参考博客：
分层图最短路
分层图最短路--最通俗易懂的讲解
小说
题目描述
由于小X是一位奆老，奆老总是忙得一刻也停不下来。他刚刚准备完食物，小X童年的挚友小S和小Z来找他帮忙了……
小S和小Z十分喜欢看网络写手“25”的小说，但由于需要付费才能阅读，而小S和小Z的零花钱有非常少，他们只能找小X靠黑科技侵入给网站，把小说给他们。
然而小X又非常的爱慕虚荣，他要小S和小Z到自己家里来取小说。
小S、小Z和小X都居住在扬中市，扬中市共有n个小区，m条主干道（假设每条主干道都是双行线）。小S家住在1号小区，小X家住在n号小区。小S每经过一条主干道需要耗费z点体力，但由于小S的人脉非常广，每当他到达一个小区，他都会和好友攀谈直到体力回满。
由于小Z也希望能看到小说，所以他答应帮助小S k次，这k次小S经过主干道不需要耗费体力。
由于小S生性懒惰，他希望耗费最少的体力到达小X家，请问他最少耗费多少体力？
注意：如果小S到小X家可以一路上都由小Z背着，那么体力上限为0；
如果小S到不了小X家，小S会很伤心，体力上限为-1；
小S和小Z十分喜欢看网络写手“25”的小说，但由于需要付费才能阅读，而小S和小Z的零花钱有非常少，他们只能找小X靠黑科技侵入给网站，把小说给他们。
然而小X又非常的爱慕虚荣，他要小S和小Z到自己家里来取小说。
小S、小Z和小X都居住在扬中市，扬中市共有n个小区，m条主干道（假设每条主干道都是双行线）。小S家住在1号小区，小X家住在n号小区。小S每经过一条主干道需要耗费z点体力，但由于小S的人脉非常广，每当他到达一个小区，他都会和好友攀谈直到体力回满。
由于小Z也希望能看到小说，所以他答应帮助小S k次，这k次小S经过主干道不需要耗费体力。
由于小S生性懒惰，他希望耗费最少的体力到达小X家，请问他最少耗费多少体力？
注意：如果小S到小X家可以一路上都由小Z背着，那么体力上限为0；
如果小S到不了小X家，小S会很伤心，体力上限为-1；
输入
第1行三个整数n,m,k，意思如题目描述。
第2到第n+1行是x,y,z指走连接x号小区和y号小区的主干道要耗费z点体力
第2到第n+1行是x,y,z指走连接x号小区和y号小区的主干道要耗费z点体力
输出
一行一个整数，表示小S最少耗费的体力。
样例输入
5 7 1
1 2 5
3 1 4
2 4 8
3 2 3
5 2 9
3 4 7
4 5 6
样例输出
4
提示
小S的行走路线：1->3->2->5，其中2->5这条主干道由小Z帮助小S通过。
对于30%的数据：n<=20;m<=100;
对于60%的数据：n<=100;m<=1000;
对于100%的数据：n<=1000;m<=10000;z<=1000000;
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 1005 ; 4 const int M = 10005; 5 6 /* */ 7 8 typedef struct Edge{ 9 int to , next , w ; 10 }Edge; 11 12 Edge e[M<<1] ; 13 14 int head[N],idx ; 15 16 void Add_edge( int u , int v ,int w ){ 17 e[idx] = Edge{ v , head[u] , w }; 18 head[u] = idx ++ ; 19 } 20 21 void Init(){ 22 memset( head , -1 , sizeof head ); 23 idx = 0; 24 } 25 26 /* */ 27 typedef struct Node{ 28 int u , w ; 29 Node ( int _u = 0 , int _w = 0 ){ 30 u = _u , w = _w ; 31 } 32 bool operator < ( const Node &rhs ) const { 33 return w > rhs.w ; 34 } 35 }Node; 36 37 int vis[N],dis[N]; 38 int n,m,k; 39 bool Dijstra( int Len ){ 40 41 memset( dis , 0x3f , sizeof dis ); 42 memset( vis , 0 ,sizeof vis ); 43 44 dis[1] = 0 ; 45 46 priority_queue < Node > Q ; 47 Q.push( Node(1,0) ); 48 49 int cnt = 0 ; 50 while( !Q.empty() ){ 51 Node cur = Q.top(); 52 Q.pop(); 53 int u = cur.u , w = cur.w ; 54 55 if( vis[u] ) continue ; 56 vis[u] = 1 ; 57 58 for( int i = head[u] ; ~i ; i = e[i].next ){ 59 int To = e[i].to ; 60 int w = e[i].w > Len ? 1 : 0 ; 61 if( dis[To] > dis[u] + w ){ 62 dis[To] = dis[u] + w ; 63 Q.push( Node(To,dis[To]) ); 64 } 65 } 66 } 67 return dis[n] <= k ; 68 } 69 int main() 70 { 71 Init(); 72 ios_base :: sync_with_stdio(false); 73 cin.tie(NULL) , cout.tie(NULL) ; 74 cin >> n >> m >> k ; 75 76 for( int i = 0,u,v,w; i < m ; i++ ){ 77 cin >> u >> v >> w ; 78 Add_edge( u,v,w ); 79 Add_edge( v,u,w ); 80 } 81 //cout << "### "<< endl; 82 int L = 0 , R = 0x3f3f3f3f ; 83 while( L < R ){ 84 int Mid = L + R >> 1 ; 85 if( Dijstra( Mid ) ){ 86 R = Mid ; 87 }else{ 88 L = Mid + 1 ; 89 } 90 } 91 if( dis[n] > 1e6+10 ){ 92 printf("-1\n"); 93 }else{ 94 printf("%d\n",R); 95 } 96 return 0; 97 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 1e6+10 ; 4 const int M = 1e6+10; 5 6 /* */ 7 8 typedef struct Edge{ 9 int to , next , w ; 10 }Edge; 11 12 Edge e[M<<1] ; 13 14 int head[N],idx ; 15 16 void Add_edge( int u , int v ,int w ){ 17 e[idx] = Edge{ v , head[u] , w }; 18 head[u] = idx ++ ; 19 } 20 21 void Init(){ 22 memset( head , -1 , sizeof head ); 23 idx = 0; 24 } 25 26 /* */ 27 typedef struct Node{ 28 int u , w ; 29 Node ( int _u = 0 , int _w = 0 ){ 30 u = _u , w = _w ; 31 } 32 bool operator < ( const Node &rhs ) const { 33 return w > rhs.w ; 34 } 35 }Node; 36 37 int vis[N],dis[N]; 38 int n,m,k; 39 void Dijstra(){ 40 41 memset( dis , 0x3f , sizeof dis ); 42 memset( vis , 0 ,sizeof vis ); 43 44 dis[1] = 0 ; 45 46 priority_queue < Node > Q ; 47 Q.push( Node(1,0) ); 48 49 int cnt = 0 ; 50 while( !Q.empty() ){ 51 Node cur = Q.top(); 52 Q.pop(); 53 int u = cur.u , w = cur.w ; 54 if( vis[u] ) continue ; 55 vis[u] = 1 ; 56 for( int i = head[u] ; ~i ; i = e[i].next ){ 57 int To = e[i].to ; 58 int w = max( e[i].w , dis[u] ); 59 if( dis[To] > w ){ 60 dis[To] = w ; 61 Q.push( Node( To,dis[To] ) ); 62 } 63 } 64 } 65 } 66 int main() 67 { 68 Init(); 69 ios_base :: sync_with_stdio(false); 70 cin.tie(NULL) , cout.tie(NULL) ; 71 cin >> n >> m >> k ; 72 73 for( int i = 0,u,v,w; i < m ; i++ ){ 74 cin >> u >> v >> w ; 75 for( int j = 0 ; j <= k ; j++ ){ 76 Add_edge( u + (j*n) , v + (j*n) , w ); 77 Add_edge( v + (j*n) , u + (j*n) , w ); 78 if( j != k ){ 79 Add_edge( u + (j*n) , v + (j+1)*n , 0 ); 80 Add_edge( v + (j*n) , u + (j+1)*n , 0 ); 81 } 82 } 83 } 84 85 Dijstra(); 86 int ans = 0x3f3f3f3f ; 87 ans = min( ans , dis[n + n*k] ) ; 88 89 printf("%d\n",ans==0x3f3f3f3f ? -1 : ans ); 90 return 0; 91 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 1e3+10 ; 4 const int M = 1e5+10 ; 5 const int K = 1e3+10 ; 6 7 /* */ 8 9 typedef struct Edge{ 10 int to , next , w ; 11 }Edge; 12 13 Edge e[M<<1] ; 14 15 int head[N],idx ; 16 17 void Add_edge( int u , int v ,int w ){ 18 e[idx] = Edge{ v , head[u] , w }; 19 head[u] = idx ++ ; 20 } 21 22 void Init(){ 23 memset( head , -1 , sizeof head ); 24 idx = 0; 25 } 26 27 /* */ 28 typedef struct Node{ 29 int u , w ; 30 Node ( int _u = 0 , int _w = 0 ){ 31 u = _u , w = _w ; 32 } 33 bool operator < ( const Node &rhs ) const { 34 return w > rhs.w ; 35 } 36 }Node; 37 38 39 int n,m,k; 40 int vis[N][K],dis[N][K]; 41 void Dijstra(){ 42 43 memset( dis , 0x3f , sizeof dis ); 44 memset( vis , 0 ,sizeof vis ); 45 46 dis[0][0] = 0 ; 47 48 priority_queue < Node > Q ; 49 Q.push( Node(0,0) ); 50 51 while( !Q.empty() ){ 52 Node cur = Q.top(); 53 Q.pop(); 54 int c = cur.u / n ; 55 int u = cur.u % n ; 56 if( vis[u][c] ) continue ; 57 vis[u][c] = 1 ; 58 for( int i = head[u] ; ~i ; i = e[i].next ){ 59 int To = e[i].to ; 60 int w = max( e[i].w , dis[u][c] ); 61 if( dis[To][c] > w && !vis[To][c] ){ 62 dis[To][c] = w ; 63 Q.push( Node( To + c * n , dis[To][c] ) ); 64 } 65 } 66 if( c < k ){ 67 for( int i = head[u] ; ~i ; i = e[i].next ){ 68 int To = e[i].to ; 69 int w = dis[u][c] ; 70 if( dis[To][c+1] > w && !vis[To][c+1] ){ 71 dis[To][c+1] = w ; 72 Q.push( Node( To + (c+1) * n , dis[To][c+1] ) ); 73 } 74 } 75 } 76 77 } 78 } 79 int main() 80 { 81 Init(); 82 ios_base :: sync_with_stdio(false); 83 cin.tie(NULL) , cout.tie(NULL) ; 84 cin >> n >> m >> k ; 85 86 for( int i = 0,u,v,w; i < m ; i++ ){ 87 cin >> u >> v >> w ; 88 u -- , v -- ; 89 Add_edge( u , v , w ); 90 Add_edge( v , u , w ); 91 } 92 93 Dijstra(); 94 int ans = 0x3f3f3f3f ; 95 for( int i = 0 ; i <= k ; i++ ){ 96 ans = min( ans , dis[n-1][i] ); 97 } 98 99 printf("%d\n",ans==0x3f3f3f3f ? -1 : ans ); 100 return 0; 101 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 2e5+10; 4 const int M = 2e6+10; 5 6 typedef struct Edge{ 7 int to , next , w ; 8 }Edge; 9 10 Edge e[M<<1] ; 11 int head[N] , idx ; 12 13 void add_edge(int u , int v , int w ){ 14 e[idx] = Edge{ v , head[u] , w }; 15 head[u] = idx ++ ; 16 } 17 void Init(){ 18 memset( head , -1 , sizeof head ); 19 idx = 0 ; 20 } 21 int n , m , k ; 22 int S , T ; 23 int dis[N] , vis[N] ; 24 25 typedef struct Node{ 26 int u , w ; 27 Node( int _u = 0 , int _w = 0 ){ 28 u = _u , w = _w ; 29 } 30 bool operator < ( const Node & rhs )const{ 31 return w > rhs.w ; 32 } 33 }Node; 34 35 void Dijstra(int S){ 36 37 memset( vis , 0 , sizeof vis ); 38 memset( dis , 0x3f , sizeof dis ); 39 dis[S] = 0 ; 40 41 priority_queue < Node > Q ; 42 Q.push( Node(S,0) ); 43 44 while( !Q.empty() ){ 45 Node cur = Q.top(); 46 Q.pop() ; 47 int u = cur.u ; 48 if( vis[u] ) continue ; 49 vis[u] = 1 ; 50 51 for( int i = head[u] ; ~i ; i = e[i].next ){ 52 int To = e[i].to ; 53 int w = e[i].w ; 54 if( !vis[To] && dis[u] + w < dis[To] ){ 55 dis[To] = dis[u] + w ; 56 Q.push( Node( To , dis[To] ) ); 57 } 58 } 59 } 60 } 61 62 int main() 63 { 64 Init(); 65 ios_base :: sync_with_stdio(false); 66 cin.tie(NULL) , cout.tie(NULL) ; 67 68 69 cin >> n >> m >> k ; 70 cin >> S >> T ; 71 72 for( int i = 0,u,v,w; i < m ; i++ ){ 73 cin >> u >> v >> w ; 74 for( int j = 0 ; j <= k ; j ++ ){ 75 add_edge( u + j*n , v + j*n , w ); 76 add_edge( v + j*n , u + j*n , w ); 77 if( j != k ){ 78 add_edge( u + j*n , v + (j+1)*n , 0 ) ; 79 add_edge( v + j*n , u + (j+1)*n , 0 ) ; 80 } 81 } 82 } 83 Dijstra(S); 84 int ans = 0x3f3f3f3f ; 85 for( int i = 0 ; i <= k ; i++ ){ 86 ans = min( ans , dis[ T+i*n ]); 87 } 88 cout << ans << endl ; 89 return 0; 90 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 5e5 + 10; 4 const int M = 5e6 + 10; 5 6 typedef struct Edge{ 7 int to , next , w ; 8 }Edge; 9 Edge e[M<<1] ; 10 11 int head[N] , idx ; 12 void Add_edge( int u , int v , int w ){ 13 e[idx] = Edge{ v , head[u] , w }; 14 head[u] = idx ++ ; 15 } 16 17 void Init(){ 18 memset( head , -1 , sizeof head ); 19 idx = 0 ; 20 } 21 typedef struct P{ 22 int x , y , No ; 23 }P; 24 P a[N] ; 25 bool cmp1(P u,P v){ 26 if( u.x == v.x ) return u.y < v.y ; 27 return u.x < v.x ; 28 } 29 bool cmp2(P u,P v ){ 30 if( u.y == v.y ) return u.x < v.x ; 31 return u.y < v.y ; 32 } 33 34 int n,m,S,T,k; 35 int dis[N],vis[N]; 36 37 typedef struct Node{ 38 int u,w; 39 Node ( int _u = 0 , int _w = 0 ):u(_u),w(_w){} 40 bool operator < (const Node &rhs )const { 41 return w > rhs.w ; 42 } 43 }Node; 44 void Dijstra(int S){ 45 memset( dis , 0x3f , sizeof dis ); 46 memset( vis , 0 , sizeof vis ); 47 48 dis[S] = 0 ; 49 priority_queue < Node > Q; 50 Q.push( Node(S,0) ); 51 52 53 while(!Q.empty() ){ 54 55 Node cur = Q.top(); 56 Q.pop(); 57 int u = cur.u; 58 if( vis[u] ) continue ; 59 vis[u] = 1 ; 60 61 //printf("#### %d ### \n",u); 62 63 for( int i = head[u] ; ~i ; i = e[i].next ){ 64 int To = e[i].to ; 65 int w = e[i].w ; 66 if( dis[To] > dis[u] + w ){ 67 dis[To] = dis[u] + w ; 68 Q.push( Node(To,dis[To] ) ); 69 } 70 } 71 } 72 } 73 74 75 int main() 76 { 77 ios_base :: sync_with_stdio(false); 78 cin.tie(NULL) , cout.tie(NULL) ; 79 80 cin >> n >> m ; 81 82 Init() ; 83 S = m + 1 , T = m + 2 ; 84 n = m + 2 ; 85 86 for( int i = 1; i <= n ; i++ ){ 87 cin >> a[i].x >> a[i].y ; 88 a[i].No = i ; 89 } 90 91 sort( a + 1 , a + 1 + n , cmp1 ); 92 for( int i = 1 ; i < n ; i ++ ){ 93 if( a[i].x == a[i+1].x ){ 94 Add_edge( a[i].No , a[i+1].No , 2 * (a[i+1].y-a[i].y) ); 95 Add_edge( a[i+1].No , a[i].No , 2 * (a[i+1].y-a[i].y) ); 96 } 97 } 98 99 sort( a + 1 , a + 1 + n , cmp2 ); 100 for( int i = 1 ; i < n ; i ++ ){ 101 if( a[i].y == a[i+1].y ){ 102 Add_edge( a[i].No+n , a[i+1].No+n , 2 * (a[i+1].x-a[i].x)); 103 Add_edge( a[i+1].No+n , a[i].No+n , 2 * (a[i+1].x-a[i].x) ); 104 } 105 } 106 107 for( int i = 1 ; i <= m ; i++ ){ 108 Add_edge( i , i+n , 1 ); 109 Add_edge( i+n , i , 1 ); 110 } 111 Add_edge( S + n , S , 0 ); 112 Add_edge( S , S + n , 0 ); 113 Add_edge( T , T + n , 0 ); 114 Add_edge( T + n , T , 0 ); 115 116 Dijstra(S); 117 printf("%d\n",dis[T] == 0x3f3f3f3f ? -1 : dis[T] ); 118 return 0; 119 }
爱情之路
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 5e5 + 10; 4 const int M = 5e6 + 10; 5 6 typedef struct Edge{ 7 int to , next , w , ch ; 8 }Edge; 9 Edge e[M<<1] ; 10 11 int head[N] , idx ; 12 void Add_edge( int u , int v , int w , int ch ){ 13 e[idx] = Edge{ v , head[u] , w , ch }; 14 head[u] = idx ++ ; 15 } 16 17 void Init(){ 18 memset( head , -1 , sizeof head ); 19 idx = 0 ; 20 } 21 typedef struct P{ 22 int x , y , No ; 23 }P; 24 P a[N] ; 25 26 int n,m,S,T,k; 27 int dis[N][5],vis[N][5]; 28 int cnt[N][5]; 29 30 typedef struct Node{ 31 int u , w , id ; 32 Node ( int _u = 0 , int _w = 0 ,int Id = 0 ):u(_u),w(_w),id(Id){} 33 bool operator < (const Node &rhs )const { 34 return w > rhs.w ; 35 } 36 }Node; 37 void Dijstra(int S){ 38 memset( dis , 0x3f , sizeof dis ); 39 memset( vis , 0 , sizeof vis ); 40 41 dis[S][0] = cnt[S][0] = 0 ; 42 43 priority_queue < Node > Q; 44 Q.push( Node(S,0,0) ); 45 46 while( !Q.empty() ){ 47 Node cur = Q.top(); 48 Q.pop(); 49 50 int u = cur.u , id = cur.id ; 51 if( vis[u][id] ) continue ; 52 vis[u][id] = 1 ; 53 54 //printf("##### %d #### \n",u); 55 for( int i = head[u] ; ~i ; i = e[i].next ){ 56 int To = e[i].to ; 57 int ch = e[i].ch ; 58 int w = e[i].w ; 59 60 if( ch == id % 4 + 1 && dis[To][ch] > dis[u][id] + w ){ 61 dis[To][ch] = dis[u][id] + w ; 62 cnt[To][ch] = dis[u][id] + 1 ; 63 Q.push( Node( To , dis[To][ch] , ch ) ) ; 64 } 65 } 66 } 67 } 68 69 70 int main() 71 { 72 ios_base :: sync_with_stdio(false); 73 cin.tie(NULL) , cout.tie(NULL) ; 74 75 cin >> n >> m ; 76 77 Init() ; 78 char ch[10]; 79 int Type ; 80 for( int i = 1 , u , v , w ; i <= m ; i++ ){ 81 cin >> u >> v >> w >> ch ; 82 switch( ch[0] ){ 83 case 'L' : Type = 1 ; break ; 84 case 'O' : Type = 2 ; break ; 85 case 'V' : Type = 3 ; break ; 86 case 'E' : Type = 4 ; break ; 87 } 88 Add_edge( u , v , w , Type ); 89 Add_edge( v , u , w , Type ); 90 } 91 Dijstra( 1 ); 92 if( dis[n][4] != 0x3f3f3f3f ){ 93 printf("%d %d\n",dis[n][4] , cnt[n][4] >> 2 ); 94 }else{ 95 puts("HOLY SHIT!"); 96 } 97 return 0; 98 }
1 #include<iostream> 2 #include<cstring> 3 #include<queue> 4 #include<algorithm> 5 using namespace std; 6 const int inf = 0x3f3f3f3f ; 7 const int N = 308 ; 8 const int M = 1e4+10; 9 int n , m , k , idx ; 10 int head[N] , ans ; 11 int vis[N][M]; 12 int dis[N][M]; 13 14 typedef struct Edge{ 15 int to , next , w, val ; 16 }Edge ; 17 Edge e[M<<1]; 18 19 typedef struct Node{ 20 int u,w,val; 21 Node( int _u = 0 , int _w = 0 , int v = 0 ) 22 :u(_u),w(_w),val(v){} 23 24 bool operator < ( const Node &rhs ) const{ 25 return w > rhs.w ; 26 } 27 }Node; 28 29 void Add_edge( int u , int v , int w , int val ){ 30 e[idx] = Edge { v , head[u] , w , val }; 31 head[u] = idx ++ ; 32 } 33 void Init(){ 34 memset( head , -1 , sizeof head ); 35 idx = 0 ; 36 } 37 void Dijstra(){ 38 memset( dis , 0x3f , sizeof dis ); 39 memset( vis , 0 , sizeof vis ); 40 dis[1][k] = 0 ; 41 priority_queue < Node > Q ; 42 Q.push( Node(1,0,k) ); 43 while( !Q.empty() ){ 44 Node cur = Q.top(); 45 Q.pop(); 46 int u = cur.u ; 47 int k = cur.val ; 48 if( vis[u][k] ) continue ; 49 vis[u][k] = 1 ; 50 for( int i = head[u] ; ~i ; i = e[i].next ){ 51 int to = e[i].to ; 52 int val = e[i].val ; 53 int w = e[i].w ; 54 55 if( k >= val ){ 56 if( dis[to][k-val] > dis[u][k] + w ){ 57 dis[to][k-val] = dis[u][k] + w ; 58 Q.push( Node( to , dis[to][k-val] , k-val ) ); 59 } 60 } 61 } 62 } 63 } 64 65 int main() 66 { 67 Init(); 68 ios_base :: sync_with_stdio(false); 69 cin.tie(NULL) , cout.tie(NULL) ; 70 cin >> k >> n >> m ; 71 for( int i = 0,u,v,w,val ; i < m ; i++ ){ 72 cin >> u >> v >> w >> val ; 73 Add_edge( u , v , w , val ); 74 //Add_edge( v , u , w , val ); 75 } 76 Dijstra(); 77 ans = inf ; 78 for( int i = 0 ; i <= k ; i++ ) 79 ans = min( ans , dis[n][i] ); 80 if( ans == inf ) 81 cout << -1 << endl ; 82 else 83 cout << ans << endl ; 84 return 0; 85 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 1e6+10; 4 const int M = 1e6+10; 5 6 typedef struct Edge{ 7 int to , next , w ; 8 }Edge ; 9 Edge e[M<<1] ; 10 11 typedef struct Node{ 12 int u , w ; 13 Node( int _u = 0 , int _w = 0 ):u(_u),w(_w){} 14 bool operator < ( const Node &rhs ) const { 15 return w > rhs.w ; 16 } 17 }Node; 18 19 int head[N] , idx ; 20 void Add_Edge( int u , int v , int w ){ 21 e[idx] = Edge{ v , head[u] , w }; 22 head[u] = idx ++ ; 23 } 24 25 int dis[N] , vis[N] ; 26 int n , m , k ; 27 28 void Init(){ 29 memset( head , -1 , sizeof head ); 30 idx = 0 ; 31 } 32 33 void Dijstra(){ 34 memset( dis , 0x3f , sizeof dis ); 35 memset( vis , 0 , sizeof vis ); 36 37 dis[1] = 0 ; 38 priority_queue < Node > Q; 39 Q.push( Node(1,0) ) ; 40 while( !Q.empty() ){ 41 Node cur = Q.top() ; 42 Q.pop() ; 43 int u = cur.u ; 44 if( vis[u] ) continue ; 45 vis[u] = 1 ; 46 47 for( int i = head[u] ; ~i ; i = e[i].next ){ 48 int To = e[i].to ; 49 int w = e[i].w ; 50 if( dis[To] > dis[u] + w ){ 51 dis[To] = dis[u] + w ; 52 Q.push( Node( To, dis[To] ) ); 53 } 54 } 55 } 56 } 57 58 int main() 59 { 60 ios_base :: sync_with_stdio(false); 61 cin.tie(NULL) , cout.tie(NULL) ; 62 Init() ; 63 cin >> n >> m >> k ; 64 for( int i = 0 ,u,v,w ; i < m ; i++ ){ 65 cin >> u >> v >> w ; 66 for( int j = 0 ; j <= k ; j++ ){ 67 Add_Edge( u + (j*n) , v + (j*n) , w ); 68 Add_Edge( v + (j*n) , u + (j*n) , w ); 69 if( j < k ){ 70 Add_Edge( u + j*n , v + (j+1)*n , w>>1 ); 71 Add_Edge( v + j*n , u + (j+1)*n , w>>1 ); 72 } 73 } 74 } 75 Dijstra(); 76 int ans = 0x3f3f3f3f ; 77 for( int i = 0 ; i <= k ; i++ ){ 78 ans = min( ans , dis[n+i*n] ) ; 79 } 80 cout << ans << endl ; 81 return 0; 82 }
1 #include<cstdio> 2 #include<cctype> 3 #include<cstring> 4 #include<queue> 5 #include<algorithm> 6 using namespace std; 7 const int N=1e5+10; 8 const int M = 255; 9 inline void read(int &x){ 10 int ans=0,f=1; 11 char c=getchar(); 12 for(;!isdigit(c);c=getchar()){ 13 if(c=='-') 14 f=-1; 15 } 16 for(;isdigit(c);c=getchar()){ 17 ans=ans*10+c-'0'; 18 } 19 x=ans*f; 20 } 21 22 typedef struct Edge{ 23 int to,next,w; 24 }Edge; 25 26 Edge edge[N]; 27 Edge e[N] ; 28 int cnt,head[M],dis[M]; 29 int Cnt,Head[M],Dis[M]; 30 int n,m; 31 32 void add_edge(int u,int v,int w){ 33 edge[cnt].to=v; 34 edge[cnt].w=w; 35 edge[cnt].next=head[u]; 36 head[u]=cnt++; 37 } 38 void Add_edge(int u,int v,int w){ 39 e[Cnt].to=v; 40 e[Cnt].w=w; 41 e[Cnt].next=Head[u]; 42 Head[u]=Cnt++; 43 } 44 45 typedef struct Cmp{ 46 bool operator () (const int &p1,const int &p2){ 47 return dis[p1]<dis[p2]; 48 } 49 }Cmp; 50 51 typedef struct cmp{ 52 bool operator () (const int &p1,const int &p2){ 53 return Dis[p1]<Dis[p2]; 54 } 55 }cmp; 56 57 int Dijstra(int k); 58 int dijstra(int k){ 59 memset(dis,0x3f,sizeof(dis)); 60 dis[k]=0; 61 priority_queue< int ,vector<int> , Cmp > q; 62 q.push(k); 63 64 while(!q.empty()){ 65 int u=q.top(); 66 q.pop(); 67 for(int i=head[u];~i;i=edge[i].next){ 68 int v=edge[i].to; 69 if(dis[v]>dis[u]+edge[i].w){ 70 dis[v]=dis[u]+edge[i].w; 71 q.push(v); 72 } 73 } 74 } 75 76 //printf("%d\n",dis[n]); 77 78 int W = 0 ; 79 for(int u=1;u<=n;u++){ 80 for(int i=head[u];~i;i=edge[i].next){ 81 if( dis[u] + edge[i].w == dis[edge[i].to] ){ 82 //printf(" %d , %d = %d \n",u,edge[i].to,edge[i].w); 83 Add_edge(u,edge[i].to,edge[i].w); 84 //Add_edge(edge[i].to,u,edge[i].w); 85 W = max ( W , edge[i].w ); 86 } 87 } 88 } 89 90 for(int u=1;u<=n;u++){ 91 for(int i=head[u];~i;i=edge[i].next){ 92 if( dis[u] + edge[i].w != dis[edge[i].to] && dis[u] + edge[i].w - W <= dis[edge[i].to]){ 93 //printf(" %d , %d = %d \n",u,edge[i].to,edge[i].w); 94 Add_edge(u,edge[i].to,edge[i].w); 95 //Add_edge(edge[i].to,u,edge[i].w); 96 } 97 } 98 } 99 100 int tmp = dis[n]; 101 int maxz = dis[n]; 102 for(int u=1;u<=n;u++){ 103 for(int i=Head[u];~i;i=e[i].next){ 104 //printf(" %d , %d = %d \n",u,e[i].to,e[i].w); 105 e[i].w = e[i].w * 2; 106 //e[i^1].w = e[i^1].w * 2 ; 107 maxz = max(Dijstra(1),maxz); 108 e[i].w = e[i].w / 2; 109 //e[i^1].w = e[i^1].w / 2 ; 110 } 111 } 112 return maxz - tmp ; 113 114 } 115 int Dijstra(int k) { 116 memset(Dis, 0x3f, sizeof(Dis)); 117 Dis[k] = 0; 118 priority_queue<int, vector<int>, cmp> q; 119 q.push(k); 120 //printf("### %d\n",Dis[0]); 121 while (!q.empty()) { 122 int u = q.top(); 123 q.pop(); 124 for (int i = Head[u]; ~i; i = e[i].next) { 125 int v = e[i].to; 126 if (Dis[v] > Dis[u] + e[i].w) { 127 Dis[v] = Dis[u] + e[i].w; 128 q.push(v); 129 //printf(" Dis[%d] , %d\n",v,Dis[v]); 130 } 131 } 132 } 133 //printf("### %d\n",Dis[n]); 134 return Dis[n]; 135 } 136 int main() 137 { 138 memset(Head,-1,sizeof(Head)); 139 memset(head,-1,sizeof(head)); 140 scanf("%d%d",&n,&m); 141 142 for(int i=0,u,v,w;i<m;i++){ 143 read(u),read(v),read(w); 144 add_edge(u,v,w); 145 add_edge(v,u,w); 146 } 147 printf("%d\n",dijstra(1)); 148 149 return 0; 150 }
P2939 [USACO09FEB]改造路Revamping Trails
1 #include<bits/stdc++.h> 2 using namespace std; 3 const int N = 4e6+10; 4 const int M = 4e6+10; 5 6 typedef struct Edge{ 7 int to , next , w ; 8 }Edge ; 9 Edge e[M<<1] ; 10 11 typedef struct Node{ 12 int u , w ; 13 Node( int _u = 0 , int _w = 0 ):u(_u),w(_w){} 14 bool operator < ( const Node &rhs ) const { 15 return w > rhs.w ; 16 } 17 }Node; 18 19 int head[N] , idx ; 20 void Add_Edge( int u , int v , int w ){ 21 e[idx] = Edge{ v , head[u] , w }; 22 head[u] = idx ++ ; 23 } 24 25 int dis[N] , vis[N] ; 26 int n , m , k ; 27 28 void Init(){ 29 memset( head , -1 , sizeof head ); 30 idx = 0 ; 31 } 32 33 void Dijstra(){ 34 memset( dis , 0x3f , sizeof dis ); 35 memset( vis , 0 , sizeof vis ); 36 37 dis[1] = 0 ; 38 priority_queue < Node > Q; 39 Q.push( Node(1,0) ) ; 40 while( !Q.empty() ){ 41 Node cur = Q.top() ; 42 Q.pop() ; 43 int u = cur.u ; 44 if( vis[u] ) continue ; 45 vis[u] = 1 ; 46 47 for( int i = head[u] ; ~i ; i = e[i].next ){ 48 int To = e[i].to ; 49 int w = e[i].w ; 50 if( dis[To] > dis[u] + w ){ 51 dis[To] = dis[u] + w ; 52 Q.push( Node( To, dis[To] ) ); 53 } 54 } 55 } 56 } 57 58 int main() 59 { 60 ios_base :: sync_with_stdio(false); 61 cin.tie(NULL) , cout.tie(NULL) ; 62 Init() ; 63 cin >> n >> m >> k ; 64 for( int i = 0 ,u,v,w ; i < m ; i++ ){ 65 cin >> u >> v >> w ; 66 for( int j = 0 ; j <= k ; j++ ){ 67 Add_Edge( u + (j*n) , v + (j*n) , w ); 68 Add_Edge( v + (j*n) , u + (j*n) , w ); 69 if( j < k ){ 70 Add_Edge( u + j*n , v + (j+1)*n , 0 ); 71 Add_Edge( v + j*n , u + (j+1)*n , 0 ); 72 } 73 } 74 } 75 Dijstra(); 76 int ans = 0x3f3f3f3f ; 77 for( int i = 0 ; i <= k ; i++ ){ 78 ans = min( ans , dis[n+i*n] ) ; 79 } 80 cout << ans << endl ; 81 return 0; 82 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long ll; 4 const int N = 3200010; 5 const int M = 5400000; 6 int n,m,k; 7 typedef struct Edge{ 8 int to , next ; 9 ll w ; 10 }Edge; 11 Edge e[M]; 12 13 typedef struct Node{ 14 int u ; 15 ll w ; 16 Node ( int _u = 0 , ll _w = 0 ):u(_u),w(_w){} 17 bool operator < ( const Node & rhs ) const { 18 return w > rhs.w ; 19 } 20 }Node; 21 22 int head[N],idx; 23 void Add_edge( int u, int v ,ll w ){ 24 e[idx] = Edge { v , head[u] , w }; 25 head[u] = idx ++ ; 26 } 27 28 void Init(){ 29 memset( head , -1 , sizeof head ); 30 idx = 0 ; 31 } 32 33 ll dis[N]; 34 bool vis[N]; 35 36 void Dijstra(){ 37 memset( dis , 0x3f , sizeof dis ); 38 memset( vis , 0 , sizeof vis ); 39 40 dis[1] = 0 ; 41 priority_queue<Node> Q; 42 Q.push( Node(1,0) ); 43 44 while( !Q.empty() ){ 45 Node cur = Q.top(); 46 Q.pop(); 47 int u = cur.u ; 48 if( vis[u] ) continue ; 49 vis[u] = 1 ; 50 51 for( int i = head[u] ; ~i ; i = e[i].next ){ 52 int to = e[i].to , w = e[i].w ; 53 if( dis[to] > dis[u] + w ){ 54 dis[to] = dis[u] + w ; 55 Q.push( Node(to,dis[to]) ); 56 } 57 } 58 } 59 } 60 int main() 61 { 62 int T; 63 scanf("%d",&T); 64 while(T--){ 65 Init(); 66 scanf("%d%d%d",&n,&m,&k); 67 for( int i = 0 ; i < m ; i++ ){ 68 int u , v ; ll w ; 69 scanf("%d%d%lld",&u,&v,&w); 70 for( int j = 0 ; j <= k ; j++ ){ 71 Add_edge( u + ( j*n ), v + j*n , w ); 72 if( j < k ){ 73 Add_edge( u + j * n , v + (j+1)*n , 0 ); 74 } 75 } 76 } 77 Dijstra(); 78 printf("%lld\n",dis[n*(k+1)]); 79 } 80 return 0; 81 }
1 #include<bits/stdc++.h> 2 using namespace std; 3 typedef long long ll; 4 const int N = 3200010; 5 const int M = 5400000; 6 int n,m,k; 7 typedef struct Edge{ 8 int to , next ; 9 ll w ; 10 }Edge; 11 Edge e[M]; 12 13 typedef struct Node{ 14 int u ; 15 ll w ; 16 Node ( int _u = 0 , ll _w = 0 ):u(_u),w(_w){} 17 bool operator < ( const Node & rhs ) const { 18 return w > rhs.w ; 19 } 20 }Node; 21 22 int head[N],idx; 23 void Add_edge( int u, int v ,ll w ){ 24 e[idx] = Edge { v , head[u] , w }; 25 head[u] = idx ++ ; 26 } 27 28 void Init(){ 29 memset( head , -1 , sizeof head ); 30 idx = 0 ; 31 } 32 33 ll dis[N]; 34 bool vis[N]; 35 36 void Dijstra(int S){ 37 memset( dis , 0x3f , sizeof dis ); 38 memset( vis , 0 , sizeof vis ); 39 40 dis[S] = 0 ; 41 priority_queue<Node> Q; 42 Q.push( Node(S,0) ); 43 44 while( !Q.empty() ){ 45 Node cur = Q.top(); 46 Q.pop(); 47 int u = cur.u ; 48 if( vis[u] ) continue ; 49 vis[u] = 1 ; 50 51 for( int i = head[u] ; ~i ; i = e[i].next ){ 52 int to = e[i].to , w = e[i].w ; 53 if( dis[to] > dis[u] + w ){ 54 dis[to] = dis[u] + w ; 55 Q.push( Node(to,dis[to]) ); 56 } 57 } 58 } 59 } 60 int main() 61 { 62 int S,T; 63 Init(); 64 scanf("%d%d%d%d%d",&n,&m,&S,&T,&k); 65 for( int i = 0 ; i < m ; i++ ){ 66 int u , v ; ll w ; 67 scanf("%d%d%lld",&u,&v,&w); 68 for( int j = 0 ; j <= k ; j++ ){ 69 Add_edge( u + ( j*n ), v + j*n , w ); 70 Add_edge( v + ( j*n ), u + j*n , w ); 71 if( j < k ){ 72 Add_edge( u + j * n , v + (j+1)*n , 0 ); 73 Add_edge( v + j * n , u + (j+1)*n , 0 ); 74 } 75 } 76 } 77 Dijstra(S); 78 ll ans = 0x3f3f3f3f3f3f3f3f; 79 for( int i = 0 ; i <= k ; i++ ){ 80 ans = min( ans , dis[T+(i*n)] ); 81 } 82 printf("%lld\n",ans); 83 return 0; 84 }