Rod Cutting Problem
Given rod of length n and prices for pieces of different lengths, determine maximum revenue obtainable by cutting rod and selling pieces. Classic DP problem demonstrating optimal substructure: optimal cut for length n includes optimal solution for remaining length.
Visualization
Interactive visualization for Rod Cutting Problem
Rod Cutting Problem
• Time: O(n²)
• Space: O(n)
• Classic DP optimization problem
Interactive visualization with step-by-step execution
Implementation
1function rodCutting(prices: number[], n: number): number {
2 const dp: number[] = Array(n + 1).fill(0);
3
4 for (let i = 1; i <= n; i++) {
5 for (let j = 1; j <= i; j++) {
6 dp[i] = Math.max(dp[i], prices[j - 1] + dp[i - j]);
7 }
8 }
9
10 return dp[n];
11}
12
13// With cuts tracking
14function rodCuttingWithCuts(prices: number[], n: number): {maxRevenue: number, cuts: number[]} {
15 const dp: number[] = Array(n + 1).fill(0);
16 const cuts: number[] = Array(n + 1).fill(0);
17
18 for (let i = 1; i <= n; i++) {
19 for (let j = 1; j <= i; j++) {
20 if (dp[i] < prices[j - 1] + dp[i - j]) {
21 dp[i] = prices[j - 1] + dp[i - j];
22 cuts[i] = j;
23 }
24 }
25 }
26
27 const cutsList: number[] = [];
28 let remaining = n;
29 while (remaining > 0) {
30 cutsList.push(cuts[remaining]);
31 remaining -= cuts[remaining];
32 }
33
34 return {maxRevenue: dp[n], cuts: cutsList};
35}Complexity
Time
O(n²)
O(n²)
O(n²)
Space
O(n)
Applications
Use Cases
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