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.