Rod Cutting Problem in DSA C# - Build from Scratch

Rod Cutting Problem

📖 Scenario: You own a workshop where you cut rods into pieces to sell. Each piece length has a price. You want to find the best way to cut a rod to get the most money.

🎯 Goal: Build a program that finds the maximum price you can get by cutting a rod of a given length using given prices for each piece length.

📋 What You'll Learn

Create an array called prices with prices for rod lengths 1 to 8.

Create an integer variable called rodLength for the length of the rod to cut.

Write a loop to calculate the maximum price for the rod using dynamic programming.

Print the maximum price for the rod length.

💡 Why This Matters

🌍 Real World

This problem models real-life situations where you want to cut raw materials into pieces to maximize profit, such as wood, metal rods, or fabric.

💼 Career

Understanding dynamic programming and optimization problems like rod cutting is useful for software engineers working on resource allocation, manufacturing software, and algorithm design.

1

Create the prices array

Create an integer array called prices with these exact values: 1, 5, 8, 9, 10, 17, 17, 20 representing prices for rod lengths 1 to 8.

DSA C#

// Create the prices array with given values
// Your code here

Hint

Use int[] prices = { ... }; to create the array with the exact values.

2

Set the rod length

Create an integer variable called rodLength and set it to 8 to represent the length of the rod to cut.

DSA C#

int[] prices = {1, 5, 8, 9, 10, 17, 17, 20};
// Create the rodLength variable and set it to 8
// Your code here

Hint

Use int rodLength = 8; to set the rod length.

3

Calculate maximum price using dynamic programming

Create an integer array called maxPrices of size rodLength + 1. Use a for loop with variable i from 1 to rodLength inclusive. Inside it, create an integer variable maxVal set to 0. Use another for loop with variable j from 1 to i inclusive. Update maxVal with the maximum of maxVal and prices[j - 1] + maxPrices[i - j]. After the inner loop, set maxPrices[i] to maxVal.

DSA C#

int[] prices = {1, 5, 8, 9, 10, 17, 17, 20};
int rodLength = 8;
// Calculate maxPrices array using dynamic programming
// Your code here

Hint

Use two nested loops and update maxPrices[i] with the best price found.

4

Print the maximum price

Print the maximum price for the rod length by writing Console.WriteLine(maxPrices[rodLength]);.

DSA C#

int[] prices = {1, 5, 8, 9, 10, 17, 17, 20};
int rodLength = 8;
int[] maxPrices = new int[rodLength + 1];
for (int i = 1; i <= rodLength; i++)
{
    int maxVal = 0;
    for (int j = 1; j <= i; j++)
    {
        maxVal = Math.Max(maxVal, prices[j - 1] + maxPrices[i - j]);
    }
    maxPrices[i] = maxVal;
}
// Print the maximum price
// Your code here

Hint

Use Console.WriteLine(maxPrices[rodLength]); to show the result.

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