# Reorder Routes to Make All Paths Lead to the City

Category

Graphs - DFS

Checkbox

Checkbox

Difficulty

Medium

Index

45

Key Ideas

The key idea to solve this problem is to perform a topological sort on the graph and then reverse the order of the sorted paths to ensure that all routes lead to the city.

Problem Number

1466

Problem Summary

This problem requires reordering the routes in a directed graph such that all paths lead to the city. The goal is to find the minimum number of routes to reorder. A key pitfall to watch out for is ensuring that the graph is properly constructed and considering the efficiency of the algorithm used to solve the problem.

Solution Summary

The best solution to solve this problem is to use depth-first search (DFS) to reorder the routes. First, create a graph to represent the routes using adjacency lists. Then, perform DFS starting from the city that all paths should lead to. During the DFS traversal, mark the visited cities and add them to the result list in reverse order. Finally, append the remaining unvisited cities to the result list. This solution ensures that all paths will lead to the desired city by reordering the routes based on the DFS traversal.

Tags

Depth-First Search

Breadth-First Search

Graph