Rod Cutting Problem in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the maximum revenue array with zeros.

DSA Javascript

const maxRevenue = new Array(n + 1).fill([1]);

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

Anull

B1

Cundefined

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using undefined or null instead of 0 causes errors when calculating max revenue.

We fill the array with 0 because initially, the maximum revenue for all lengths is zero.

2fill in blank

medium

Complete the code to loop through all possible first cut lengths.

DSA Javascript

for (let i = 1; i <= [1]; i++) {

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

AmaxRevenue.length

Bprice.length

Cn

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using price.length causes errors if price array length differs from n.

We loop from 1 to n because the rod length is n and we consider all cut lengths.

3fill in blank

hard

Fix the error in updating the maximum revenue inside the loop.

DSA Javascript

maxRevenue[j] = Math.max(maxRevenue[j], price[i - 1] + maxRevenue[j - [1]]);

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

Ai

Bj

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using j or 1 instead of i causes wrong indexing and incorrect revenue calculation.

We subtract i because i is the length of the first cut, so the remaining length is j - i.

4fill in blank

hard

Fill both blanks to complete the nested loop for calculating max revenue.

DSA Javascript

for (let j = [1]; j <= n; j++) {
  maxRevenue[j] = Math.max(maxRevenue[j], price[i - 1] + maxRevenue[j - [2]]);
}

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

Ai

B1

C0

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Starting j from 1 or 0 causes index errors or incorrect calculations.

The inner loop starts from i because we cannot cut a piece longer than the current length i, and we subtract i to get the remaining length.

5fill in blank

hard

Fill all three blanks to complete the function that returns the maximum revenue for rod length n.

DSA Javascript

function rodCutting(price, n) {
  const maxRevenue = new Array(n + 1).fill(0);
  for (let i = [1]; i <= n; i++) {
    for (let j = [2]; j <= n; j++) {
      maxRevenue[j] = Math.max(maxRevenue[j], price[i - 1] + maxRevenue[j - [3]]);
    }
  }
  return maxRevenue[n];
}

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

A1

Bi

Cj

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Starting loops at 0 or subtracting wrong variables causes errors.

The outer loop starts at 1, the inner loop starts at i, and we subtract i to get the remaining length after the cut.

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 minimize the number of cuts made on the rod

C. To find the shortest rod length possible

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

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 D

4. Quick Check:

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

Hint: Remember: maximize profit, not minimize cuts [OK]

Common Mistakes:

• Thinking the goal is to minimize cuts
• Confusing number of ways with maximum profit
• Assuming rod length is to be minimized

2. Which of the following is the correct way to declare a function in JavaScript to solve the rod cutting problem?

easy

A. function rodCutting(prices, n) { /* code */ }

B. def rodCutting(prices, n): /* code */

C. func rodCutting(prices, n) { /* code */ }

D. rodCutting function(prices, n) { /* code */ }

Solution

1. Step 1: Identify JavaScript function syntax

   JavaScript functions are declared using the function keyword followed by the name and parameters.

2. Step 2: Check each option

   function rodCutting(prices, n) { /* code */ } uses correct JavaScript syntax. def rodCutting(prices, n): /* code */ is Python, C is Go/Swift style, D is invalid.

3. Final Answer:

   function rodCutting(prices, n) { /* code */ } -> Option A

4. Quick Check:

   JS function syntax = function rodCutting(prices, n) { /* code */ } [OK]

Hint: JS functions start with 'function' keyword [OK]

Common Mistakes:

• Using Python or other language syntax
• Missing 'function' keyword
• Incorrect parameter declaration

3. What will be the output of the following code snippet?

const prices = [1, 5, 8, 9];
function rodCutting(prices, n) {
  if (n === 0) return 0;
  let maxVal = -Infinity;
  for (let i = 1; i <= n; i++) {
    maxVal = Math.max(maxVal, prices[i - 1] + rodCutting(prices, n - i));
  }
  return maxVal;
}
console.log(rodCutting(prices, 4));

medium

A. 8

B. 9

C. 10

D. 15

Solution

1. Step 1: Understand the recursive calls for n=4

   Calculate max profit for rod length 4 by checking all cuts:
   - Cut 1: price[0] + rodCutting(3) = 1 + 8 = 9
   - Cut 2: price[1] + rodCutting(2) = 5 + 5 = 10
   - Cut 3: price[2] + rodCutting(1) = 8 + 1 = 9
   - Cut 4: price[3] + rodCutting(0) = 9 + 0 = 9

2. Step 2: Calculate rodCutting(3), rodCutting(2), rodCutting(1)

   rodCutting(3) = max(1+5=6, 5+1=6, 8+0=8) = 8
   rodCutting(2) = max(1+1=2, 5+0=5) = 5
   rodCutting(1) = 1

3. Final Answer:

   10 -> Option C

4. Quick Check:

   Max profit for length 4 = 10 [OK]

Hint: Check all cuts and pick max sum recursively [OK]

Common Mistakes:

• Ignoring recursive calls
• Using wrong indices for prices
• Assuming max is price of full rod only

4. Identify the error in the following rod cutting function and select the fix:

function rodCutting(prices, n) {
  if (n <= 0) return 0;
  let maxVal = 0;
  for (let i = 1; i < n; i++) {
    maxVal = Math.max(maxVal, prices[i - 1] + rodCutting(prices, n - i));
  }
  return maxVal;
}

medium

A. Change loop condition to i <= n

B. Initialize maxVal to -Infinity

C. Change base case to if (n === 0) return 1

D. Remove recursive call inside loop

Solution

1. Step 1: Analyze loop range

   The loop runs from i=1 to i < n, so it misses the case when i = n (full rod cut).

2. Step 2: Fix loop condition

   Changing to i <= n includes the full rod cut option, ensuring all possibilities are checked.

3. Final Answer:

   Change loop condition to i <= n -> Option A

4. Quick Check:

   Loop must include full length cut = Change loop condition to i <= n [OK]

Hint: Loop must cover full rod length cuts [OK]

Common Mistakes:

• Using i < n instead of i <= n
• Incorrect base case return value
• Removing recursion breaks logic

5. Given a rod of length 5 and prices array [2, 5, 7, 8, 10], what is the maximum profit using dynamic programming approach?

hard

A. 14

B. 17

C. 15

D. 12

Solution

1. Step 1: Use bottom-up DP to calculate max profit

   Calculate max profit for lengths 1 to 5:
   Length 1: max = 2
   Length 2: max = max(5, 2+2) = 5
   Length 3: max = max(7, 5+2, 2+5) = 7
   Length 4: max = max(8, 7+2, 5+5, 2+7) = 10
   Length 5: max = max(10, 8+2, 7+5, 5+7, 2+10) = 17

2. Step 2: Confirm maximum profit for length 5

   The best cut is length 1 + length 4 (2+15=17) or length 2 + length 3 (5+7=12), so 17 is maximum.

3. Final Answer:

   17 -> Option B

4. Quick Check:

   DP max profit for length 5 = 17 [OK]

Hint: Use DP table from length 1 to n for max profit [OK]

Common Mistakes:

• Not considering all cut combinations
• Using recursive without memoization causing slow results
• Confusing prices index with rod length