1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
|
/*
* @Author: wangzhiyu
* @Date: 2023-09-03 02:29:26
* @Last Modified by: wangzhiyu
* @Last Modified time: 2024-07-30 22:47:07
*/
#include <cmath>
#include <cstring>
#include <time.h>
#include <iostream>
#include <vector>
#include <unistd.h> // for linux
// #include <windows.h> // for windows
using namespace std;
using ll = long long;
constexpr int LIM1 = 205; // 预分配阙值
constexpr int INF = 0x3f3f3f3f; // 近似无限大
/// @brief 图论相关
namespace graph {
int n;
/// @brief 节点数据结构
struct Node {
int nxt;
int w;
};
vector<Node> edges[LIM1];
/// @brief 增加一条边
/// @param from
/// @param to
/// @param w 权值
void addedge(int from, int to, int w) { edges[from].push_back({to, w}); }
/// @brief 删除某边
/// @param from
/// @param to
void deledge(int from, int to) { // delete an edge
for (auto i = edges[from].begin(); i != edges[from].end();) {
if ((*i).nxt == to) {
i = edges[from].erase(i);
} else {
i++;
}
}
}
/// @brief 查询某边的权值
/// @param from
/// @param to
/// @return 权值
int queryedge(int from, int to) { // to query an edge's weight
if (from == to)
return 0;
for (auto i = edges[from].begin(); i != edges[from].end(); i++) {
if ((*i).nxt == to) {
return (*i).w;
}
}
return INF;
}
/*
void dfs_launcher(){
for(int i = 1; i <= n; i++){
dfs(i);
}
}
void dfs(int begin, ){
cerr << "Access: " << begin;
dfs(edges[begin].nxt);
}
*/
/// @brief Floyd 最短路算法
/// @param spec 待展示的点标号
void sp_f(int spec) { // Floyd algorithm
int sp[LIM1][LIM1];
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
sp[i][j] = queryedge(i, j);
}
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
for (int k = 1; k <= n; k++) {
sp[i][j] = min(sp[i][j], sp[i][k] + sp[k][j]);
}
}
}
for (int i = 1; i <= n; i++) {
string dist = to_string(sp[spec][i]);
if (dist == to_string(INF))
dist = "∞"; // unable to reach
cerr << spec << " -[" << dist << "]-> " << i << " (floyd)" << endl;
}
}
/// @brief 输出某点详情
/// @param idx 特定点索引
void print(int idx) { // to print a particular vertex's detail information
cout << "Print: " << idx << endl << " > ";
for (auto &i : edges[idx]) {
cout << i.nxt << "(" << i.w << ")"
<< " ";
}
for (int i = 1; i <= idx ; i++){
}
cout << endl;
}
/// @brief Dijkstra 单源最短路径算法
/// @param begin 源点标号
void sp_dij(int begin) { // Dijkstra algorithm
bool vis[LIM1]; // visiting status
fill(vis + 1, vis + n + 1, 0); // clear status
int sp[LIM1]; // shortest path's distance
for (int i = 1; i <= n; i++) { // initalize distance
sp[i] = queryedge(begin, i);
}
vis[begin] = 1; // mark beginner's visit
for (int k = 1; k <= n - 1; k++) { // this loop makes every vertex
// successfully marked (except beginner)
int best_transfer; // best transfer vertex
int mindistance = INF; // temp min distance
for (int i = 1; i <= n; i++) { // calc best_transfer
if (queryedge(begin, i) < mindistance && vis[i] != 1) {
mindistance = queryedge(begin, i);
best_transfer = i;
}
}
// once best_transfer confirmed, mark its visit
vis[best_transfer] = 1;
for (int i = 1; i <= n; i++) { // recalc transferred distance
if (vis[i] != 1) {
if (queryedge(begin, best_transfer) +
queryedge(best_transfer, i) <
queryedge(begin, i)) {
sp[i] = queryedge(begin, best_transfer) +
queryedge(best_transfer, i);
}
}
}
}
// print result
for (int i = 1; i <= n; i++) {
string dist = to_string(sp[i]);
if (dist == to_string(INF))
dist = "∞"; // unable to reach
cerr << begin << " -[" << dist << "]-> " << i << " (dijkstra)" << endl;
}
}
/// @brief 自然地初始化图
/// @param data 格式化的图数据, 参照 https://csacademy.com/app/graph_editor/,
/// 第一行和最后一行必须是换行符
void naturally_init(string data) {
// raw string feature required, last line must be \n;
bool flag = 0; // dotmode/edgemode
string formatted[3];
int k = 0;
while (*(data.begin()) != '\n')
data.erase(data.begin()); // erase beginner
data.erase(data.begin());
for (char i : data) {
if (!flag) {
if (i != '\n')
formatted[0].push_back(i);
else {
n++;
formatted[0] = "";
}
}
if (i == ' ') flag = 1;
if (flag) {
if (i != ' ' && i != '\n')
formatted[k % 3].push_back(i);
else
k++;
if (i == '\n') {
addedge(stoi(formatted[0]), stoi(formatted[1]),
stoi(formatted[2]));
formatted[0] = "";
formatted[1] = "";
formatted[2] = "";
}
}
}
cerr << "Automatically initialization finished" << endl;
cerr << "Node number: " << n << endl;
}
} // namespace graph
/// @brief 实用函数与性能分析
namespace utils {
/// @brief 输出分割符
void spilt() { cerr << "------------------------" << endl; }
time_t lasttime = INF, currtime = 0;
/// @brief 自动计时器
void autoclock() {
cerr << clock();
cerr << fixed << endl;
cerr << "\033[31m";
if(lasttime == INF){
cerr << "[TIMG GAP] INIT\033[0m" << endl;
lasttime = clock();
return;
}
currtime = clock();
double dur;
dur = (double)(currtime - lasttime);
cerr << "[TIME GAP] "<< dur/CLOCKS_PER_SEC << endl;
lasttime = clock();
cerr << "\033[0m";
}
} // namespace utils
int main() {
string original_graph = R"( 格式化的图数据:
1
2
3
4
5
6
7
8
9
10
6 2 9
2 4 3
4 5 2
1 4 2
1 5 9
2 3 2
2 7 6
1 9 8
1 3 4
9 10 4
4 6 3
2 5 8
2 8 2
2 10 2
8 9 7
3 7 6
)";
graph::naturally_init(original_graph);
cout << fixed; // 禁用科学计数法输出
cout << graph::queryedge(1, 3) << endl;
cout << graph::queryedge(1, 3) << endl;
cout << graph::queryedge(4, 9) << endl;
graph::print(1);
graph::print(2);
utils::spilt();
utils::autoclock();
graph::sp_f(2);
utils::autoclock();
graph::sp_dij(2);
utils::autoclock();
utils::spilt();
graph::sp_f(3);
graph::sp_dij(3);
return 0;
}
|