PO3613 Cow Relays——矩阵乘法+快速幂(迭代)的变形应用

状态设计:d[i,j](k)表示经过k条边的i到j的最短路。因为用了迭代的方法,所以可以省略。

状态转移:d[i,j](M)=d[i,k](M >>1)+d[k,j](M>>1)

代码:

program poj3613;//By_thispoet

const

	maxn=105;

var

	i,j,k,m,n,p,q,s,e,tot		:longint;

	num							:array[0..maxn*10]of longint;

	d,b,map						:array[0..maxn,0..maxn]of longint;



function hash(i:longint):longint;

begin

	if num[i]=0 then

		begin

			inc(tot);num[i]:=tot;

		end;

	exit(num[i]);

end;



function min(i,j:int64):int64;

begin

	if i<j then exit(i);exit(j);

end;



begin

	readln(n,m,s,e);

	filldword(map,sizeof(map)shr 2,maxlongint);

	while m>0 do

		begin

			readln(j,p,q);

			p:=hash(p);q:=hash(q);

			map[p,q]:=j;map[q,p]:=j;

			dec(m);

		end;

	filldword(d,sizeof(d)shr 2,maxlongint);

	for i:=1 to tot do d[i,i]:=0;

	while n>0 do

		begin

			if n and 1=1 then

				begin

					filldword(b,sizeof(b)shr 2,maxlongint);

					for i:=1 to tot do

						for j:=1 to tot do

							for k:=1 to tot do

								if (map[i,k]<maxlongint)and(d[k,j]<maxlongint) then b[i,j]:=min(b[i,j],map[i,k]+d[k,j]);

					d:=b;

				end;

			filldword(b,sizeof(b)shr 2,maxlongint);

			for i:=1 to tot do

				for j:=1 to tot do

					for k:=1 to tot do

						if (map[i,k]<maxlongint)and(map[k,j]<maxlongint) then b[i,j]:=min(b[i,j],map[i,k]+map[k,j]);

			map:=b;

			n:=n >> 1;

		end;

	writeln(d[num[s],num[e]]);

end.

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