贝尔曼福特算法,分别用C语言，C++,java,python编写出来

贝尔曼福特算法是求解单元最短路径问题的一种算法，由理查德贝尔曼和莱斯特福特创立的。有时候这种算法也被称为Moore-Bellman-ford算法，因为Edward F . Moore也为这个算法的发展做出了贡献。

它的原理是对图进行|V|-1次松弛操作，得到所有可能的最短路径。其优于迪克斯彻算法的方面是边的权值可以为负数、实现简单，缺点是时间复杂度过高，高达O(|V||E|）。但算法可以进行若干种优化，提高了效率。

贝尔曼福特算法,分别用C语言，C++,java,python编写出来
下面是贝尔曼福特算法（Bellman-Ford Algorithm）的不同语言实现示例：
1. C语言：

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
struct Edge {
int src, dest, weight;
};
struct Graph {
int V, E;
struct Edge* edge;
};
struct Graph* createGraph(int V, int E) {
struct Graph* graph = (struct Graph*)malloc(sizeof(struct Graph));
graph->V = V;
graph->E = E;
graph->edge = (struct Edge*)malloc(E * sizeof(struct Edge));
return graph;
}
void BellmanFord(struct Graph* graph, int src) {
int V = graph->V;
int E = graph->E;
int dist[V];
for (int i = 0; i < V; i++)
dist[i] = INT_MAX;
dist[src] = 0;
for (int i = 1; i <= V – 1; i++) {
for (int j = 0; j < E; j++) {
int u = graph->edge[j].src;
int v = graph->edge[j].dest;
int weight = graph->edge[j].weight;
if (dist[u] != INT_MAX && dist[u] + weight < dist[v])
dist[v] = dist[u] + weight;
}
}
for (int i = 0; i < E; i++) {
int u = graph->edge[i].src;
int v = graph->edge[i].dest;
int weight = graph->edge[i].weight;
if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {
printf(“Graph contains negative weight cycle\n”);
return;
}
}
printf(“Vertex\tDistance from Source\n”);
for (int i = 0; i < V; i++)
printf(“%d\t%d\n”, i, dist[i]);
}

2. C++:

#include <iostream>
#include <climits>
#include <vector>
struct Edge {
int src, dest, weight;
};
struct Graph {
int V, E;
std::vector<Edge> edges;
};
void BellmanFord(Graph graph, int src) {
int V = graph.V;
int E = graph.E;
std::vector<int> dist(V, INT_MAX);
dist[src] = 0;
for (int i = 1; i <= V – 1; i++) {
for (int j = 0; j < E; j++) {
int u = graph.edges[j].src;
int v = graph.edges[j].dest;
int weight = graph.edges[j].weight;
if (dist[u] != INT_MAX && dist[u] + weight < dist[v])
dist[v] = dist[u] + weight;
}
}
for (int i = 0; i < E; i++) {
int u = graph.edges[i].src;
int v = graph.edges[i].dest;
int weight = graph.edges[i].weight;
if (dist[u] != INT_MAX && dist[u] + weight < dist[v]) {
std::cout << “Graph contains negative weight cycle\n”;
return;
}
}
std::cout << “Vertex\tDistance from Source\n”;
for (int i = 0; i < V; i++)
std::cout << i << “\t” << dist[i] << “\n”;
}

3. Java:

import java.util.Arrays;
class Edge {
int src, dest, weight;
Edge() {
src = dest = weight = 0;
}
}
class Graph {
int V, E;
Edge[] edges;
Graph(int V, int E) {
this.V = V;
this.E = E;
edges = new Edge[E];
for (int i = 0; i < E; i++)
edges[i] = new Edge();
}
}
class BellmanFord {
void BellmanFord(Graph graph, int src) {
int V = graph.V, E = graph.E;
int[] dist = new int[V];
Arrays.fill(dist, Integer.MAX_VALUE);
dist[src] = 0;
for (int i = 1; i < V; ++i) {
for (int j = 0; j < E; ++j) {
int u = graph.edges[j].src;
int v = graph.edges[j].dest;
int weight = graph.edges[j].weight;
if (dist[u] != Integer.MAX_VALUE && dist[u] + weight < dist[v])
dist[v] = dist[u] + weight;
}
}
for (int j = 0; j < E; ++j) {
int u = graph.edges[j].src;
int v = graph.edges[j].dest;
int weight = graph.edges[j].weight;
if (dist[u] != Integer.MAX_VALUE && dist[u] + weight < dist[v]) {
System.out.println(“Graph contains negative weight cycle”);
return;
}
}
System.out.println(“Vertex\tDistance from Source”);
for (int i = 0; i < V; ++i)
System.out.println(i + “\t” + dist[i]);
}

}

4. Python:

class Edge:
def __init__(self, src, dest, weight):
self.src = src
self.dest = dest
self.weight = weight
class Graph:
def __init__(self, V, E):
self.V = V
self.E = E
self.edges = []
def BellmanFord(graph, src):
V = graph.V
E = graph.E
dist = [float(‘inf’)] * V
dist[src] = 0
for _ in range(V – 1):
for i in range(E):
u = graph.edges[i].src
v = graph.edges[i].dest
weight = graph.edges[i].weight
if dist[u] != float(‘inf’) and dist[u] + weight < dist[v]:
dist[v] = dist[u] + weight
for i in range(E):
u = graph.edges[i].src
v = graph.edges[i].dest
weight = graph.edges[i].weight
if dist[u] != float(‘inf’) and dist[u] + weight < dist[v]:
print(“Graph contains negative weight cycle”)
return
print(“Vertex\tDistance from Source”)
for i in range(V):
print(i, “\t”, dist[i])
V = 5  # Number of vertices
E = 8  # Number of edges

这些示例展示了使用不同编程语言实现贝尔曼福特算法的方式。根据您选择的编程语言，使用相应的示例来实现贝尔曼福特算法。

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