Reorder Routes to Make All Paths Lead to the City Zero
There are n cities numbered from 0 to n - 1 and n - 1 roads such that there is only one way to travel between two different cities; this network forms a tree. Last year, the ministry of transport decided to orient the roads in one direction because they are too narrow.
Roads are represented by connections, where connections[i] = [ai, bi] represents a road from city ai to city bi.
This year, there will be a big event in the capital, city 0, and many people want to travel to this city.
Your task is to reorient some roads such that each city can visit city 0. Return the minimum number of edges changed.
It is guaranteed that each city can reach city 0 after reordering.
Example 1
Input
n = 6, connections = [[0,1],[1,3],[2,3],[4,0],[4,5]]Output
3Changing the direction of 3 edges allows every city to reach city 0.
Example 2
Input
n = 5, connections = [[1,0],[1,2],[3,2],[3,4]]Output
2Changing the direction of 2 edges allows every city to reach city 0.
Constraints
- 2 <= n <= 5 * 10^4
- connections.length == n - 1
- connections[i].length == 2
- 0 <= ai, bi <= n - 1
- ai != bi