图的两个顶点之间的最小边数
给定一个具有 N 个顶点和 M 个边的无向图 G(V, E)。我们需要找到给定顶点对（u，v）之间的最小边数。
例子：
Input : For given graph G. Find minimum number
of edges between (1, 5).
Output : 2
Explanation: (1, 2) and (2, 5) are the only
edges resulting into shortest path between 1
and 5.这个想法是从给定的输入顶点（u）之一执行 BFS。在 BFS 时，维护一个 distance[n] 数组并将所有顶点初始化为零。现在，假设在 BFS 期间，顶点 x 从队列中弹出，我们将所有相邻的未访问顶点 (i) 推回队列，同时我们应该更新distance[i] = distance[x] + 1; .
最后，distance[v] 给出了 u 和 v 之间的最小边数。
算法：
int minEdgeBFS(int u, int v, int n)
{
// visited[n] for keeping track of visited
// node in BFS
bool visited[n] = {0};
// Initialize distances as 0
int distance[n] = {0};
// queue to do BFS.
queue Q;
distance[u] = 0;
Q.push(u);
visited[u] = true;
while (!Q.empty())
{
int x = Q.front();
Q.pop();
for (int i=0; iC++
// C++ program to find minimum edge
// between given two vertex of Graph
#include
using namespace std;
// function for finding minimum no. of edge
// using BFS
int minEdgeBFS(vector edges[], int u,
int v, int n)
{
// visited[n] for keeping track of visited
// node in BFS
vector visited(n, 0);
// Initialize distances as 0
vector distance(n, 0);
// queue to do BFS.
queue Q;
distance[u] = 0;
Q.push(u);
visited[u] = true;
while (!Q.empty())
{
int x = Q.front();
Q.pop();
for (int i=0; i edges[], int u, int v)
{
edges[u].push_back(v);
edges[v].push_back(u);
}
// Driver function
int main()
{
// To store adjacency list of graph
int n = 9;
vector edges[9];
addEdge(edges, 0, 1);
addEdge(edges, 0, 7);
addEdge(edges, 1, 7);
addEdge(edges, 1, 2);
addEdge(edges, 2, 3);
addEdge(edges, 2, 5);
addEdge(edges, 2, 8);
addEdge(edges, 3, 4);
addEdge(edges, 3, 5);
addEdge(edges, 4, 5);
addEdge(edges, 5, 6);
addEdge(edges, 6, 7);
addEdge(edges, 7, 8);
int u = 0;
int v = 5;
cout << minEdgeBFS(edges, u, v, n);
return 0;
} Java
// Java program to find minimum edge
// between given two vertex of Graph
import java.util.LinkedList;
import java.util.Queue;
import java.util.Vector;
class Test
{
// Method for finding minimum no. of edge
// using BFS
static int minEdgeBFS(Vector edges[], int u,
int v, int n)
{
// visited[n] for keeping track of visited
// node in BFS
Vector visited = new Vector(n);
for (int i = 0; i < n; i++) {
visited.addElement(false);
}
// Initialize distances as 0
Vector distance = new Vector(n);
for (int i = 0; i < n; i++) {
distance.addElement(0);
}
// queue to do BFS.
Queue Q = new LinkedList<>();
distance.setElementAt(0, u);
Q.add(u);
visited.setElementAt(true, u);
while (!Q.isEmpty())
{
int x = Q.peek();
Q.poll();
for (int i=0; i edges[], int u, int v)
{
edges[u].add(v);
edges[v].add(u);
}
// Driver method
public static void main(String args[])
{
// To store adjacency list of graph
int n = 9;
Vector edges[] = new Vector[9];
for (int i = 0; i < edges.length; i++) {
edges[i] = new Vector<>();
}
addEdge(edges, 0, 1);
addEdge(edges, 0, 7);
addEdge(edges, 1, 7);
addEdge(edges, 1, 2);
addEdge(edges, 2, 3);
addEdge(edges, 2, 5);
addEdge(edges, 2, 8);
addEdge(edges, 3, 4);
addEdge(edges, 3, 5);
addEdge(edges, 4, 5);
addEdge(edges, 5, 6);
addEdge(edges, 6, 7);
addEdge(edges, 7, 8);
int u = 0;
int v = 5;
System.out.println(minEdgeBFS(edges, u, v, n));
}
}
// This code is contributed by Gaurav Miglani Python3
# Python3 program to find minimum edge
# between given two vertex of Graph
import queue
# function for finding minimum
# no. of edge using BFS
def minEdgeBFS(edges, u, v, n):
# visited[n] for keeping track
# of visited node in BFS
visited = [0] * n
# Initialize distances as 0
distance = [0] * n
# queue to do BFS.
Q = queue.Queue()
distance[u] = 0
Q.put(u)
visited[u] = True
while (not Q.empty()):
x = Q.get()
for i in range(len(edges[x])):
if (visited[edges[x][i]]):
continue
# update distance for i
distance[edges[x][i]] = distance[x] + 1
Q.put(edges[x][i])
visited[edges[x][i]] = 1
return distance[v]
# function for addition of edge
def addEdge(edges, u, v):
edges[u].append(v)
edges[v].append(u)
# Driver Code
if __name__ == '__main__':
# To store adjacency list of graph
n = 9
edges = [[] for i in range(n)]
addEdge(edges, 0, 1)
addEdge(edges, 0, 7)
addEdge(edges, 1, 7)
addEdge(edges, 1, 2)
addEdge(edges, 2, 3)
addEdge(edges, 2, 5)
addEdge(edges, 2, 8)
addEdge(edges, 3, 4)
addEdge(edges, 3, 5)
addEdge(edges, 4, 5)
addEdge(edges, 5, 6)
addEdge(edges, 6, 7)
addEdge(edges, 7, 8)
u = 0
v = 5
print(minEdgeBFS(edges, u, v, n))
# This code is contributed by PranchalKC#
// C# program to find minimum edge
// between given two vertex of Graph
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
// Method for finding minimum no. of edge
// using BFS
static int minEdgeBFS(ArrayList []edges, int u,
int v, int n)
{
// visited[n] for keeping track of visited
// node in BFS
ArrayList visited = new ArrayList();
for(int i = 0; i < n; i++)
{
visited.Add(false);
}
// Initialize distances as 0
ArrayList distance = new ArrayList();
for(int i = 0; i < n; i++)
{
distance.Add(0);
}
// queue to do BFS.
Queue Q = new Queue();
distance[u] = 0;
Q.Enqueue(u);
visited[u] = true;
while (Q.Count != 0)
{
int x = (int)Q.Dequeue();
for(int i = 0; i < edges[x].Count; i++)
{
if ((bool)visited[(int)edges[x][i]])
continue;
// Update distance for i
distance[(int)edges[x][i]] = (int)distance[x] + 1;
Q.Enqueue((int)edges[x][i]);
visited[(int)edges[x][i]] = true;
}
}
return (int)distance[v];
}
// Method for addition of edge
static void addEdge(ArrayList []edges,
int u, int v)
{
edges[u].Add(v);
edges[v].Add(u);
}
// Driver code
public static void Main(string []args)
{
// To store adjacency list of graph
int n = 9;
ArrayList []edges = new ArrayList[9];
for(int i = 0; i < 9; i++)
{
edges[i] = new ArrayList();
}
addEdge(edges, 0, 1);
addEdge(edges, 0, 7);
addEdge(edges, 1, 7);
addEdge(edges, 1, 2);
addEdge(edges, 2, 3);
addEdge(edges, 2, 5);
addEdge(edges, 2, 8);
addEdge(edges, 3, 4);
addEdge(edges, 3, 5);
addEdge(edges, 4, 5);
addEdge(edges, 5, 6);
addEdge(edges, 6, 7);
addEdge(edges, 7, 8);
int u = 0;
int v = 5;
Console.Write(minEdgeBFS(edges, u, v, n));
}
}
// This code is contributed by rutvik_56Javascript
输出：
3