找出無向圖中所有的環的演算法
阿新 • • 發佈：2019-02-03
本文給出了一個找到無向圖中所有的環的遞迴演算法，該演算法是基於DFS（深度優先搜尋）的，大概的思路是：在深度優先搜尋無向圖的過程中，當遇到起始點的時候，會認定為出現環（在本文中只是找出了無向圖中所有的長度大於等於3的環（長度為1和2的環沒有意思），所以在深搜的過程中，當遇到的是起始點的時候，還需要進行判斷是否是環），當確定是出現了環之後，根據是否在遇到環之前的那個點還有其他的路徑，來決定是進一步的進行深度優先搜尋還是進行回退，在進行深度優先搜尋的過程中，將訪問過的節點標記，若當前的節點無路可走（不能進行深度優先搜尋了），在回退的過程中，將標記取消。演算法的過程就下圖做簡單的介紹：
假設以1為起點進行深度優先搜尋，經過訪問2，3，4，5，6會得到一個環，因為節點6還有下一條路徑可走，此時程式會進入7，8，9，10這些點進行深度優先搜尋，但是都再沒有回到節點1，於是程式會一層一層的在從7，8，9，10（不一定是這樣的順序）這些點退出來。退至節點6，5，4直到3節點(將6，5，4的標記全部取消)找到了下一條路徑5，在走到6，此時又發現了另一條環1->2->3->5->6->1.以此類推。
主要程式碼如下：
<span style="font-family:Courier New;font-size:12px;">void DFS(int startVertax) { setVisitedFlag(startVertax, 1); int nextVertax; push_stack(&loop_stack, startVertax); nextVertax = firstAdjacentVertax(startVertax); innerStep++; for( ; ; ) { if( nextVertax != -1 ) { if( visitedFlag[nextVertax] == 1 && nextVertax == heap && innerStep == 2 ) //從1到2，又從2到1，這不算是一個環 { nextVertax = nextAdjacentVertax(startVertax, nextVertax); continue; } else if( visitedFlag[nextVertax] == 1 && nextVertax == heap && innerStep != 2 ) //找到了一個環 { printf("loop length: %d\t", innerStep); print_stack(loop_stack); nextVertax = nextAdjacentVertax(startVertax, nextVertax); continue; } else if( visitedFlag[nextVertax] == 0 )<span style="white-space:pre"> </span>//進行遞迴 { DFS(nextVertax); } if( isRecall == 1 ) //進行回退 { innerStep--; temp = nextVertax; nextVertax = nextAdjacentVertax(startVertax, nextVertax); pop_stack(&loop_stack, &pop_value); setVisitedFlag(temp, 0); isRecall = 0; continue; } nextVertax = nextAdjacentVertax(startVertax, nextVertax); } else if( nextVertax == -1 ) { isRecall = 1; break; } } } void DFSTraverse() { initialVisitedFlagArray(); initializeSequenceStack(&loop_stack); int i; for( heap = 1; heap <= vertax_size; heap++ ) { for( i = 1; i <= vertax_size; i++ ) { visitedFlag[i] = 0; } /* printf("print the visitedFlag array: "); for( i = 1; i <= vertax_size; i++ ) { printf("%d ", visitedFlag[i]); } printf("\n"); */ if( visitedFlag[heap] == 0 ) { printf("\n-------------------the loop start and end with %d----------------\n", heap); clear_stack(&loop_stack); innerStep = 0; isRecall = 0; DFS(heap); } } }</span>
對於上圖的程式的執行結果為：（需要注意的是：對於無向圖中的每一條環會出現兩次，因為是有方向的：順時針和逆時針）。
完整程式碼
<span style="font-family:Courier New;">#include<stdio.h> #include<stdlib.h> #include<string.h> #include<math.h> int eage_size; int vertax_size; char filename_eage[200]; char filename_vertax[200]; int** eage_set; char** vertax_set; int** adjacentMatrix; int* visitedFlag; typedef struct SequenceStack { int* base; int* top; int stackSize; }SequenceStack; void readEageDataFromFile(); void readVertaxDataFromFile(); void createAdjacentMatrix(); void DFS(int); void DFSTraverse(); void initialVisitedFlagArray(); void printVisitedVertax(int); void setVisitedFlag(int,int); int firstAdjacentVertax(int); int nextAdjacentVertax(int,int); void initializeSequenceStack(SequenceStack*); void pop_stack(SequenceStack*, int*); void push_stack(SequenceStack*, int); void print_stack(SequenceStack); int empty_stack(SequenceStack); void clear_stack(SequenceStack*); void test_stack(); int main(int argc, char* argv[]) { if( argc != 5 ) { printf("\tThis algorithm require 3 parameters" "\n\t\t1:the size of eage" "\n\t\t2:the filename contain eage-data" "\n\t\t3:the size of vertax" "\n\t\t4:the filename contain vertax-data"); exit(0); } eage_size = atoi(argv[1]); strcat(filename_eage, argv[2]); vertax_size = atoi(argv[3]); strcat(filename_vertax, argv[4]); printf("eage_size : %d, vertax_size : %d, filename-eage : %s, filename-vertax : %s\n", eage_size, vertax_size, filename_eage, filename_vertax); readEageDataFromFile(); readVertaxDataFromFile(); createAdjacentMatrix(); DFSTraverse(); //test_stack(); return 0; } void readEageDataFromFile() { FILE* f_read; if( NULL == (f_read = fopen(filename_eage, "r"))) { printf("open file(%s) error!\n", filename_eage); exit(0); } //create dynamic array for storing original data form file @filename eage_set = (int**)malloc(sizeof(int*) * (eage_size + 1)); if( !eage_set ) { printf("malloc error: eage_set**\n"); exit(0); } int i; for( i = 1; i <= eage_size; i++ ) { eage_set[i] = (int*)malloc(sizeof(int) * (2 + 1)); if( !eage_set[i] ) { printf("eage_set[%d] malloc error", i); exit(0); } } //read original data from file for( i = 1; i <= eage_size; i++ ) { if( 2 != fscanf(f_read, "%d %d", &eage_set[i][1], &eage_set[i][2])) { printf("fscanf error： %d\n", i); exit(0); } } //test printf("\n show the origin data from file\n"); for( i = 1; i <= eage_size; i++ ) { printf("%d\t%d\n", eage_set[i][1], eage_set[i][2]); } printf("\n"); //test END } void readVertaxDataFromFile() { //create the dynamic array for saving vertax-set information vertax_set = (char**)malloc(sizeof(char*) * (vertax_size + 1)); if( !vertax_set ) { printf("vertax_set malloc error"); exit(0); } int i; for( i = 1; i <= vertax_size; i++ ) { vertax_set[i] = (char*)malloc(sizeof(char) * (20 + 1)); if( !vertax_set[i] ) { printf("vertax_set[%d] malloc error"); exit(0); } } //open file FILE* f_read; if( NULL == (f_read = fopen(filename_vertax, "r"))) { printf("open file(%s) error", filename_vertax); exit(0); } //read vertax-set information for( i = 1; i <= vertax_size; i++ ) { if( 1 != fscanf(f_read, "%s ", vertax_set[i]) ) { printf("fscanf vertax_set[%d] error", i); exit(0); } } //test for( i = 1; i <= vertax_size; i++ ) { printf("%s\n", vertax_set[i]); } printf("\n"); //test END } void createAdjacentMatrix() { //create the dynamic array for saving adjcaent matrix adjacentMatrix = (int**)malloc(sizeof(int*) * (vertax_size + 1)); if( !adjacentMatrix ) { printf("adjacentMatrix** malloc error"); exit(0); } int i; for( i = 1; i <= vertax_size; i++ ) { adjacentMatrix[i] = (int*)malloc(sizeof(int) * (vertax_size + 1)); if( !adjacentMatrix[i] ) { printf("adjacentMatrix[%d] malloc error"); exit(0); } } //initial the value of adjacentMatrix int j; for( i = 1; i <= vertax_size; i++ ) { for( j = 1; j <= vertax_size; j++ ) { adjacentMatrix[i][j] = 0; } } //set the value for adjacentMatrix for( i = 1; i <= eage_size; i++ ) { adjacentMatrix[eage_set[i][1]][eage_set[i][2]] = 1; adjacentMatrix[eage_set[i][2]][eage_set[i][1]] = 1; } //test printf("\n show the information about adjacent matrix: \n"); for( i = 1; i <= vertax_size; i++ ) { for( j = 1; j <= vertax_size; j++ ) { printf("%d ", adjacentMatrix[i][j]); } printf("\n"); } //test END } int loop_count; int heap; int innerStep = 0; int temp; int isRecall; SequenceStack loop_stack; int pop_value; void DFS(int startVertax) { setVisitedFlag(startVertax, 1); int nextVertax; push_stack(&loop_stack, startVertax); nextVertax = firstAdjacentVertax(startVertax); innerStep++; for( ; ; ) { if( nextVertax != -1 ) { if( visitedFlag[nextVertax] == 1 && nextVertax == heap && innerStep == 2 ) { nextVertax = nextAdjacentVertax(startVertax, nextVertax); continue; } else if( visitedFlag[nextVertax] == 1 && nextVertax == heap && innerStep != 2 ) { print_stack(loop_stack); nextVertax = nextAdjacentVertax(startVertax, nextVertax); continue; } else if( visitedFlag[nextVertax] == 0 ) { DFS(nextVertax); } if( isRecall == 1 ) { innerStep--; temp = nextVertax; nextVertax = nextAdjacentVertax(startVertax, nextVertax); pop_stack(&loop_stack, &pop_value); setVisitedFlag(temp, 0); isRecall = 0; continue; } nextVertax = nextAdjacentVertax(startVertax, nextVertax); } else if( nextVertax == -1 ) { isRecall = 1; break; } } } void DFSTraverse() { initialVisitedFlagArray(); initializeSequenceStack(&loop_stack); int i; for( heap = 1; heap <= vertax_size; heap++ ) { for( i = 1; i <= vertax_size; i++ ) { visitedFlag[i] = 0; } /* printf("print the visitedFlag array: "); for( i = 1; i <= vertax_size; i++ ) { printf("%d ", visitedFlag[i]); } printf("\n"); */ if( visitedFlag[heap] == 0 ) { printf("\n-------------------the loop start and end with %d----------------\n", heap); clear_stack(&loop_stack); innerStep = 0; //printf("isRecall : %d, findLoop : %d, hasOthers : %d\n", isRecall, findLoop, hasOthers); isRecall = 0; DFS(heap); } } } void initialVisitedFlagArray() { visitedFlag = (int*)malloc(sizeof(int) * (vertax_size + 1)); if( !visitedFlag ) { printf("visitedFlag* malloc error"); exit(0); } int i; for( i = 1; i <= vertax_size; i++ ) visitedFlag[i] = 0; } void printVisitedVertax(int vertaxID) { printf("visited: %d \n", vertaxID); } void setVisitedFlag(int vertaxID, int value) { visitedFlag[vertaxID] = value; } int firstAdjacentVertax(int vertaxID) { int i; for( i = 1; i <= vertax_size; i++ ) { if( adjacentMatrix[vertaxID][i] == 1 ) return i; } return -1; } int nextAdjacentVertax(int vertaxID, int nextVertaxID) { int i; for( i = nextVertaxID + 1; i <= vertax_size; i++ ) { if( adjacentMatrix[vertaxID][i] == 1 ) return i; } return -1; } void initializeSequenceStack(SequenceStack* stack) { stack->base = (int*)malloc(sizeof(int) * (vertax_size + 1)); if( !stack->base ) { printf("Sequence stack malloc error!\n"); exit(0); } stack->top = stack->base; stack->stackSize = vertax_size; } void pop_stack(SequenceStack* stack, int* value) { if( empty_stack(*stack) == 1 ) { printf("stack is empty , can not to pop!\n"); exit(0); } *value = *(--(stack->top)); } void push_stack(SequenceStack* stack, int value) { *(stack->top) = value; (stack->top)++; } int empty_stack(SequenceStack stack) { return stack.top == stack.base ? 1 : 0; } void print_stack(SequenceStack stack) { int temp = *(stack.base); while( stack.top != stack.base ) { printf("%d->", *((stack.base)++)); } printf("%d\n", temp); } void clear_stack(SequenceStack* stack) { stack->top = stack->base; }</span>