runs up to n times, resulting in O(n^2).

🚀 Application

expert

Maximum Revenue and Cuts for Rod Cutting

Given prices and rod length, which option correctly outputs the maximum revenue and the cuts made to achieve it?

DSA C#

using System;
using System.Collections.Generic;

class RodCutting {
    public static (int, List<int>) MaxRevenueWithCuts(int[] prices, int length) {
        int[] dp = new int[length + 1];
        int[] cuts = new int[length + 1];
        dp[0] = 0;
        for (int i = 1; i <= length; i++) {
            int max_val = int.MinValue;
            for (int j = 1; j <= i; j++) {
                if (max_val < prices[j - 1] + dp[i - j]) {
                    max_val = prices[j - 1] + dp[i - j];
                    cuts[i] = j;
                }
            }
            dp[i] = max_val;
        }
        List<int> resultCuts = new List<int>();
        int temp = length;
        while (temp > 0) {
            resultCuts.Add(cuts[temp]);
            temp -= cuts[temp];
        }
        return (dp[length], resultCuts);
    }

    static void Main() {
        int[] prices = {1, 5, 8, 9, 10};
        int length = 5;
        var result = MaxRevenueWithCuts(prices, length);
        Console.WriteLine(result.Item1);
        Console.WriteLine(string.Join(",", result.Item2));
    }
}

A 12 and cuts: 3,2

B 13 and cuts: 1,4

C 13 and cuts: 2,3

D 10 and cuts: 2,3

💡 Hint

Trace the cuts array to find the pieces that sum to max revenue.

The maximum revenue for length 5 is 13, achieved by cuts of length 2 and 3.

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