Table of contents
Given problem
Suppose we have the a array that describes the order of cars before going to the tunnel.
n = 5 // the number of cars
a = [3,5,2,1,4]
After all cars go out of the tunnel, the order of cars is in the b array.
b = [4,3,2,5,1]
In the tunnel, we have a rule that each car donâ€™t across the other car. So, how many do cars across the other cars?
Constraints of this problem:
 1 <= n <= 10^5
 1 <= a[i] <= 10^5
 1 <= b[i] <= 10^5
Some test cases:
Example 1:
Input: n = 5
a = [3,5,2,1,4]
b = [4,3,2,5,1]
Output: 2
Example 2:
Input: n = 3
a = [1,2,3]
b = [1,2,3]
Output: 0
Example 3:
Input: n = 5
a = [4,3,5,1,2]
b = [4,5,2,1,3]
Output: 3
Example 4:
Input: n = 5
a = [2,5,3,4,1]
b = [4,1,5,2,3]
Output: 3
Using brute force solution
In this problem, we need to start using brute force algorithm.
 Using two loops to iterate elements of two arrays  a, b.

a is the order of cars before going to the tunnel. So a is used as the standard array, and the outer loop.
b is the order of cars after going out of the tunnel. So b is used to compare with a array.
 To maintain the order to cars in a array with b array, we will use prevIndex to mark an index as the position of a[prevIndex  1] car.
public static int countNumberOfCarsPenalized(int n, int[] a, int[] b) {
int prevIndex = 0;
int count = 0;
for (int i = 0; i < n && prevIndex < n; ++i) {
for (int j = prevIndex; j < n && prevIndex < n; ++j) {
if (a[i] == b[j]) {
++count;
prevIndex = j + 1;
break;
}
}
}
return n  count;
}
The complexity of this solution:
 Time complexity: O(n^2)
 Space complexity: O(1)
Using two pointers
To improve the time complexity of the brute force algorithm, we will use two pointers technique to deal with it.
Belows are some description for this solution:
 aPointer, bPointer is pointers that used to iterate the a, b array.
 Use map to save all penalized cars to reduce the time to search car.

When the car as b[bPointer] is belong to the map, skip it, and go to the next car.
Otherwise, compare the car at aPointer and bPointer. If it is equal, increment both aPointer and bPointer. If not, only increment bPointer and save this car in that map to mark it as a penalized car.
public static void main(String[] args) {
// Test case 1
// int n = 5;
// int[] a = {3,5,2,1,4};
// int[] b = {4,3,2,5,1};
// Test case 2
// int n = 3;
// int[] a = {1,2,3};
// int[] b = {1,2,3};
// Test case 3
int n = 5;
int[] a = {4,3,5,1,2};
int[] b = {4,5,2,1,3};
int res = countNumberOfCarsPenalized(n, a, b);
System.out.println(res);
}
public static int countNumberOfCarsPenalized(int n, int[] a, int[] b) {
int aPointer = 0;
int bPointer = 0;
Map<Integer, Integer> penalizedCars = new HashMap<>();
while (aPointer < n  bPointer < n) {
if (penalizedCars.containsKey(a[aPointer])) {
++aPointer;
} else if (a[aPointer] != b[bPointer]) {
penalizedCars.put(b[bPointer], penalizedCars.getOrDefault(b[bPointer], 0));
++bPointer;
} else {
++aPointer;
++bPointer;
}
}
return penalizedCars.size();
}
The complexity of this solution:
 Time complexity: O(n)
 Space complexity: O(1)
Wrapping up
Refer: