Define Rn to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i>0, let p[i] denote the selling price of a rod whose length is i meters. Consider the array of prices:
p[1]=1, p[2]=5, p[3]=8, p[4]=9, p[5]=10, p[6]=17, p[7]=18
Which of the following statements is/are correct about R7?
(A) R7=18
(B) R7=19
(C) R7 is achieved by three different solutions
(D) R7 cannot be achieved by a solution consisting of three pieces
Answer: (A) (C)
Explanation: According to given data,
Number of pieces | Possible max profits with combination of rod size |
7 | 7 (1, 1, 1, 1, 1, 1, 1) |
6 | 10 (2, 1, 1, 1, 1, 1) |
5 | 13 (2, 2, 1, 1, 1) |
4 | 16 (2, 2, 2, 1) |
3 | 18 (2, 2, 3) |
2 | 18 (6, 1) |
1 | 18 (7) |
Therefore,
Option (A) and (C) are correct.
Refer – Cutting a Rod | DP-13, and solution – https://ide.geeksforgeeks.org/lbBeyHa3xd