Design a simple tour guide system for a park, and design data structures and algorithms to realize corresponding functions. Requirements:
(1) Contains no less than 8 scenic spots. The vertices in the figure represent the scenic spots in the park, including the name of the scenic spot, the introduction of the scenic spot and other information; the path is represented by the edge, and the weight on the edge represents the distance between the scenic spots
;
Query related information of scenic spots;
(4) Provide tourists with a shortest path between any two scenic spots;
the graph I designed:
the adjacency matrix of the graph:
#include<bits/stdc++.h>
using namespace std;
int Map[100][100];//图的邻接矩阵
//初始化邻接矩阵,需要传入图的路劲数,和图的节点数
void Init(int n,int m) {
//舍弃数组第0的位置
for (int i = 1; i <= m;i++) {
for (int j = 1; j <= m;j++) {
Map[i][j] = i != j ? 1000 : 0;
}
}
while (n--) {
int i, j, c;
cin >> i >> j >> c;
Map[i][j] = Map[j][i] = c;//这种就是无向图
}
}
int Path[10][10] = {
0};//储存路劲节点的前驱
int D[10][10] = {
0};//储存最短的路径
void Floyed(int m) {
for (int i = 1; i <= m;i++) {
for (int j = 1; j <= m;j++) {
D[i][j] = Map[i][j];//这个位置赋值也为了下面三层循环使用
if (D[i][j]<1000&&i!=j) {
Path[i][j] = i;//这个位置说明从i能到j，但不一定是最近的
}
else {
Path[i][j] = -1;//这样就说明i到j之间没有直接路劲
}
}
}
for (int k = 1; k <= m;k++) {
for (int i = 1; i <= m;i++) {
for (int j = 1; j <= m;j++) {
//这句话的意思就是以k节点作为中间节点如果从i到k+在从k到j的值小于原本从i到j路劲的值，就可以换条路走
if (D[i][k]+D[k][j]<D[i][j]) {
D[i][j] = D[i][k] + D[k][j];
//更新j的节点前驱,表示原来从i->j的路换成从i->k->j更近，注意这里的k节点的前驱为i并没有修改这个值
Path[i][j] = k;
}
}
}
}
}
//得到从i到j的路径
list<int> GetPath (int i,int j) {
list<int> lis;
lis.push_back(j);
int k = Path[i][j];
while (k!=i) {
lis.push_back(k);
k = Path[i][k];
}
lis.push_back(k);
lis.reverse();//翻转列表
return lis;
}
int main() {
int n, m;
//节点，和路径的数目
cin >> m >> n;
Init(n,m);
Floyed(m);
list<int> l = GetPath(1 ,8);
cout<<"从a到h的路径";
for (int i: l) {
cout << i<<"->";
}
return 0;
}
Test Data
8 14
1 2 4
1 3 3
2 3 3
2 4 5
2 5 9
3 4 5
3 8 5
4 5 7
4 6 6
4 7 5
4 8 4
5 6 3
6 7 2
7 8 6