题目:http://www.lydsy.com/JudgeOnline/problem.php?id=3040
用二叉堆优化Dijkstra算法的话是O( ( n + m ) log n ),明显会TLE,所以要用斐波那契堆或者配对堆来优化,这两种堆插入的复杂度均为O(1),因此可以Dijkstra优化到O( n log n + m ),A过此题。。。(斐波那契堆代码实在是太那啥了不敢写,应该手残了一下配对堆,没想到一次就水过了。一篇关于配对堆不错的介绍:)
代码(配对堆,事实上跟二叉堆一样好写,代码也很短):
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std ;
#define ll long long
#define MAXN 1000001
struct edge {
edge *next ;
int t , d ;
} *head[ MAXN ] ;
void AddEdge( int s , int t , int d ) {
edge *p = new( edge ) ;
p -> t = t , p -> d = d , p -> next = head[ s ] ;
head[ s ] = p ;
}
ll dist[ MAXN ] ;
bool f[ MAXN ] ;
const ll inf = ( ll )( 0x7fffffff ) * ( ll )( 0x7fffffff ) ;
int n , m ;
ll T , rxa , rxc , rya , ryc , rp ;
struct node {
int left , right , child ;
node( ) {
left = right = child ;
}
} h[ MAXN ] ;
int roof = 0 ;
int Join( int v , int u ) {
if ( dist[ v ] < dist[ u ] ) swap( v , u ) ;
h[ v ].left = u , h[ v ].right = h[ u ].child , h[ h[ u ].child ].left = v ;
h[ u ].child = v ;
return u ;
}
void Push( int v ) {
if ( ! roof ) roof = v ; else roof = Join( roof , v ) ;
}
int Top( ) {
return roof ;
}
void Update( int v ) {
if ( v != roof ) {
if ( h[ h[ v ].left ].child == v ) {
h[ h[ v ].left ].child = h[ v ].right ;
} else {
h[ h[ v ].left ].right = h[ v ].right ;
}
if ( h[ v ].right ) h[ h[ v ].right ].left = h[ v ].left ;
h[ v ].left = h[ v ].right = 0 ;
roof = Join( roof , v ) ;
}
}
int sta[ MAXN ] , top ;
void Pop( ) {
if ( ! h[ roof ].child ) roof = 0 ; else {
top = 0 ;
int t = h[ roof ].child ;
while ( t ) {
if ( h[ t ].right ) {
int k = h[ h[ t ].right ].right ;
int v = h[ t ].right ;
h[ t ].left = h[ t ].right = h[ v ].left = h[ v ].right = 0 ;
sta[ ++ top ] = Join( v , t ) ;
t = k ;
} else {
sta[ ++ top ] = t ;
h[ t ].left = h[ t ].right = 0 ;
break ;
}
}
roof = sta[ top ] ;
for ( int i = top - 1 ; i ; -- i ) roof = Join( roof , sta[ i ] ) ;
}
}
void Dijstra( ) {
memset( f , false , sizeof( f ) ) ;
for ( int i = 0 ; i ++ < n ; ) dist[ i ] = inf ;
dist[ 1 ] = 0 , Push( 1 ) , f[ 1 ] = true ;
for ( int i = 0 ; i ++ < n - 1 ; ) {
int v = Top( ) ; Pop( ) , f[ v ] = false ;
if ( v == n ) break ;
for ( edge *p = head[ v ] ; p ; p = p -> next ) if ( dist[ p -> t ] > dist[ v ] + ( ll )( p -> d ) ) {
dist[ p -> t ] = dist[ v ] + ( ll )( p -> d ) ;
if ( ! f[ p -> t ] ) Push( p -> t ) , f[ p -> t ] = true ; else Update( p -> t ) ;
}
}
}
int main( ) {
scanf( "%d%d" , &n , &m ) ;
scanf( "%lld%lld%lld%lld%lld%lld" , &T , &rxa , &rxc , &rya , &ryc , &rp ) ;
memset( head , 0 , sizeof( head ) ) ;
ll x = 0 , y = 0 , z = 0 ;
for ( int i = 0 ; i ++ < T ; ) {
x = ( x * rxa + rxc ) % rp ;
y = ( y * rya + ryc ) % rp ;
ll a = x % n + 1 , b = y % n + 1 ;
if ( a > b ) swap( a , b ) ;
ll d = ( ll )( 100000000 ) - 100 * a ;
AddEdge( a , b , d ) ;
}
for ( int i = 0 ; i ++ < m - T ; ) {
int s , t ; ll d ; scanf( "%d%d%lld" , &s , &t , &d ) ;
AddEdge( s , t , d ) ;
}
Dijstra( ) ;
printf( "%lld\n" , dist[ n ] ) ;
return 0 ;
}