In this article, we will learn about the solution to the problem statement given below.
Problem statement − We are given a rod of length n and an array of prices that contains prices of all pieces of the size which are smaller than n. We need to determine the maximum value obtainable by cutting up the rod and selling its pieces.
We will be using a dynamic programming approach to solve the problem.
Now let’s observe the solution in the implementation below−
# A Dynamic Programming solution for Rod cutting problem INT_MIN = -32767 # cut function def cutRod(price, n): val = [0 for x in range(n + 1)] val = 0 # bottom up manner for i in range(1, n + 1): max_val = INT_MIN for j in range(i): max_val = max(max_val, price[j] + val[i-j-1]) val[i] = max_val return val[n] # main arr = [2, 4, 7, 9, 11, 16, 16, 21] size = len(arr) print("Maximum Obtainable Value is " + str(cutRod(arr, size)))
Maximum Obtainable Value is 21
All the variables are declared in the local scope and their references are seen in the figure above.
In this article, we have learned about how we can make a Python Program for Cutting a Rod.