Zomato OA 2022 - Traffic Vicinity Calculation
Somewhere, at some point in time, there is/will be a vehicular traveling system where 1 Kilometer is the basic unit of traversal. A vehicle can either stay at rest or travel a distance which is a multiple of 1 Km, i.e., distances like 2, 3, 4, 10, and 35 Km are valid, but distances like 2.5, 6.34, and 0.25 Km are invalid.
During the age of this system, there is a traffic policeman who stands at the intersection of 4 roads. Due to development in the city, a few barriers are placed on some of the roads at certain distances from the intersection point.
Measurements are based on Cartesian coordinates, where each unit represents a kilometer. You enter into the system and are provided with the coordinates of the intersection point, the maximum north distance a vehicle can cover, the maximum eastern distance a vehicle can cover, and the coordinates of the barriers.
You have to determine the sum of the total kilometers in which the policeman has vicinity.
Example:
- The coordinate of the intersection point: (4, 3)
- The maximum north distance: 8 Km
- The maximum east distance: 8 Km
- Coordinates of barriers: (1, 3), (4, 6), (5, 3)
Input Format
- First line: Two integers denoting maximum north and east distance.
- Second line: Two integers denoting the coordinates of the intersection.
- Third line: An integer 'k' denoting the number of barriers.
- Next line: Coordinates of barriers.
Output Format
- An integer denoting the sum of the kilometers in which the police officer has his vicinity.
Constraints
- 1 <= north distance, east distance <= 10000
- (0, 0) <= coordinates of intersection <= (10000, 10000)
- 1 <= number of barriers <= 1000
- (0, 0) <= coordinates of barriers <= (10000, 10000)
Example
Sample Input:
8 8
4 3
3
1 3 4 6 5 3