third

.vs/ProjectSettings.json

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+}

.vs/VSWorkspaceState.json

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Debug/Dijkstra算法.tlog/Dijkstra算法.lastbuildstate

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+Debug|Win32|C:\Visual Studio\Dijkstra算法\|

Dijkstra算法.cpp

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+#include<stdio.h>
+#include<stdlib.h>
+#define MaxNv 100
+#define INFINITY 65535
+#define False -1
+#define True 1
+#define ERROR -1
+
+struct GNode {	//图的结构 
+	int Ne;
+	int Nv;
+	int G[MaxNv][MaxNv];
+};
+typedef struct GNode* MGraph;
+
+MGraph CreateGraph(int NvNum) {	//初始化图 
+	int i, j;
+	MGraph Graph = (MGraph)malloc(sizeof(struct GNode));
+	Graph->Nv = NvNum;
+	Graph->Ne = 0;
+	for (i = 0; i < Graph->Nv; i++)
+		for (j = 0; j < Graph->Nv; j++) {
+				Graph->G[i][j] = INFINITY;
+		}
+	return Graph;
+}
+
+MGraph InsertEdge(MGraph Graph, int V1, int V2,int Weight) {	//插入边 
+	Graph->G[V1][V2] = Graph->G[V2][V1] = Weight;
+	return Graph;
+}
+
+MGraph BuildGraph() {		//建图函数 
+	int NvNum, NeNum,Weight;
+	int i;
+	scanf_s("%d", &NvNum);
+	MGraph Graph = CreateGraph(NvNum);
+	scanf_s("%d", &NeNum);
+	Graph->Ne = NeNum;
+	int V1, V2;
+	for (i = 0; i < Graph->Ne; i++) {
+		scanf_s("%d%d%d", &V1, &V2, &Weight);
+		InsertEdge(Graph, V1, V2, Weight);
+	}
+	return Graph;
+}
+
+int FindMin(MGraph Graph, int dist[], int collected[]) {	//寻找未被收录且dist最小的点的下标
+	int i, min = INFINITY, vertex;
+	for (i = 0; i < Graph->Nv; i++) {
+		if (collected[i]==False&&dist[i] < min) {
+			min = dist[i];
+			vertex = i;
+		}
+	}
+	if (min < INFINITY)
+		return vertex;
+	else
+		return ERROR;
+}
+
+bool Dijkstra(MGraph Graph, int dist[], int path[], int s) {
+	int v, w;
+	int collected[MaxNv];
+	for (v = 0; v < Graph->Nv; v++) {
+		dist[v] = Graph->G[s][v];	//初始化所有点的dist为该点到起始点的权值
+		//初始化所有点的path
+		if (Graph->G[s][v] < INFINITY)	//若与起点之间有边
+			path[v] = s;				//则path为起始点下标表示父节点
+		else				//若与起始点之间没有边
+			path[v] = -1;	//则path为-1表示没有父节点
+		collected[v] = False;	//初始化所有点都未被收录
+	}
+	collected[s] = True;		//将起始点收录
+	dist[s] = 0;				//初始化时为INFINITY，这里再初始化为0
+	while (1) {					//开始算法循环
+		v = FindMin(Graph, dist, collected);	//在未收录的点里面找dist最小的
+		if (v == ERROR)							//该连通分支找完返回ERROR
+			break;
+		collected[v] = True;					//收录该点
+		for (w = 0; w < Graph->Nv; w++) {					//对于所有点
+			if (dist[v] + Graph->G[v][w] < dist[w]) {		//若点v的收录可使其他点dist减小
+				dist[w] = dist[v] + Graph->G[v][w];			//则更新dist
+				path[w] = v;
+			}
+		}
+	}
+	return true;
+}
+
+int main(void) {
+	int dist[MaxNv], path[MaxNv], tmp[MaxNv];
+	int i = 1, v, j;
+	MGraph Graph = BuildGraph();
+	Dijkstra(Graph, dist, path, 0);
+	scanf_s("%d", &v);
+	tmp[0] = v;
+	while (1) {			//逆序输出路径
+		v = path[v];
+		tmp[i] = v;
+		i++;
+		if (path[v] == -1)
+			break;
+	}
+	for (j = i-1; j >=0; j--) {
+		printf("%d ", tmp[j]);
+	}
+	return 0;
+}
+/*
+10
+17
+0 1 2
+0 3 5
+1 2 5
+1 3 2
+2 4 8
+2 5 4
+3 5 4
+3 6 2
+4 5 2
+6 5 3
+4 7 5
+5 7 9
+5 8 6
+6 8 7
+7 8 3
+7 9 4
+8 9 8
+P236 图
+*/

Dijkstra算法.sln

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