巧妙的性质：一个点最多只会与他横纵坐标最近的那4个点连边。所以我们sort sort连边建图。跑dijkstra
1 #include <cstdio>
2 #include <cstring>
3 #include <vector>
4 #include <queue>
5 #include <algorithm>
6 #include <cmath>
7 #include <iostream>
8 using namespace std;
9 const int maxn = 200003;
10 int n;
11 int first[maxn],to[maxn*8],next[maxn*8],dis[maxn*8],eg;
12 inline void addedge(int x,int y,int d) {
13 next[++eg] = first[x];first[x] = eg;
14 to[eg] = y;dis[eg] = d;
15 }
16 inline void add(int x,int y,int d) {
17 addedge(x,y,d);
18 addedge(y,x,d);
19 }
20 struct Point {
21 int x,y,key;
22 void read() {
23 scanf("%d%d",&x,&y);
24 }
25 }dian[maxn];
26 bool cmp1(const Point& p,const Point& q) {
27 return p.x < q.x;
28 }
29 bool cmp2(const Point& p,const Point& q) {
30 return p.y < q.y;
31 }
32 struct rp {
33 int v,key;
34 rp(int _v = 0,int _key = 0) {
35 v = _v;key = _key;
36 }
37 };
38 struct cmp {
39 bool operator()(const rp& a,const rp& b) {
40 return a.v > b.v;
41 }
42 };
43 priority_queue<rp,vector<rp>,cmp>dui;
44 int dist[maxn];
45 bool vis[maxn];
46 inline void dijkstra(int u) {
47 memset(dist,0x3f,sizeof(dist));
48 dist[u] = 0;
49 rp a = rp(0,1);
50 dui.push(a);
51 while(!vis[n]) {
52 rp zxr_handsome = dui.top();
53 dui.pop();
54 if(vis[zxr_handsome.key]) continue;
55 vis[zxr_handsome.key] = 1;
56 for(int i = first[zxr_handsome.key];i;i = next[i]) {
57 int v = to[i];
58 int newdist = dist[zxr_handsome.key] + dis[i];
59 if(newdist < dist[v]) {
60 dist[v] = newdist;
61 dui.push(rp(newdist,v));
62 }
63 }
64 }
65 cout << dist[n] << endl;
66 }
67 int main() {
68 scanf("%d",&n);
69 for(int i = 1 ; i <= n ; ++i) dian[i].read(),dian[i].key = i;
70 sort(dian+1,dian+1+n,cmp1);
71 /*for(int i = 1 ; i <= n ; ++i) {
72 printf("%d ",dian[i].x);
73 }
74 cout << endl << endl;*/
75 for(int i = 2 ; i <= n ; ++i)
76 add(dian[i].key,dian[i-1].key,dian[i].x - dian[i-1].x);
77 sort(dian+1,dian+1+n,cmp2);
78 for(int i = 2 ; i <= n ; ++i)
79 add(dian[i].key,dian[i-1].key,dian[i].y - dian[i-1].y);
80 dijkstra(1);
81 }
然后据说这道题SPFA过不了，，我就过了一发。。
1 #include <cstdio>
2 #include <cstring>
3 #include <vector>
4 #include <queue>
5 #include <algorithm>
6 #include <cmath>
7 #include <iostream>
8 using namespace std;
9 const int maxn = 200003;
10 int n;
11 int first[maxn],to[maxn*8],next[maxn*8],dis[maxn*8],eg;
12 inline void addedge(int x,int y,int d) {
13 next[++eg] = first[x];first[x] = eg;
14 to[eg] = y;dis[eg] = d;
15 }
16 inline void add(int x,int y,int d) {
17 addedge(x,y,d);
18 addedge(y,x,d);
19 }
20 struct Point {
21 int x,y,key;
22 void read() {
23 scanf("%d%d",&x,&y);
24 }
25 }dian[maxn];
26 bool cmp1(const Point& p,const Point& q) {
27 return p.x < q.x;
28 }
29 bool cmp2(const Point& p,const Point& q) {
30 return p.y < q.y;
31 }
32 int dist[maxn];
33 bool ins[maxn];
34 inline void spfa(int u) {
35 deque<int>Q;
36 Q.push_front(u);
37 memset(dist,0x3f,sizeof(dist));
38 dist[u] = 0;
39 while(!Q.empty()) {
40 int u = Q.front();
41 Q.pop_front();
42 ins[u] = false;
43 for(int i = first[u];i;i = next[i]) {
44 int v = to[i];
45 int newdist = dist[u] + dis[i];
46 if(newdist < dist[v]) {
47 dist[v] = newdist;
48 if(!ins[v]) {
49 if(Q.empty()) {
50 Q.push_front(v);
51 } else {
52 int top = Q.front();
53 if(dist[top] < dist[v]) Q.push_back(v);
54 else Q.push_front(v);
55 }
56 ins[v] = 1;
57 }
58 }
59 }
60 }
61 cout << dist[n];
62 }
63 int main() {
64 scanf("%d",&n);
65 for(int i = 1 ; i <= n ; ++i) dian[i].read(),dian[i].key = i;
66 sort(dian+1,dian+1+n,cmp1);
67 for(int i = 2 ; i <= n ; ++i)
68 add(dian[i].key,dian[i-1].key,dian[i].x - dian[i-1].x);
69 sort(dian+1,dian+1+n,cmp2);
70 for(int i = 2 ; i <= n ; ++i)
71 add(dian[i].key,dian[i-1].key,dian[i].y - dian[i-1].y);
72 spfa(1);
73 }
所以说双端队列就是好用。
时间： 2024-10-10 05:54:45