ztx
[AHOI2005]LANE 航线规划
[国家集训队2011]旅游(宋方睿)

[NOI2014]魔法森林

ztx posted @ 2015年1月17日 17:35 in 动态树 with tags LCT , 470 阅读
/****************************************\
* Author : ztx
* Title  : [NOI2014]魔法森林
* ALG    : LCT+Kruskal
* CMT    :
* 把边按a从小到大排序
* 然后一条条加边
* 动态维护b的最小生成树
* 假设现在加入的边是(x,y) a b
* 那么答案=min(答案,a+树上1到n路径上的b的最大值)
* Time   :
\****************************************/
/****************************************\
* Author : ztx
* Title  : [NOI2014]魔法森林
* ALG    : LCT+Kruskal
* CMT    :
* 把边按a从小到大排序
* 然后一条条加边
* 动态维护b的最小生成树
* 假设现在加入的边是(x,y) a b
* 那么答案=min(答案,a+树上1到n路径上的b的最大值)
* Time   :
\****************************************/

#include <cstdio>
#include <algorithm>

int CH , NEG ;

inline int GETCHAR() {
	static const int LEN = 1<<15 ;
	static char BUF[LEN] , *S = BUF , *T = BUF ;
	if (S == T) {
		T = (S=BUF)+fread(BUF , 1 , LEN , stdin) ;
		if (S == T) return EOF ;
	}
	return *S ++ ;
}

inline void read(int& ret) {
    ret = 0 ; while (CH=GETCHAR() , CH<'!') ;
    while (ret = (ret<<1)+(ret<<3)+CH-'0' , CH=GETCHAR() , CH>'!') ;
}

#define  maxn  50010LL
#define  maxm  100010LL
#define  maxt  150010LL
#define  infi  0x7f7f7f7fLL

int n , m , Q , ans = infi , ansa ;

struct EDGE { int u , v , a , b ; } e[maxm] ;

bool Cmpa(const EDGE& a , const EDGE& b) {
	if (a.a == b.a) return a.b < b.b ;
	else return a.a < b.a ;
}


int fa[maxt] = {0} , ch[maxt][2] = {0} ;
int maxb[maxt] = {0}/*Here are the labels stored*/ , val[maxt] = {0} ;
bool rev[maxt] = {0} ;

#define  null     0LL
#define  left(u)  ch[u][0]
#define  right(u) ch[u][1]

inline void Exchange(int& a , int& b) { int c = a ; a = b ; b = c ; }

inline bool Isrt(int u) { return (fa[u]==null)||(left(fa[u])!=u&&right(fa[u])!=u) ; }

inline void Maintain(int u) {
	maxb[u] = u ;
	if (left(u) && val[maxb[left(u)]]>val[maxb[u]]) maxb[u] = maxb[left(u)] ;
	if (right(u) && val[maxb[right(u)]]>val[maxb[u]]) maxb[u] = maxb[right(u)] ;
}

inline void Clear(int u) {
	if (!u) return ;
	if (!Isrt(u)) Clear(fa[u]) ;
	if (rev[u]) {
		rev[u] = false ;
		rev[left(u)] ^= true ;
		rev[right(u)] ^= true ;
		Exchange(left(u) , right(u)) ;
	}
}

inline void zig(int x) {
    /* right rotate */
    int y = fa[x] , z = fa[y] ;
    if (left(z) == y) left(z) = x ; else if(right(z) == y) right(z) = x ; fa[x] = z ;
    fa[right(x)] = y ; left(y) = right(x) ; fa[y] = x ; right(x) = y ;
    Maintain(y) , Maintain(x) ;
}

inline void zag(int x) {
    /* left rotate */
    int y = fa[x] , z = fa[y] ;
    if (left(z) == y) left(z) = x ; else if(right(z) == y) right(z) = x ; fa[x] = z ;
    fa[left(x)] = y ; right(y) = left(x) ; fa[y] = x ; left(x) = y ;
    Maintain(y) , Maintain(x) ;
}

inline void Splay(int x) {
	Clear(x) ;
	int y , z ;
	while (!Isrt(x)) {
		y = fa[x] , z = fa[y] ;
		if (Isrt(y)) {
			if (left(y) == x) zig(x) ; else zag(x) ;
		} else {
			if (left(z) == y) {
				if (left(y) == x) zig(x) , zig(x) ;
				else zag(x) , zig(x) ;
			} else if (right(z) == y) {
				if (right(y) == x) zag(x) , zag(x) ;
				else zig(x) , zag(x) ;
			}
		}
	}
}

inline void Access(int u) {
	for (int v = null ; u ; u = fa[u]) Splay(u) , right(u) = v , v = u , Maintain(u) ;
}

inline void Makeroot(int u) {
	Access(u) , Splay(u) , rev[u] ^= true ;
}

inline void Link(int u , int v) {
	Makeroot(u) , fa[u] = v ;
}

inline void Cut(int u , int v) {
	Makeroot(u) ; Access(v) , Splay(v) , fa[u] = left(v) = null ;
}

inline int Query(int u , int v) {
	Makeroot(u) ; Access(v) , Splay(v) ; return maxb[v] ;
}


int f[maxn] = {0} ;
inline int GetAnc(int u) { return f[u] ? f[u] = GetAnc(f[u]) : u ; }
inline bool Union(int u , int v) {
	u = GetAnc(u) , v = GetAnc(v) ;
	if (u == v) return false ;
	f[u] = v ; return true ;
}

int i , j , cnt = 0 ;
int main() {
	#define READ
	#ifdef  READ
		freopen("magicalforest.in" ,"r",stdin ) ;
		freopen("magicalforest.out","w",stdout) ;
	#endif

	read(n) , read(m) ;
	for (i = 1 ; i <= m ; i ++ ) {
		read(e[i].u) , read(e[i].v) , read(e[i].a) , read(e[i].b) ;
	}

	std::sort(e+1 , e+m+1 , Cmpa) ;
	for (i = 1 ; i <= m ; i ++ ) {
		val[i+n] = e[i].b , maxb[i+n] = i+n ;
		/* Edges are regarded as points */
	}

	/* Kruskal */
	cnt = 0 ;
	for (i = 1 ; i <= m ; i ++ ) {
		if (Union(e[i].u , e[i].v)) {
			Link(e[i].u , i+n) , Link(e[i].v , i+n) ;
		} else {
			j = Query(e[i].u , e[i].v) ;
			if (e[i].b < val[j]) {
				Cut(e[j-n].u , j) , Cut(e[j-n].v , j) ;
				Link(e[i].u , i+n) , Link(e[i].v , i+n) ;

			}
		}
		if (GetAnc(1) == GetAnc(n)) {
			ansa = val[Query(1 , n)]+e[i].a ;
			if (ansa < ans) ans = ansa ;
		}
	}
	if (ans == infi) ans = -1 ;
	printf("%d\n", ans ) ;

	#ifdef  READ
		fclose(stdin) ; fclose(stdout) ;
	#else
		getchar() ; getchar() ;
	#endif
	return 0 ;
}
/*
4 5
1 2 19 1
2 3 8 12
2 4 12 15
1 3 17 8
3 4 1 17

3 1
1 2 1 1

*/

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