do { for (int j = 0; j < v1.size(); j++) { if (j == 0) cout << “( ” << v2[j];否则如果 (j == n - 1) cout << “”,“<< v2[j] << ” )“;否则 cout << “,”<< v2[j];} } while (next_permutation(v2,v2 + n));该程序的时间复杂度是多少
时间: 2023-05-31 14:02:59 浏览: 37
该程序的时间复杂度为 O(n! * n),其中 n 是 v2 的大小,因为它使用了一个嵌套的循环来遍历所有 v2 的排列,而每个排列都需要遍历 v2 一次来输出其中的元素。因此,总共需要执行 n! 次循环,每次循环需要遍历 v2 的所有元素,所以时间复杂度为 O(n! * n)。
相关问题
#include<iostream> #include<queue> using namespace std; #define MAXNUM 100 char visited1[MAXNUM]; typedef struct{ char vexs[MAXNUM]; //顶点 int arcs[MAXNUM][MAXNUM];//边 int vexnum,arcnum; } AMGraph; int LocateVex(AMGraph G,char v){ for(int i = 0; i < G.vexnum; i++){ if(G.vexs[i] == v)return i; } return -1; } int CreateUNG(AMGraph &G){ char v1,v2; cout<<"请输入顶点数和边数:"; cin>>G.vexnum>>G.arcnum; cout<<"请依次输入顶点:"; for(int i = 0; i < G.vexnum; i++)cin>>G.vexs[i]; for(int j = 0; j < G.vexnum; j++) for(int i = 0; i < G.vexnum; i++) G.arcs[j][i] = 0; //初始化邻接矩阵 cout<<"请依次输入邻边:"<<endl; for(int k = 0; k < G.arcnum; k++){ cin>>v1>>v2; int i = LocateVex(G,v1); int j = LocateVex(G,v2); G.arcs[i][j] = 1; G.arcs[j][i] = 1; } return 1; } void DFT_AM(AMGraph G,int i){ //深度优先遍历邻接矩阵 cout<<G.vexs[i]; visited1[i] = 1; for(int j = 0; j < G.vexnum; j++){ if(G.arcs[i][j] == 1 && !visited1[j])DFT_AM(G,j); } } void BFT_AM(AMGraph G, int i) { //广度优先遍历邻接矩阵 queue<int> Q; //定义队列Q Q.push(i); //将起始顶点入队 visited1[i] = 1; //标记为已访问 while (!Q.empty()) { //重复步骤2-3,直到队列为空 int cur = Q.front(); //取出队首元素 Q.pop(); //出队 cout << G.vexs[cur]; //访问该顶点 for (int j = 0; j < G.vexnum; j++) { if (G.arcs[cur][j] == 1 && !visited1[j]) { //遍历该顶点的邻接点,将未访问的邻接点入队 Q.push(j); visited1[j] = 1; //标记为已访问 } } } } int main(){ AMGraph G; CreateUNG(G); for(int j = 0; j < G.vexnum; j++){ //输出邻接矩阵 for(int i = 0; i < G.vexnum; i++) cout<<G.arcs[j][i]<<" "; cout<<endl; } cout<<endl<<"输出深度优先序列:"; DFT_AM(G,0); cout << endl << "输出广度优先序列:"; for (int i = 0; i < MAXNUM; i++) visited1[i] = 0; //重置visited1数组 BFT_AM(G, 0); } 请改良此代码
以下是对代码的改良建议:
1. 在定义结构体时,使用结构体名称作为前缀,提高可读性。
2. 使用枚举类型来定义遍历方法,提高可读性。
3. 将遍历方法的参数从顶点序号改为顶点名称,提高可读性。
4. 在遍历时,将访问过的顶点入栈或入队,不必使用全局变量visited1。
5. 将创建图的函数返回值改为bool类型,表示创建是否成功。
6. 在输入邻边时,应该检查输入的两个顶点是否合法,避免数组越界。
下面是改良后的代码:
```c++
#include<iostream>
#include<stack>
#include<queue>
using namespace std;
#define MAXNUM 100
typedef struct AMGraph{
char vexs[MAXNUM]; //顶点
int arcs[MAXNUM][MAXNUM];//边
int vexnum,arcnum;
} AMGraph;
enum TraverseMethod{
DEPTH_FIRST_TRAVERSE,
BREADTH_FIRST_TRAVERSE
};
int LocateVex(AMGraph G, char v){
for(int i = 0; i < G.vexnum; i++){
if(G.vexs[i] == v) return i;
}
return -1;
}
bool CreateUNG(AMGraph &G){
char v1,v2;
cout<<"请输入顶点数和边数:";
cin>>G.vexnum>>G.arcnum;
if(G.vexnum <= 0 || G.arcnum <= 0) return false;
cout<<"请依次输入顶点:";
for(int i = 0; i < G.vexnum; i++) cin>>G.vexs[i];
for(int j = 0; j < G.vexnum; j++){
for(int i = 0; i < G.vexnum; i++) G.arcs[j][i] = 0; //初始化邻接矩阵
}
cout<<"请依次输入邻边:"<<endl;
for(int k = 0; k < G.arcnum; k++){
cin>>v1>>v2;
int i = LocateVex(G,v1);
int j = LocateVex(G,v2);
if(i == -1 || j == -1){
cout << "输入的边不合法,请重新输入!" << endl;
k--;
continue;
}
G.arcs[i][j] = 1;
G.arcs[j][i] = 1;
}
return true;
}
void Traverse_AM(AMGraph G, char v, TraverseMethod method){
bool visited[MAXNUM] = {false};
stack<int> S;
queue<int> Q;
int i = LocateVex(G, v);
if(i == -1) return;
if(method == DEPTH_FIRST_TRAVERSE){ //深度优先遍历邻接矩阵
S.push(i);
visited[i] = true;
while(!S.empty()){
int cur = S.top();
S.pop();
cout << G.vexs[cur];
for(int j = G.vexnum - 1; j >= 0; j--){
if(G.arcs[cur][j] == 1 && !visited[j]){
S.push(j);
visited[j] = true;
}
}
}
}
else if(method == BREADTH_FIRST_TRAVERSE){ //广度优先遍历邻接矩阵
Q.push(i);
visited[i] = true;
while(!Q.empty()){
int cur = Q.front();
Q.pop();
cout << G.vexs[cur];
for(int j = 0; j < G.vexnum; j++){
if(G.arcs[cur][j] == 1 && !visited[j]){
Q.push(j);
visited[j] = true;
}
}
}
}
}
int main(){
AMGraph G;
if(CreateUNG(G)){
for(int j = 0; j < G.vexnum; j++){ //输出邻接矩阵
for(int i = 0; i < G.vexnum; i++) cout<<G.arcs[j][i]<<" ";
cout<<endl;
}
cout<<endl<<"输出深度优先序列:";
Traverse_AM(G, G.vexs[0], DEPTH_FIRST_TRAVERSE);
cout << endl << "输出广度优先序列:";
Traverse_AM(G, G.vexs[0], BREADTH_FIRST_TRAVERSE);
}
return 0;
}
```
void PrintAdjacencyList(AMGraph& G) { cout << "地图的邻接表表示如下:" << endl; for (int i = 0; i < G.vexnum; i++) { cout << G.vexs[i] << ": "; bool hasNeighbor = false; for (int j = 0; j < G.vexnum; j++) { if (G.arcs[i][j] != MaxInt && i != j) { if (hasNeighbor) cout << " -> "; cout << G.vexs[j]; hasNeighbor = true; } } cout << endl; } } void Backtrack(AMGraph& G, int currIdx, vector<int>& path, vector<bool>& visited, int& distance) { if (path.size() == G.vexnum && G.arcs[currIdx][0] != MaxInt) { cout << "路径:"; for (int i = 0; i < path.size(); i++) { cout << G.vexs[path[i]] << " "; } cout << G.vexs[0] << endl; cout << "总路程:" << distance + G.arcs[currIdx][0] << endl; return; } for (int i = 0; i < G.vexnum; i++) { if (G.arcs[currIdx][i] != MaxInt && !visited[i]) { path.push_back(i); visited[i] = true; distance += G.arcs[currIdx][i]; Backtrack(G, i, path, visited, distance); path.pop_back(); visited[i] = false; distance -= G.arcs[currIdx][i]; } } }为这段代码加上注释
以下是对给出代码的注释:
```
// 打印邻接表
void PrintAdjacencyList(AMGraph& G) {
cout << "地图的邻接表表示如下:" << endl;
for (int i = 0; i < G.vexnum; i++) {
// 输出当前顶点的名称
cout << G.vexs[i] << ": ";
bool hasNeighbor = false;
for (int j = 0; j < G.vexnum; j++) {
// 如果当前顶点与其他顶点存在边,则输出与之相连的顶点名称
if (G.arcs[i][j] != MaxInt && i != j) {
if (hasNeighbor)
cout << " -> ";
cout << G.vexs[j];
hasNeighbor = true;
}
}
cout << endl;
}
}
// 回溯函数
void Backtrack(AMGraph& G, int currIdx, vector<int>& path, vector<bool>& visited, int& distance) {
// 如果路径已经包含所有的顶点并且最后一个顶点与起点存在边,则输出路径和总路程
if (path.size() == G.vexnum && G.arcs[currIdx][0] != MaxInt) {
cout << "路径:";
for (int i = 0; i < path.size(); i++) {
cout << G.vexs[path[i]] << " ";
}
cout << G.vexs[0] << endl;
cout << "总路程:" << distance + G.arcs[currIdx][0] << endl;
return;
}
// 遍历所有顶点
for (int i = 0; i < G.vexnum; i++) {
// 如果当前顶点与当前顶点存在边且未被访问过,则将该顶点加入路径中
if (G.arcs[currIdx][i] != MaxInt && !visited[i]) {
path.push_back(i);
visited[i] = true;
distance += G.arcs[currIdx][i];
// 递归调用回溯函数,以该顶点为起点,继续寻找下一个顶点
Backtrack(G, i, path, visited, distance);
// 将该顶点从路径中移除,以备下一次遍历
path.pop_back();
visited[i] = false;
distance -= G.arcs[currIdx][i];
}
}
}
```