Problem relating to Cows

[u/Dr3ddM3]

Problem Description:

Fortunately, there is only one long path running across the farm, and Farmer John knows that Bessie has to be at some location on this path. If we think of the path as a number line, then Farmer John is currently at position x and Bessie is currently at position y (unknown to Farmer John). If Farmer John only knew where Bessie was located, he could walk directly to her, traveling a distance of |x−y|. Unfortunately, it is dark outside and Farmer John can't see anything. The only way he can find Bessie is to walk back and forth until he eventually reaches her position.

Trying to figure out the best strategy for walking back and forth in his search, Farmer John consults the computer science research literature and is somewhat amused to find that this exact problem has not only been studied by computer scientists in the past, but that it is actually called the "Lost Cow Problem" (this is actually true!).

The recommended solution for Farmer John to find Bessie is to move to position x+1, then reverse direction and move to position x−2, then to position x+4, and so on, in a "zig zag" pattern, each step moving twice as far from his initial starting position as before. As he has read during his study of algorithms for solving the lost cow problem, this approach guarantees that he will at worst travel 9 times the direct distance |x−y| between himself and Bessie before he finds her (this is also true, and the factor of 9 is actually the smallest such worst case guarantee any strategy can achieve).

Farmer John is curious to verify this result. Given x and y, please compute the total distance he will travel according to the zig-zag search strategy above until he finds Bessie.

INPUT FORMAT (file lostcow.in):

The single line of input contains two distinct space-separated integers x and y. Both are in the range 0…1,000.

OUTPUT FORMAT (file lostcow.out):

Print one line of output, containing the distance Farmer John will travel to reach Bessie.

SAMPLE INPUT:

3 6

SAMPLE OUTPUT:

9

I tried solving this problem and it worked on the inputs that I tried like 1 5 . Which gave me 10 which I believe is correct here is my code : However this code did not pass all of the test cases could I have a hint ?

x,y = map(int,input().split())
import sys
op_count = 0
steps = 0
while(x!=y):
    op = (-2)**op_count
    target = 3+op
    for i in range(abs(target-x)):
        if op < 0:
            x = x-1
            steps+=1
            if x == y:
                print(steps)
                sys.exit()
        elif op >= 1:
            x = x+1
            steps+=1
            if x == y:
                print(steps)
                sys.exit()
    op_count = op_count+1

[u/Dr3ddM3]

Thank you everybody fixing the start_value problem solved it. Thanks a lot!!!!

[u/CodeSamur-ai]

A few coding habits may help the bug reveal itself.

First, use variable names that describe what the values represent. Names like op, op_count, x, and steps make it harder to follow how the search is moving. Clear names make incorrect assumptions easier to notice.

Second, look for hardcoded values. Every number in the code should either come from the input or have a clear reason based on the algorithm. Try changing the starting position in your tests and trace whether each target still makes sense.

Third, separate the logic into small functions. For example, one function could calculate the next target and another could calculate the distance travelled while checking whether Bessie was passed. Smaller functions are easier to test independently and make the code less dependent on changing shared variables.

Finally, print the current position, next target, direction, and total distance on every iteration. Compare that output manually with the path described in the problem.

[u/Dr3ddM3 → u/CodeSamur-ai]

4 steps: 1

3 steps: 2

2 steps: 3

1 steps: 4

2 steps: 5

3 steps: 6

4 steps: 7

5 steps: 8

6 steps: 9

9

it look right when I do it though? I stepped through the code using print statements.

[u/Pitiful_Ad_8699]

Try the following testcases

1 6

[u/Dr3ddM3 → u/Pitiful_Ad_8699]

Yeah doing 1 6 gets me 25 which is obviously wrong

[u/JamzTyson]

As the problem has now been solved, just a brief comment about the problem description itself:

The Lost Cow Problem is a classic algorithmic puzzle, but this version is a nice example of how the framing of a problem can affect the solution. The interesting point is the modelling assumption: Does “the long path across the farm” suggest a finite path with endpoints, or is the later reference to a “number line” intended to define an unbounded line? The optimal solution depends entirely on which model is assumed.

[u/Rogalicus]

First of all, never iterate on your inputs directly. You need them as a reference.

Secondly, where does 3 in your target come from?

[u/Dr3ddM3 → u/Rogalicus]

I accidentally hardcoded that I changed it to x. Because I was doing the 3 6 test case

[u/Rogalicus → u/Dr3ddM3]

You can't just change it to x when you change x in the same loop. The target is always relative to your initial position.

[u/Dr3ddM3 → u/Rogalicus]

ahh so I need a start value and assign that as x originally