不难想到从小到大穷举a，判断在携带不超过a个B型精灵的情况下最少携带多少个B型精灵
这是一个经典的问题，显然要求出最小生成树，树上1到N路径上最大的边即是答案
所以我们要动态维护一个最小生成树可以用link cut tree维护
根据最小生成树的回路性质，我们加入一条边(u,v)，保留树上u-v路径上最大边和新边中小的那个
由于这里维护的是边权，我们可以把每条边当做一个点p(u,v)，连接(u,v)时，即是连接(u,p)和（v,p)
然后记录下路径上最大点权的编号即可
1 var son:array[0..150010,1..2] of longint; 2 q,f,w,fa,v:array[0..150010] of longint; 3 rev:array[0..150010] of boolean; 4 s,e,a,b:array[0..150010] of longint; 5 ans,i,n,m:longint; 6 7 function min(a,b:longint):longint; 8 begin 9 if a>b then exit(b) else exit(a); 10 end; 11 12 function getf(x:longint):longint; 13 begin 14 if f[x]<>x then f[x]:=getf(f[x]); 15 exit(f[x]); 16 end; 17 18 procedure swap(var a,b:longint); 19 var c:longint; 20 begin 21 c:=a; 22 a:=b; 23 b:=c; 24 end; 25 26 function root(x:longint):boolean; 27 begin 28 exit((son[fa[x],1]<>x) and (son[fa[x],2]<>x)); 29 end; 30 31 procedure update(x:longint); 32 begin 33 w[x]:=x; 34 if v[w[son[x,1]]]>v[w[x]] then w[x]:=w[son[x,1]]; 35 if v[w[son[x,2]]]>v[w[x]] then w[x]:=w[son[x,2]]; 36 end; 37 38 procedure push(x:longint); 39 begin 40 if rev[x] then 41 begin 42 rev[son[x,1]]:=not rev[son[x,1]]; 43 rev[son[x,2]]:=not rev[son[x,2]]; 44 swap(son[x,1],son[x,2]); 45 rev[x]:=false; 46 end; 47 end; 48 49 procedure rotate(x,w:longint); 50 var y:longint; 51 begin 52 y:=fa[x]; 53 if not root(y) then 54 begin 55 if son[fa[y],1]=y then son[fa[y],1]:=x 56 else son[fa[y],2]:=x; 57 end; 58 fa[x]:=fa[y]; 59 son[y,3-w]:=son[x,w]; 60 if son[x,w]<>0 then fa[son[x,w]]:=y; 61 son[x,w]:=y; 62 fa[y]:=x; 63 update(y); 64 end; 65 66 procedure splay(x:longint); 67 var y,t,i:longint; 68 begin 69 t:=0; 70 i:=x; 71 while not root(i) do 72 begin 73 inc(t); 74 q[t]:=i; 75 i:=fa[i]; 76 end; 77 inc(t); 78 q[t]:=i; 79 for i:=t downto 1 do 80 push(q[i]); 81 while not root(x) do 82 begin 83 y:=fa[x]; 84 if root(y) then 85 begin 86 if son[y,1]=x then rotate(x,2) 87 else rotate(x,1); 88 end 89 else begin 90 if son[fa[y],1]=y then 91 begin 92 if son[y,1]=x then rotate(y,2) 93 else rotate(x,1); 94 rotate(x,2); 95 end 96 else begin 97 if son[y,1]=x then rotate(x,2) 98 else rotate(y,1); 99 rotate(x,1); 100 end; 101 end; 102 end; 103 update(x); 104 end; 105 106 procedure access(x:longint); 107 var y:longint; 108 begin 109 y:=0; 110 repeat 111 splay(x); 112 son[x,2]:=y; 113 update(x); 114 y:=x; 115 x:=fa[x]; 116 until x=0; 117 end; 118 119 procedure sort(l,r: longint); 120 var i,j,x,y: longint; 121 begin 122 i:=l; 123 j:=r; 124 x:=a[(l+r) div 2]; 125 repeat 126 while a[i]<x do inc(i); 127 while x<a[j] do dec(j); 128 if not(i>j) then 129 begin 130 swap(s[i],s[j]); 131 swap(e[i],e[j]); 132 swap(a[i],a[j]); 133 swap(b[i],b[j]); 134 inc(i); 135 j:=j-1; 136 end; 137 until i>j; 138 if l<j then sort(l,j); 139 if i<r then sort(i,r); 140 end; 141 142 procedure makeroot(x:longint); 143 begin 144 access(x); 145 splay(x); 146 rev[x]:=not rev[x]; 147 end; 148 149 procedure path(x,y:longint); 150 begin 151 makeroot(x); 152 access(y); 153 splay(y); 154 end; 155 156 procedure link(x,y:longint); 157 begin 158 makeroot(x); 159 fa[x]:=y; 160 end; 161 162 procedure cut(x,y:longint); 163 begin 164 makeroot(x); 165 access(y); 166 splay(y); 167 son[y,1]:=0; 168 fa[x]:=0; 169 end; 170 171 procedure deal(i:longint); 172 var x,y,z:longint; 173 begin 174 x:=getf(s[i]); 175 y:=getf(e[i]); 176 if x<>y then 177 begin 178 f[x]:=y; 179 link(s[i],n+i); 180 link(e[i],n+i); 181 end 182 else begin 183 x:=s[i]; 184 y:=e[i]; 185 path(x,y); 186 z:=w[y]; 187 if v[z]>b[i] then 188 begin 189 cut(s[z-n],z); 190 cut(e[z-n],z); 191 link(s[i],n+i); 192 link(e[i],n+i); 193 end; 194 end; 195 end; 196 197 begin 198 readln(n,m); 199 for i:=1 to m do 200 readln(s[i],e[i],a[i],b[i]); 201 for i:=1 to n do 202 f[i]:=i; 203 sort(1,m); 204 for i:=1 to m do 205 begin 206 v[n+i]:=b[i]; 207 w[n+i]:=n+i; 208 end; 209 ans:=2147483647; 210 i:=0; 211 while i<m do 212 begin 213 inc(i); 214 deal(i); 215 while a[i]=a[i+1] do 216 begin 217 inc(i); 218 deal(i); 219 end; 220 if getf(1)=getf(n) then 221 begin 222 path(1,n); 223 ans:=min(ans,a[i]+v[w[n]]); 224 end; 225 end; 226 if ans=2147483647 then writeln(-1) 227 else writeln(ans); 228 end.
