Compute Total Manual Distance

Problem Statement

You are given a list of actions, where each action is a tuple (direction, steps). The direction is either 1 (representing clockwise/forward) or -1 (representing counter-clockwise/backward) along a circular track of size M.

Starting at position 0, you must process the list of actions sequentially. Your task is to calculate the total distance traveled across the track. The distance is defined as the absolute number of steps moved, regardless of the direction. However, if the movement causes the position to wrap around the track, you must account for the specific track boundaries.

Given the track size M (an integer) and an array of actions (a list of pairs), return the total units moved.

Function Signature

def calculate_total_distance(M: int, actions: List[Tuple[int, int]]) -> int:

Constraints

• M >= 1
• actions length = 0

Examples

Example 1:

• Input: M = 10, actions = [(1, 3), (-1, 2), (1, 6)]
• Output: 11
• Explanation: Start at 0. Move +3 (pos 3), move -2 (pos 1), move +6 (pos 7). Total distance: 3 + 2 + 6 = 11.

Example 2:

• Input: M = 5, actions = [(1, 7)]
• Output: 7
• Explanation: Moving 7 steps on a track of size 5 results in a net position change, but the total distance moved remains 7.

Edge Cases

• What happens if M=1?
• What happens if the steps are 0?
• What happens if the total steps move multiple full circles?