分治算法练习（一）
分治算法_小车问题
AYYZOJ p1428
COGS p559
具体讲解见此课件
1 //分治 2 program car1(input,output); 3 const zero=1e-4; 4 var s,a,b,c,c0,c1,t1,t2,t3,t4:real; 5 BEGIN 6 assign(input,'car.in'); 7 assign(output,'car.out'); 8 reset(input); 9 rewrite(output); 10 readln(s,a,b); 11 c0:=0; 12 c1:=s; 13 repeat 14 c:=(c0+c1)/2; 15 t3:=c/b; //甲到K乘汽车用时；也是乙走到C用时。即 乙TAC=甲TAK 16 t1:=t3+(s-c)/a; //甲到终点用时。即 甲TAB 17 t4:=(c-t3*a)/(a+b); //乙从C走，车从K来接乙相遇用时。即 乙TCD 18 t2:=t3+t4+(s-(t3+t4)*a)/b; //乙到终点用时。即 乙TAB 19 if t1<t2 then c1:=c else c0:=c; //甲的时间短，走得快，则让汽车少载一段甲；乙的时间短，走得快，则让汽车多载一段甲 20 until abs(t1-t2)<zero; 21 writeln(t1:0:2); 22 close(input); 23 close(output) 24 end. 25 26 ------------------------------------------------------------------ 27 //数学 28 var 29 s,a,b,k,x,t:real; 30 begin 31 assign(input,'car.in'); 32 reset(input); 33 assign(output,'car.out'); 34 rewrite(output); 35 readln(s,a,b); 36 k:=s*(a+b)/(3*a+b); 37 t:=k/b+(s-k)/a; 38 writeln(t:0:2); 39 close(input);close(output); 40 end.
分治算法_取余运算
AYYZOJ p1429
COGS p1130
具体讲解在这个课件中
1 program p1429; 2 var 3 b,p,k,i,len,rest,temp:longint; 4 binary:array[1..32] of longint; 5 begin 6 readln(b,p,k); 7 len:=0; 8 temp:=p; 9 while temp<>0 do 10 begin 11 len:=len+1; 12 binary[len]:=temp mod 2; 13 temp:=temp div 2; 14 end; 15 rest:=1; 16 for i:=len downto 1 do 17 begin 18 temp:=rest*rest mod k; 19 if binary[i]=1 then rest:=b mod k*temp mod k 20 else rest:=temp; 21 end; 22 writeln(b,'^',p,' mod ',k,'=',rest); 23 end.
1 Program cogs1130; 2 Var 3 B,P,K,ANS:Longint; 4 Begin 5 Assign(Input,'dmod.in'); 6 Assign(Output,'dmod.out'); 7 Reset(Input); 8 Rewrite(Output); 9 Readln(B,P,K); 10 ANS:=1; 11 B:=B Mod K; 12 While P<>0 Do 13 Begin 14 If P And 1=1 {p mod 2=1} Then ANS:=ANS*B Mod K; 15 P:=P Shr 1; {p:=p div 2}{p:=p>>1} 16 B:=B*B Mod K; 17 End; 18 Writeln(ANS); 19 Close(Input); 20 Close(Output); 21 End.
分治算法_成绩排序
AYYZOJ p1431
1 program p1431; 2 Var a,b:array[1..10000] of longint; 3 i,j,t,n:longint;flag:boolean; 4 Begin 5 readln(n); 6 for i:=1 to N do Readln(b[i],a[i]); 7 for j:=1 to N-1 do begin 8 flag:=true; 9 for i:=1 to N-j do 10 if a[i]>a[i+1] then begin 11 t:=a[i];a[i]:=a[i+1];a[i+1]:=t; 12 t:=b[i];b[i]:=b[i+1];b[i+1]:=t; 13 flag:=false; 14 end; 15 if flag then break; 16 end; 17 for i:=1 to N do writeln(b[i],' ',a[i]); 18 end.
分治算法_循环比赛
AYYZOJ p1433
这个课件讲得很清楚了
1 program p1433; 2 var 3 i,j,h,m,n:integer; 4 a:array[1..100,1..100] of integer; 5 begin 6 readln(m); 7 n:=1; a[1,1]:=1; h:=1; 8 for i:=1 to m do n:=n*2; 9 repeat 10 for i:=1 to h do 11 for j:=1 to h do 12 begin 13 a[i,j+h]:=a[i,j]+h; 14 a[i+h,j]:=a[i,j+h]; 15 a[i+h,j+h]:=a[i,j]; 16 end; 17 h:=h*2; 18 until h=n; 19 for i:=1 to n do 20 begin 21 for j:=1 to n do write(a[i,j]:4); writeln; 22 end; 23 end.
分治算法_棋子移动
AYYZOJ p1435
COGS p1161
这个课件讲得很清楚了
1 const max=100; 2 var n,st,sp:integer; 3 c:array[1..max] of char; {工作场所} 4 5 procedure print; {打印} 6 var i:integer; 7 begin 8 write('step',st:2,':'); 9 for i:=1 to 2*n+2 do write(c[i]); 10 writeln; 11 st:=st+1 12 end; 13 14 procedure init(n:integer); {初始化} 15 var i:integer; 16 begin 17 st:=0; 18 sp:=2*n+1; 19 for i:=1 to n do c[i]:='o'; 20 for i:=n+1 to 2*n do c[i]:='*'; 21 c[2*n+1]:='-';c[2*n+2]:='-'; 22 print 23 end; 24 25 procedure move(k:integer); {移动一步}//将两个横线（空）移到k处（以左横线位置为序号） 26 var j:integer; 27 begin 28 for j:=0 to 1 do begin c[sp+j]:=c[k+j];c[k+j]:='-';end; 29 sp:=k; 30 print 31 end; 32 33 procedure mv(n:integer); {主要过程} 34 var i,k:integer; 35 begin 36 if n=4 then begin 37 move(4); 38 move(8); 39 move(2); 40 move(7); 41 move(1) 42 end 43 else begin 44 move(n); 45 move(2*n-1); 46 mv(n-1) 47 end 48 end; 49 50 begin {main} 51 assign(input,'chessman.in'); 52 assign(output,'chessman.out'); 53 reset(input); 54 rewrite(output); 55 readln(n); 56 init(n); 57 mv(n); 58 close(input); 59 close(output) 60 end.
