Taxi Booking

Problem Statement - link #

You are going to book a taxi. There are infinite number of points 1, 2, 3… on the X axis and your current position is cur. There are N Taxis near you, and the position of those taxis is given as an array pos. Where pos[i] denotes the position of the ith taxi. You are also given an array time. Where time[i] denotes the time taken by the ith taxi to cover 1 unit of distance. Your task is to find the minimum time to board a taxi.

Your Task:

You don’t need to read input or print anything. Your task is to complete the function minimumTime() which takes two integers N and cur, and 2 arrays pos, and time as input parameters and returns the minimum time required to board the taxi.

Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)

Examples #

Example 1:

Input:
N = 3, cur = 4
pos = [1, 5, 6]
time = [2, 3, 1]
Output:
2
Explanation:
Total time taken by the 1st taxi will be: (4-1)*2 = 6
Total time taken by the 2nd taxi will be: (5-4)*3 = 3
Total time taken by the 3rd taxi will be: (6-4)*1 = 2
So, the minimum time will be 2 sec.

Example 2:

Input:
N = 2, cur = 1
pos = [1, 6]
time = [10, 3]
Output:
0
Explanation:
Total time taken by the 1st taxi will be: (1-1)*10 = 0
Total time taken by the 2nd taxi will be: (6-1)*3 = 15
So, the minimum time will be 0 sec.

Constraints #

• 1 <= N <= 10^5
• 1 <= cur <= 10^5
• 1 <= pos[i] <= 10^5
• 1 <= time[i] <= 10^5

Solutions #

class Solution {
  public:
    int minimumTime(int N,int cur,vector<int> &pos,vector<int> &time){
        int res = INT_MAX;
        for(int i = 0; i < N; i++) {
            res = min(res, abs(pos[i] - cur) * time[i]);
        }
        return res;
    }
};