Rod Cutting
Problem Statement
Given a rod of length 'n', we are asked to cut the rod and sell the pieces in a way that will maximize the profit. We are also given the price of every piece of length 'i' where '1 <= i <= n'.
Example:
Lengths: [1, 2, 3, 4, 5]
Prices: [2, 6, 7, 10, 13]
Rod Length: 5
Let's try different combinations of cutting the rod:
Five pieces of length 1 => 10 price
Two pieces of length 2 and one piece of length 1 => 14 price
One piece of length 3 and two pieces of length 1 => 11 price
One piece of length 3 and one piece of length 2 => 13 price
One piece of length 4 and one piece of length 1 => 12 price
One piece of length 5 => 13 price
This shows that we get the maximum price (14) by cutting the rod into two pieces of length '2' and one piece of length '1'.
Try it yourself
Try solving this question here:
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Build the mental picture, not memorization.
I just read a lesson on **Rod Cutting** (DSA) and want to truly understand it. Explain Rod Cutting from first principles using ONE vivid real-world analogy and a visual mental model — draw it as ASCII art or a clear step-by-step diagram — with a concrete example using real numbers. Then ask me one question to check I got the mental picture, and wait for my reply. If you're unsure or a claim isn't standard, say so and reason from first principles instead of guessing.
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