I'm trying to compute the x-coordinate of the nth arm of a spiral using both an iterative and a recursive function. However, I am not getting the expected output from the code. I have written two functions: spiral_iterative and spiral_recursive, which are supposed to return specific values based on the input. However, the output is incorrect for some cases.
Problem: Here is a description of what I am expecting:
Test Case 1: Input: spiral_iterative(0, 8, 1) and spiral_recursive(0, 8, 1) Expected Output: 4.0
Test Case 2: Input: spiral_iterative(0, 8, 2) and spiral_recursive(0, 8, 2) Expected Output: 6.0
Test Case 3: Input: spiral_iterative(0, 8, 3) and spiral_recursive(0, 8, 3) Expected Output: 5.0
Test Case 4 (Large n): Input: spiral_iterative(0, 16, 5) and spiral_recursive(0, 16, 5) Expected Output: 11.0
Additional details: I'm working with Python 3.x. The logic behind the functions seems to be based on adjusting the left and right values with each iteration/recursion to find the mid-point. Thank you for your help!
But the output is not as expected.
def spiral_iterative(left, right, n):
"""
An iterative function to compute the x-coordinate of the nth arm of the spiral.
Parameters:
left: integer
right: integer
n: integer
Return:
result: float
"""
mid = (left + right) / 2
for i in range(3, n):
mid = (left + right) / 2
left = mid
mid = (left + right) / 2
right = mid
return mid
def spiral_recursive(left, right, n):
"""
A recursive function to compute the x-coordinate of the nth arm of the spiral.
Arguments:
left: integer
right: integer
n: integer
Return:
result: float
"""
if n < 1:
return left
else:
mid = (left + right) / 2
if n % 2 == 0:
left = mid
else:
right = mid
return spiral_recursive(left, right, n - 1)
# Test Case 1
print(spiral_iterative(0, 8, 1)) # Expected: 4.0
print(spiral_recursive(0, 8, 1)) # Expected: 4.0
# Test Case 2
print(spiral_iterative(0, 8, 2)) # Expected: 6.0
print(spiral_recursive(0, 8, 2)) # Expected: 6.0
# Test Case 3
print(spiral_iterative(0, 8, 3)) # Expected: 5.0
print(spiral_recursive(0, 8, 3)) # Expected: 5.0
# Test Case 4 (Large n)
print(spiral_iterative(0, 16, 5)) # Expected: 11.0
print(spiral_recursive(0, 16, 5)) # Expected: 11.0
What I expect: For spiral_iterative(0, 8, 1), I expect 4.0. For spiral_recursive(0, 8, 1), I expect 4.0. I expect similar outputs for the other test cases as well. What is happening: The output is incorrect and does not match the expected values. It seems like the iterative and recursive functions do not behave as expected. Could someone help me identify what might be causing the issue in the code?
This answer's version: loops run exactly n times for each step in spiral computation.
Your version: Incorrectly, the loop started at i=3 up to n-1 so n=1 and n=2 do not execute. For n=3 and higher the left, mid and right were updated multiple times within an iteration incorrectly.
Corrected Methods:
def spiral_iterative(left, right, n):
for step in range(1, n + 1):
mid = (left + right) / 2
left, right = (mid, right) if step % 2 == 1 else (left, mid)
return mid
def spiral_recursive(left, right, n):
if n <= 0:
raise ValueError("Step number 'n' must be a positive integer.")
def helper(current_left, current_right, current_step):
mid = (current_left + current_right) / 2
if current_step == n:
return mid
if current_step % 2 == 1:
# Odd step: move to the right half by updating the left boundary.
return helper(mid, current_right, current_step + 1)
else:
# Even step: move to the left half by updating the right boundary.
return helper(current_left, mid, current_step + 1)
return helper(left, right, 1)
Test Cases:
Test Case 1:
spiral_iterative(0, 8, 1): 4.0 (Expected: 4.0)
spiral_recursive(0, 8, 1): 4.0 (Expected: 4.0)
Test Case 2:
spiral_iterative(0, 8, 2): 6.0 (Expected: 6.0)
spiral_recursive(0, 8, 2): 6.0 (Expected: 6.0)
Test Case 3:
spiral_iterative(0, 8, 3): 5.0 (Expected: 5.0)
spiral_recursive(0, 8, 3): 5.0 (Expected: 5.0)
Test Case 4:
spiral_iterative(0, 16, 4): 11.0 (Expected: 11.0)
spiral_recursive(0, 16, 4): 11.0 (Expected: 11.0)
Test Case 5:
spiral_iterative(0, 16, 5): 10.5 (Expected: 10.5)
spiral_recursive(0, 16, 5): 10.5 (Expected: 10.5)