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Bus Routes

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program to solve the Bus Routes problem. You are given an array `routes` where `routes[i]` is an array of bus stops on the i-th bus route. You start at the bus stop `source` and want to go to the bus stop `target`. Return the least number of buses you must take to travel from `source` to `target`. Return -1 if it is not possible to reach the destination.

Example 1
    
  
  • Input: routes = [[1,2,7],[3,6,7]], source = 1, target = 6
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  • Output: 2
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  • Explanation: 
      
      
    • Start at bus stop 1.
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    • Take the first bus route to bus stop 7.
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    • Take the second bus route to bus stop 6.
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    • This requires a minimum of 2 buses.
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    •
Example 2
    
  
  • Input: routes = [[7,12,15],[4,5,7],[6,15,19],[2,3,19]], source = 15, target = 12
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  • Output: -1
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  • Explanation: 
      
      
    • You cannot reach bus stop 12 from bus stop 15 with the given routes.
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    • Bus stop 15 is on routes 0 and 2, but neither of these routes contains bus stop 12.
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Constraints
    
  
  • 1 ≤ routes.length ≤ 500
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  • 1 ≤ routes[i].length ≤ 100
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  • All values in routes[i] are unique
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  • 0 ≤ routes[i][j] < 10^6
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  • 0 ≤ source, target < 10^6
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  • Time Complexity: O(N * M) where N is number of routes and M is maximum number of stops in a route
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  • Space Complexity: O(N + S) where S is the total number of stops
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GraphAlgorithmsCapgeminiPhillips
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Hint
Solution

Solution Hints

    
  
  • Create a graph that maps each bus stop to all bus routes that include this stop
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  • Use BFS to find the shortest path from source to target
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  • Keep track of visited routes to avoid cycles
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  • Count the number of different buses needed
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  • Return -1 if target cannot be reached
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Steps to solve by this approach:

 Step 1: Check if source and target are the same - if so, return 0.
 Step 2: Create a mapping from each bus stop to all the routes that include it.
 Step 3: Use BFS to find the shortest path, starting from the source stop.
 Step 4: For each stop, explore all connected routes that haven't been visited yet.
 Step 5: For each route, explore all stops that haven't been visited yet.
 Step 6: If target is found, return the number of buses taken plus 1.
 Step 7: If the queue becomes empty without finding the target, return -1.

Submitted Code :