Loop Invariant for Cut Rod Implementation CLRS

Question

I was wondering what the loop invariant would be for the loop present in lines 4 - 6 of this code and how to prove it during intialization, mantience, and termination.

def cut_rod(p, n):
    if n == 0:
        return 0
    q = -inf
    for i = 1 to n:
        q = max(q, p[i] + cut_rod(p, n-i))
    return q

I wasn't really sure where to start here so some insight would be great :)

A loop invariant is some predicate (condition) that holds for every iteration of the loop., thus the loop invariant would be ```1 >= i < n``` — itprorh66, Nov 13 '22 at 16:12
No I mean't 1 >= 1, since the loop begins with 1 and ends with n — itprorh66, Nov 13 '22 at 17:20

score 0 · Answer 1 · answered Nov 13 '22 at 17:08

0

I would say that after each iteration q = min price of rod with len n cut containing at least 1 piece of len <= i.

This can be proven inductively.

answered Nov 13 '22 at 17:08

Dimitrius

564
6
21

score 0 · Answer 2 · answered Jan 11 '23 at 14:48

0

with the q = -inf initialisation you're guaranteed to return the max of q and the recursion of this function

answered Jan 11 '23 at 14:48

Amy

59
6

Loop Invariant for Cut Rod Implementation CLRS

2 Answers2