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Distance Traveled by Two Trains together in the same Direction
  • Difficulty Level : Expert
  • Last Updated : 31 Mar, 2021

Given two arrays A[] and B[], each consisting of N integers, containing the speeds of two trains travelling in the same direction, at each time unit, the task is to find the total distance travelled by the two trains together(side by side) throughout the journey.

Examples:

Input: A[] = {1, 2, 3, 2, 4}, B[] = {2, 1, 3, 1, 4} 
Output:
Explanation : 
Since A[1] + A[0] = B[0] + B[1], both the trains have travelled same distance after 2 units of time. 
Now, since A[2] = B[2] = 3, both the trains have traveled this distance together. 
After the 3rd unit of time, the speed of the trains are different. 
Therefore, the total distance traveled by the two trains together is 3.
Input: A[] = {1, 1, 3, 2, 4}, B[] = {3, 1, 2, 1, 4} 
Output:

Approach: 
Follow the steps below to solve the problem:

  • Traverse both the arrays simultaneously.
  • For every ith index check if sum(A[0] .. A[i – 1]) is equal to sum(B[0] .. B[i – 1]) as well as if A[i] and B[i] are equal or not.
  • If the above two conditions are satisfied, add A[i] to the answer.
  • Finally, after traversal of the complete array, print answer.

Below is the implementation of above approach:



C++




// C++ Program to find the distance
// traveled together by the two trains
#include <iostream>
using namespace std;
 
// Function to find the distance traveled together
int calc_distance(int A[], int B[], int n)
{
 
    // Stores distance travelled by A
    int distance_traveled_A = 0;
 
    // Stpres distance travelled by B
    int distance_traveled_B = 0;
 
    // Stores the total distance
    // travelled together
    int answer = 0;
 
    for (int i = 0; i < 5; i++) {
 
        // Sum of distance travelled
        distance_traveled_A += A[i];
        distance_traveled_B += B[i];
 
        // Condition for traveling
        // together
        if ((distance_traveled_A
             == distance_traveled_B)
            && (A[i] == B[i])) {
            answer += A[i];
        }
    }
    return answer;
}
 
// Driver Code
int main()
{
 
    int A[5] = { 1, 2, 3, 2, 4 };
    int B[5] = { 2, 1, 3, 1, 4 };
    int N = sizeof(A) / sizeof(A[0]);
 
    cout << calc_distance(A, B, N);
    return 0;
}

Java




// Java program to find the distance
// traveled together by the two trains
import java.util.*;
import java.lang.*;
 
class GFG{
     
// Function to find the distance traveled together
static int calc_distance(int A[], int B[], int n)
{
 
    // Stores distance travelled by A
    int distance_traveled_A = 0;
 
    // Stpres distance travelled by B
    int distance_traveled_B = 0;
 
    // Stores the total distance
    // travelled together
    int answer = 0;
 
    for(int i = 0; i < 5; i++)
    {
 
        // Sum of distance travelled
        distance_traveled_A += A[i];
        distance_traveled_B += B[i];
 
        // Condition for traveling
        // together
        if ((distance_traveled_A ==
             distance_traveled_B) &&
             (A[i] == B[i]))
        {
            answer += A[i];
        }
    }
    return answer;
}
 
// Driver code
public static void main (String[] args)
{
    int A[] = { 1, 2, 3, 2, 4 };
    int B[] = { 2, 1, 3, 1, 4 };
    int N = A.length;
     
    System.out.println(calc_distance(A, B, N));    
}
}
 
// This code is contributed by offbeat

Python3




# Python3 program to find the distance
# traveled together by the two trains
 
# Function to find the distance
# traveled together
def calc_distance(A, B, n):
 
    # Stores distance travelled by A
    distance_traveled_A = 0
 
    # Stpres distance travelled by B
    distance_traveled_B = 0
 
    # Stores the total distance
    # travelled together
    answer = 0
 
    for i in range(5):
 
        # Sum of distance travelled
        distance_traveled_A += A[i]
        distance_traveled_B += B[i]
 
        # Condition for traveling
        # together
        if ((distance_traveled_A ==
             distance_traveled_B) and
            (A[i] == B[i])):
            answer += A[i]
     
    return answer
 
# Driver Code
A = [ 1, 2, 3, 2, 4 ]
B = [ 2, 1, 3, 1, 4 ]
 
N = len(A)
 
print(calc_distance(A, B, N))
 
# This code is contributed by sanjoy_62

C#




// C# program to find the distance
// traveled together by the two trains
using System;
 
class GFG{
 
// Function to find the distance
// traveled together
static int calc_distance(int []A, int []B,
                         int n)
{
 
    // Stores distance travelled by A
    int distance_traveled_A = 0;
 
    // Stpres distance travelled by B
    int distance_traveled_B = 0;
 
    // Stores the total distance
    // travelled together
    int answer = 0;
 
    for(int i = 0; i < 5; i++)
    {
 
        // Sum of distance travelled
        distance_traveled_A += A[i];
        distance_traveled_B += B[i];
 
        // Condition for traveling
        // together
        if ((distance_traveled_A ==
             distance_traveled_B) &&
             (A[i] == B[i]))
        {
            answer += A[i];
        }
    }
    return answer;
}
 
// Driver Code
public static void Main(string []s)
{
    int []A = { 1, 2, 3, 2, 4 };
    int []B = { 2, 1, 3, 1, 4 };
    int N = A.Length;
 
    Console.Write(calc_distance(A, B, N));
}
}
 
// This code is contributed by rutvik_56

Javascript




<script>
// javascript program to find the distance
// traveled together by the two trains
// Function to find the distance traveled together
    function calc_distance(A , B , n)
    {
 
        // Stores distance travelled by A
        var distance_traveled_A = 0;
 
        // Stpres distance travelled by B
        var distance_traveled_B = 0;
 
        // Stores the total distance
        // travelled together
        var answer = 0;
 
        for (i = 0; i < 5; i++) {
 
            // Sum of distance travelled
            distance_traveled_A += A[i];
            distance_traveled_B += B[i];
 
            // Condition for traveling
            // together
            if ((distance_traveled_A == distance_traveled_B) && (A[i] == B[i])) {
                answer += A[i];
            }
        }
        return answer;
    }
 
    // Driver code
     
        var A = [ 1, 2, 3, 2, 4 ];
        var B = [ 2, 1, 3, 1, 4 ];
        var N = A.length;
 
        document.write(calc_distance(A, B, N));
 
// This code is contributed by aashish1995
</script>
Output: 
3

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

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