Circular Array Loop
To solve this coding challenge, we'll follow a systematic approach to detect cycles in a circular array. The detailed explanation and pseudocode below will guide you through the solution.
Explanation:
The problem involves detecting a cycle in a circular array where each element represents the number of steps to move forward or backward. Our goal is to identify if there's a cycle that meets the criteria:- Every element in the sequence is either all positive or all negative.
- The cycle length must be greater than 1. Key approach :
- Traverse each element of the array to treat it as the starting point of a potential cycle.
- Use two pointers (slow and fast) to detect a cycle (similar to Floyd's Tortoise and Hare algorithm).
- If a cycle is detected, check if all elements in the cycle move in the same direction.
- If no valid cycle is detected from a starting point, mark all elements along the path as visited to avoid reprocessing. Key constraint : Since the array is circular, moving past the last element means wrapping around to the first element and vice versa when moving backward.
-
Define a function
next_index
- Loop through each element of the array to check for cycles:
- If the element has been visited (marked by setting to 0), skip it.
-
Use
slow
fast
-
Move
slow
fast
-
Check for cycle detection (when
slow
fast
- Ensure the cycle length is greater than 1.
- If no valid cycle is found, mark all traversed elements to avoid rechecking.
Detailed Steps in Pseudocode:
Pseudocode:
# Utility function to get the next index in a circular manner
def next_index(nums, current_index):
n = length of nums
next_index = (current_index + nums[current_index]) % n
# Handle wrap-around for negative indices
if next_index < 0:
next_index += n
return next_index
# Main function to detect a circular array loop
def circular_array_loop(nums):
n = length of nums
# Iterate through each element in the array
for i in range(n):
# Skip if the element is marked as visited
if nums[i] == 0:
continue
# Initialize slow and fast pointers
slow = i
fast = next_index(nums, i)
# Loop to detect cycle
while nums[slow] * nums[fast] > 0 and nums[fast] * nums[next_index(nums, fast)] > 0:
# Check if the slow and fast pointers meet
if slow == fast:
# Check if the cycle length is greater than 1
if slow == next_index(nums, slow):
break
return True
# Move slow pointer by one step
slow = next_index(nums, slow)
# Move fast pointer by two steps
fast = next_index(nums, next_index(nums, fast))
# Mark all nodes along the current path as visited
slow = i
current_value = nums[i]
while nums[slow] * current_value > 0:
next_slow = next_index(nums, slow)
nums[slow] = 0 # Mark as visited
slow = next_slow
# No valid cycle found
return False
This pseudocode outlines a method to efficiently detect cycles in a circular array by leveraging the two-pointer technique and ensuring minimal additional space complexity by leveraging in-place modifications. By carefully managing traversal and marking visited nodes, we ensure that each node is processed optimally.