In the city of Merzbow, there is a strange parking lot where two autos (A) should be parked between two cars (C), and a bike (B) should be parked between two autos. The parking pattern strictly follows:
C A B A C A B A C ...
You are given the following vehicle capacities:
Each car can accommodate 5 passengers.
Each auto can accommodate 3 passengers.
Each bike can accommodate 2 passengers.
The parking lot is a straight line that is completely full, and cars are parked at both ends of the lot.
Determine:
The total number of vehicles in the parking lot.
The total number of passengers who can be seated in all the vehicles.
Input Format:
A single positive integer N denoting the number of cars in the parking lot.
Output Format:
First line: A positive integer representing the total number of vehicles.
Second line: A positive integer representing the total number of passengers.
The parking sequence follows a strict repeating block of vehicles inserted after the very first car.
This means for every new car added to the lot after the first one, we also add exactly two autos and one bike.
By grouping these vehicles based on the number of cars, we can calculate the totals instantly using a direct mathematical formula.
Approach
1. Finding the Vehicle Counts
If there are N cars, the number of gaps between those cars is exactly N - 1. The problem states the pattern between any two cars is always A B A (two autos and one bike). Therefore, the total number of autos is 2 * (N - 1) and the total number of bikes is 1 * (N - 1).
2. Applying the Capacities
Once we know the exact count of each vehicle type, calculating the answers is just straightforward arithmetic.
Total vehicles is simply N + autos + bikes.
Total passengers is (N * 5) + (autos* 3) + (bikes* 2).
Because we boil this down to a formula, we completely avoid loops, making our solution as fast as mathematically possible!
function calculateParkingLot(N):
// Calculate the count of each vehicle type between the cars
autos = 2 * (N - 1)
bikes = 1 * (N - 1)
totalVehicles = N + autos + bikes
totalPassengers = (N * 5) + (autos * 3) + (bikes * 2)
print(totalVehicles)
print(totalPassengers)
Time Complexity
Time: O(1) - The entire solution relies on a direct mathematical formula, executing instantly regardless of how large N gets.
Space: O(1) - Only a few variables are needed to store the intermediate calculations.
Problem 1 -: The Strange Parking Lot Solution
Overview
Approach
1. Finding the Vehicle Counts
If there are N cars, the number of gaps between those cars is exactly N - 1. The problem states the pattern between any two cars is always A B A (two autos and one bike). Therefore, the total number of autos is 2 * (N - 1) and the total number of bikes is 1 * (N - 1).
2. Applying the Capacities
Once we know the exact count of each vehicle type, calculating the answers is just straightforward arithmetic.
Because we boil this down to a formula, we completely avoid loops, making our solution as fast as mathematically possible!
Time Complexity