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數據結構----單源最短路徑Dijkstra

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原理：參考趣學數據結構

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代碼：

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stack.h 棧代碼

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#pragma once #include<stdio.h> #define maxSize 100 typedef struct stack {int * base;int * top; }stack; bool init(stack & Stack) {//棧的初始化Stack.base = new int[maxSize];if (!Stack.base) {return false;}Stack.top = Stack.base;return true; } bool push(stack & Stack,int e) {//入棧if (Stack.top - Stack.base == maxSize) {//滿棧，不能再插入return false;}*(Stack.top) = e;Stack.top++;return true; } bool pop(stack & Stack, int &e) {//出棧if (Stack.base == Stack.top) {//棧空return false;}Stack.top--;e = *(Stack.top);return true; } int getTop(stack &Stack) {if (Stack.base == Stack.top) {//棧空return -1;}return *(Stack.top - 1); } void printStack(stack Stack) {//遍歷棧中的元素while (Stack.base != Stack.top) {printf("%d ", *(Stack.top - 1));Stack.top--;} } bool empty(stack Stack) {//棧空的判斷if (Stack.base == Stack.top) {return true;}return false; } void testStack() {//測試棧是否有問題stack Stack;init(Stack);int value;while (1) {scanf_s("%d", &value);if (value == -1) {break;}push(Stack, value);}printStack(Stack); }

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dijkstra.cpp

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#include<stdio.h> #include<stdlib.h> #include"stack.h" #define N 100 #define elemType int //const int MAX_INT = (1 << 31) - 1; //const int MAX_INT = 0X7fffffff; #define INF (((unsigned int)(-1)) >> 1) typedef struct GraphMatrix {elemType vNode[N][N];int vNum, eNum; }GraphMatrix; void findPath(GraphMatrix G, int dist[], int p[], int u, stack &Stack);//聲明 void initGMaxtix(GraphMatrix &G) {//初始化鄰接矩陣printf("輸入頂點數和邊數\n");scanf_s("%d%d", &G.vNum, &G.eNum);for (int i = 0; i < G.vNum; i++) {//初始化鄰接矩陣for (int j = 0; j < G.vNum; j++) {G.vNode[i][j] = G.vNode[j][i]=INF;}}printf("輸入頂點v1到頂點v2和其邊的權重\n");for (int i = 0; i < G.eNum; i++ ) {int v1, v2,weights;scanf_s("%d%d%d", &v1, &v2,&weights);G.vNode[v1][v2] = G.vNode[v2][v1] = weights;} } void print4(GraphMatrix G) {printf("鄰接矩陣如下:\n");for (int i = 0; i < G.vNum; i++) {for (int j = 0; j < G.vNum; j++) {printf("%d ", G.vNode[i][j]);}printf("\n");} } void print41(int result[], int length) {for (int i = 0; i < length; i++) {printf("%d ", result[i]);}printf("\n"); } void Dijkstra(GraphMatrix G, int u) {//單源最短路徑，分為兩個集合求解bool flag[N];//標識是否加入第一個頂點集int dist[N], p[N];//分別為單源點到其他點的距離和這段距離所經過的那些頂點的記錄數組pp[u] = -1;dist[u] = 0;for (int i = 0; i < G.vNum; i++) {flag[i] = false;//每一個頂點都默認沒有訪問dist[i] = G.vNode[u][i];if (G.vNode[u][i]==INF) {//對距離數組和記錄數組初始化p[i] = -1;}else {p[i] = u;}}flag[u] = true;for (int i = 0; i < G.vNum - 1; i++) {//G.vNum-1次連接//找沒有被訪問的最小元素int min=INF;int t=u;for (int j = 0; j < G.vNum; j++) {if (!flag[j] && dist[j] < min) {t = j;min = dist[j];}}if (t == u) {break;//全部頂點加入到第一個頂點集合中}flag[t] = true;//加入到第一個頂點集合中//更新距離數組for (int j = 0; j < G.vNum; j++) {if (!flag[j] && dist[t] + G.vNode[t][j] < dist[j]) {dist[j] = dist[t] + G.vNode[t][j];p[j] = t;}}}//print41(dist, G.vNum);stack Stack;init(Stack);printf("輸出單源最短路徑的最優方案\n");findPath(G, dist, p, u, Stack); } void findPath(GraphMatrix G,int dist[], int p[],int u,stack &Stack) {for (int i = 0; i < G.vNum; i++) {if (p[i]==-1) {//起點到起點printf("%d---%d不可達!\n",u,i);continue;}push(Stack, i);int x = p[i];while (x != -1) {//入棧查找路徑push(Stack, x);x = p[x];}int e;while (!empty(Stack)) {//出棧遍歷路徑printf("%d", getTop(Stack));pop(Stack, e);if (Stack.top - Stack.base >= 1) {printf("---");}}printf(" 這段路徑的距離為:%d\n", dist[i]);} } int main() {GraphMatrix G;initGMaxtix(G);print4(G);printf("\n");Dijkstra(G,0);system("pause");return 0; }

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測試截圖：

時間復雜度為O(n)，空間復雜度為O(n)!

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