資料結構—圖—各種演算法程式碼
#include<iostream>
using namespace std;
const int maxSize = 99999;
int v[maxSize];int main()
{
return 0;
}
/*
圖的儲存結構的定義
float MGraph[5][5];
for (int i = 0; i < 5;++i)
for (int j = 0; j < 5; ++j)
MGraph[i][j] = MAX;*///圖的鏈式儲存結構的結構體定義
typedef struct ArcNode
{
int adjV; //頂點
struct ArcNode* next;
}ArcNode; //分支結構體
typedef struct
{
int data;
int count;
ArcNode* first;
}VNode; //頂點
typedef struct
{
VNode adjList[maxSize];
int n, e;
}AGraph; //圖,兩個變量表示邊和頂點的個數
//圖的深度優先遍歷演算法
void Visit(int a)
{
cout << endl;
}
void DFS(int v, AGraph *G)
{
//圖的標誌陣列,初值為全0,當被訪問過一次就置為1
int visit[maxSize];
visit[v] = 1;
Visit(v);
//取與所選頂點相關的第一條邊
ArcNode *q = G->adjList[v].first;
while (q != NULL)
{
//判斷q所指的邊的另一邊頂點是否被訪問過
if (visit[q->adjV] == 0)
DFS(q->adjV, G);
q = q->next;
}
}//圖的廣度優先遍歷演算法
void BFS(AGraph *G, int v, int visit[maxSize])
{
ArcNode *p;
int que[maxSize], front = 0, rear = 0;
int j;
visit[v] = 1;
Visit(v);
rear = (rear + 1) % maxSize;
//以頂點的陣列下標代替頂點資訊,下標入隊,則相當於對應的頂點入隊
que[rear] = v;
//隊不空,則一直進行迴圈
while (front != rear)
{
front = (front + 1) % maxSize;
j = que[front];
//p定義為a[v]所相鄰的第一條邊
p = G->adjList[j].first;
while (p!=NULL)
{
//檢測邊另一端的頂點是否訪問過
if (visit[p->adjV] == 0)
{
Visit(p->adjV);
visit[p->adjV] = 1;
rear = (rear + 1) % maxSize;
que[rear] = p->adjV;
}
p = p->next;
}
}
}//Prim演算法求最小權值和
//引數分別為頂點個數,圖(應該是[n][n].但編譯器不允許使用引數,先用整數代替,起始頂點,權值和)
void Prim( int n, float MGraph[][50], int v0, float &sum)
{
//同樣應該引數是n和n,編譯器不允許使用變數,先用常量代替
//lowCost代表當前頂點到其他邊的權值,vSet表示已經選中的頂點
int lowCost[50], vSet[50];
int v, k, min;
//陣列初始化
for (int i = 0; i < n; i++)
{
lowCost[i] = MGraph[v0][i];
vSet[i] = 0;
}
v = v0;
vSet[v] = 1;
sum = 0;for (int i = 0; i < n-1; i++)
{
//min初值設定為無窮大
min = INFINITY;
for (int j = 0; j < n; j++)
{
if (vSet[j] == 0 && lowCost[j] < min)
{
min = lowCost[j];
k = j;
}
}
vSet[k] = 1;
v = k;
sum += min;
//新併入了頂點,需要更新每個頂點到其他頂點的lowCost值
for (int j = 0; j < n;++j)
if (vSet[j] == 0 && MGraph[v][j] < lowCost[j])
lowCost[j] = MGraph[v][j];
}
}//Kruscal演算法求最小生成樹
//結構體定義
typedef struct
{
int a, b;
int w;
}Road;
Road road[maxSize];
//通過並查集陣列找根結點int getRoot(int p) //並查集為v[]
{
while (p != v[p])
p = v[p];
return p;
}
void sort(Road road[], int e)
{
//代表road函式按照e排序
cout << endl;
}
void Kruscal(Road road[], int n, int e, int &sum)
{
int a, b;
sum = 0;
for (int i = 0; i < n; ++i)
v[i] = i;
//把邊陣列按照權值排序
sort(road, e);
for (int i = 0; i < e; ++i)
{
a = getRoot(road[i].a);
b = getRoot(road[i].b);
if (a!=b)
{
v[a] = b;
sum += road[i].w;
}}
}//Dijkstra最短路徑
void Dijkstra(int n, float MGraph[][50], int v0, int dist[], int path[])
{
//初始化
int set[maxSize];
int min, v;
for (int i = 0; i < n; i++)
{
dist[i] = MGraph[v0][i];
set[i] = 0;
if (MGraph[v0][i] < INFINITY)
path[i] = v0;
else
path[i] = -1;
}
set[v0] = 1; path[v0] = -1;
//對剩餘頂點進行處理
for (int i = 0; i < n-1; i++)
{
//挑選距離最近的頂點,set值設定為1
min = INFINITY;
for (int j = 0; j < n;++j)
if (set[j] == 0 && dist[j] < min)
{
v = j;
min = dist[j];
}
set[v] = 1;
//更新dist和path陣列
for (int j = 0; j < n; ++j)
{
if (set[j] == 0 && dist[v] + MGraph[v][j] < dist[j])
{
dist[j] = dist[v] + MGraph[v][j];
path[j] = v;
}
}
}
}//Floyd最短路徑
//求A和Path陣列的程式碼
void Floyd(int n, float MGraph[][50], int Path[][50])
{
int i, j, v;
int A[50][50];
for ( i = 0; i < n; i++)
{
for ( j = 0; j < n; j++)
{
A[i][j] = MGraph[i][j];
Path[i][j] = -1;
}
}
for ( v = 0; v < n; v++)
for ( i = 0; i < n; i++)
for ( j = 0; j < n; j++)
if (A[i][j]>A[i][v]+A[v][j])
{
A[i][j] = A[i][v] + A[v][j];
Path[i][j] = v;
}
}
//根據已定義的path陣列尋找最短路徑
//u為路徑起點,v為路徑終點
void printPath(int u, int v, int path[][maxSize])
{
if (path[u][v] == -1)
//直接輸出
cout << endl;
else
{
int mid = path[u][v];
printPath(u, mid, path);
printPath(mid, v, path);
}
}//拓撲排序演算法
int TopSort(AGraph *G)
{
int i, j, n = 0;
int stack[maxSize], top = -1;
ArcNode *p;for ( i = 0; i < G->n; i++)
{
if (G->adjList[i].count == 0)
stack[++top] = i;
}while (top != -1)
{
i = stack[top--];
++n;
std::cout << i << " ";
p = G->adjList[j].first;
while (p != NULL)
{
j = p->adjV;
--(G->adjList[j].count);
if (G->adjList[j].count == 0)
stack[++top] = j;
p = p->next;
}
}if (n == G->n)
return 1;
else
return 0;
}