【NOI2010】 成长快乐
这里存放这道题的程序，题解在：http://blog.sina.com.cn/s/blog_86942b1401015c3u.html
case 1： 手算。
case 2：搜索
program nemo4;
{for case 2}
const zero=1e-10;
max=10000000;
type
ty1=record
w,x,y,p,q:extended;
end;
ty2=record
t,x,y:extended;
s:longint;
end;
var
v,w,x,y,tot_t,all:extended;
n,i,tot:longint;
fish:array[0..10000] of ty1;
step,tmp:array[0..10000] of ty2;
get:array[0..10000] of boolean;
//==============================
procedure find(s:longint; x,y,w,now:extended);
var
j:longint;
a,b,c,d,fx,fy,t:extended;
begin
if (s=n+1)or(now-tot_t>zero) then exit;
for j:=1 to n do
if not get[j] and (fish[j].w-w<-zero) then
begin
fx:=fish[j].x+fish[j].p*now;
fy:=fish[j].y+fish[j].q*now;
a:=sqr(v)-sqr(fish[j].p)-sqr(fish[j].q);
b:=2*fish[j].p*(x-fx)+2*fish[j].q*(y-fy);
c:=-sqr(x-fx)-sqr(y-fy);
t:=max;
if abs(a)<zero then
begin
if abs(b)<zero then continue;
if -c/b>-zero then t:=-c/b;
end else
begin
if sqr(b)-4*a*c<-zero then continue;
d:=(-b+sqrt(sqr(b)-4*a*c))/(2*a);
if d>-zero then t:=d;
d:=(-b-sqrt(sqr(b)-4*a*c))/(2*a);
if (d>-zero)and(d>t) then t:=d;
end;
if t-max>-zero then continue;
tmp[s+1].x:=fx+fish[j].p*t;
tmp[s+1].y:=fy+fish[j].q*t;
tmp[s+1].s:=j;
tmp[s+1].t:=now+t;
get[j]:=true;
find(s+1,tmp[s+1].x,tmp[s+1].y,w+fish[j].w,now+t);
get[j]:=false;
end;
if all-w<-zero then
begin
tot:=s; all:=w;
for j:=1 to s do step[j]:=tmp[j];
end;
end;
//==============================
begin
assign(input,'nemo2.in'); reset(input);
assign(output,'nemo2.out'); rewrite(output);
read(w,v,tot_t,x,y);
read(n); tot:=0; all:=0;
for i:=1 to n do read(fish[i].w,fish[i].x,fish[i].y,fish[i].p,fish[i].q);
find(0,x,y,w,0);
writeln(tot);
writeln(all-w:0:6);
for i:=1 to tot do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
case 3：模拟：
program nemo3;
{for case 3}
const zero=1e-10;
max=100000000;
type
ty1=record
w,x,y,p,q:extended;
end;
ty2=record
t,x,y:extended;
s:longint;
end;
var
v,w,x,y,tot_t,a,b,c,d,now,time,all:extended;
n,i,j,t,tot:longint;
fish:array[0..10000] of ty1;
step:array[0..10000] of ty2;
dis:array[0..10000] of extended;
get:array[0..10000] of boolean;
//==============================
begin
assign(input,'nemo3.in'); reset(input);
assign(output,'nemo3.out'); rewrite(output);
read(w,v,tot_t,x,y);
read(n); time:=0; tot:=0; all:=0;
for i:=1 to n do read(fish[i].w,fish[i].x,fish[i].y,fish[i].p,fish[i].q);
for i:=1 to n do
begin
for j:=1 to n do dis[j]:=max;
for j:=1 to n do
if not get[j] and (fish[j].w-w<-zero) then
begin
a:=sqr(v)-sqr(fish[j].p)-sqr(fish[j].q);
b:=2*fish[j].p*(x-fish[j].x)+2*fish[j].q*(y-fish[j].y);
c:=-sqr(x-fish[j].x)-sqr(y-fish[j].y);
if abs(a)<zero then
begin
if abs(b)<zero then continue;
dis[j]:=-c/b;
if dis[j]<-zero then dis[j]:=max;
end else
begin
if sqr(b)-4*a*c<-zero then continue;
d:=(-b+sqrt(sqr(b)-4*a*c))/(2*a);
if d>-zero then dis[j]:=d;
d:=(-b-sqrt(sqr(b)-4*a*c))/(2*a);
if d>-zero then dis[j]:=d;
end;
end;
now:=max; t:=0;
for j:=1 to n do
if not get[j] and (fish[j].w-w<-zero) and (now-dis[j]>zero) then
begin
t:=j;
now:=dis[j];
end;
if t=0 then break;
time:=time+now;
if time-tot_t>zero then break;
get[t]:=true;
inc(tot);
step[tot].x:=fish[t].x+fish[t].p*now;
step[tot].y:=fish[t].y+fish[t].q*now;
step[tot].s:=t;
step[tot].t:=time;
x:=step[tot].x; y:=step[tot].y;
w:=w+fish[t].w;
all:=all+fish[t].w;
for j:=1 to n do
if not get[j] then
begin
fish[j].x:=fish[j].x+fish[j].p*now;
fish[j].y:=fish[j].y+fish[j].q*now;
end;
end;
writeln(tot);
writeln(all:0:6);
for i:=1 to tot do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
case 4 and 10：随机化贪心
program nemo5;
{for case 4/10}
const zero=1e-10;
max=10000000;
type
ty1=record
w,x,y,p,q:extended;
end;
ty2=record
t,x,y:extended;
s:longint;
end;
var
v,w0,x0,y0,tot_t,all,x,y:extended;
n,tot,i,tot_s,t:longint;
fish:array[0..10000] of ty1;
step,tmp:array[0..10000] of ty2;
get:array[0..10000] of boolean;
sx:array[0..10000] of longint;
s:array[0..10000] of extended;
//==============================
procedure sort(l,r:longint);
var
i,j,tmp1:longint;
tmp2,m:extended;
begin
i:=l; j:=r; m:=s[(i+j) >> 1];
repeat
while s[i]>m do inc(i);
while s[j]<m do dec(j);
if i<=j then
begin
tmp1:=sx[i]; sx[i]:=sx[j]; sx[j]:=tmp1;
tmp2:=s[i]; s[i]:=s[j]; s[j]:=tmp2;
inc(i); dec(j);
end;
until i>j;
if i<r then sort(i,r);
if j>l then sort(l,j);
end;
//==============================
function calc(t:longint; x,y,now:extended):extended;
var
fx,fy,a,b,c,d,k:extended;
begin
k:=max;
fx:=fish[t].x+now*fish[t].p;
fy:=fish[t].y+now*fish[t].q;
a:=sqr(v)-sqr(fish[t].p)-sqr(fish[t].q);
b:=2*fish[t].p*(x-fx)+2*fish[t].q*(y-fy);
c:=-sqr(x-fx)-sqr(y-fy);
if abs(a)<zero then
begin
if abs(b)<zero then exit(k);
if -c/b>-zero then k:=-c/b;
end else
begin
if sqr(b)-4*a*c<-zero then exit(k);
d:=(-b+sqrt(sqr(b)-4*a*c))/(2*a);
if d>-zero then k:=d;
d:=(-b-sqrt(sqr(b)-4*a*c))/(2*a);
if (d>-zero)and(d>k) then k:=d;
end;
exit(k);
end;
//==============================
procedure insert(fx:longint; now:extended);
begin
inc(tot_s);
s[tot_s]:=fish[fx].w/sqr(sqr(calc(fx,x,y,now)));
sx[tot_s]:=fx;
end;
//==============================
function get_rand:longint;
var
i,j,k:longint;
begin
for j:=1 to tot_s do
if (s[j]-s[j+1])/s[j]>0.031 then break;
for k:=1 to j do
if random(maxlongint) and 1=1 then break;
for i:=1 to k do
begin
if random() < exp(-10/t) then break;
end;
exit(sx[i]);
end;
//==============================
procedure main;
var
now,w,turn:extended;
now_tot,t,j,i:longint;
begin
fillchar(get,sizeof(get),0);
fillchar(tmp,sizeof(tmp),0);
now:=0; now_tot:=0; x:=x0; y:=y0; w:=w0;
for j:=1 to n do
begin
tot_s:=0;
for i:=1 to n do
if not get[i] and(fish[i].w-w<-zero) then insert(i,now);
sort(1,tot_s);
if tot_s<1 then break;
t:=get_rand;
turn:=calc(t,x,y,now);
if turn>max-1000 then continue;
now:=now+turn;
if now-tot_t>zero then break;
get[t]:=true;
inc(now_tot);
tmp[now_tot].x:=fish[t].x+fish[t].p*now;
tmp[now_tot].y:=fish[t].y+fish[t].q*now;
tmp[now_tot].s:=t;
tmp[now_tot].t:=now;
x:=tmp[now_tot].x; y:=tmp[now_tot].y;
w:=w+fish[t].w;
end;
if w>all then
begin
tot:=now_tot;
all:=w;
step:=tmp;
end;
end;
//==============================
begin
assign(input,'nemo10.out'); reset(input);
readln(tot); readln(all);
for i:=1 to tot do
read(step[i].t,step[i].x,step[i].y,step[i].s);
close(input);
assign(input,'nemo10.in'); reset(input);
assign(output,'nemo10.out'); rewrite(output);
randomize;
read(w0,v,tot_t,x0,y0);
read(n); all:=all+w0;
for i:=1 to n do read(fish[i].w,fish[i].x,fish[i].y,fish[i].p,fish[i].q);
t:=20;
while t>0 do
begin
main;
dec(t);
end;
writeln(tot);
writeln(all-w0:0:6);
for i:=1 to tot do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
case 5/6：接元宝
program nemo6;
{for case 5/6}
const zero=1e-10;
type
ty1=record
w,x,y,p,q:extended;
end;
ty2=record
t,x,y:extended;
s:longint;
end;
var
v,w0,x0,y0,tot_t,all,best:extended;
n,tot,i,j,t:longint;
fish:array[0..10000] of ty1;
step:array[0..10000] of ty2;
f,fall:array[0..10000] of extended;
sa,g:array[0..10000] of longint;
//====================
procedure sort(l,r:longint);
var
i,j,tmp1:longint;
tmp2,m:extended;
begin
i:=l; j:=r; m:=fall[(i+j) >> 1];
repeat
while fall[i]<m do inc(i);
while fall[j]>m do dec(j);
if i<=j then
begin
tmp2:=fall[i]; fall[i]:=fall[j]; fall[j]:=tmp2;
tmp1:=sa[i]; sa[i]:=sa[j]; sa[j]:=tmp1;
inc(i); dec(j);
end;
until i>j;
if i<r then sort(i,r);
if j>l then sort(l,j);
end;
//====================
function check(l,r:longint):boolean;
begin
if abs(fish[sa[l]].x-fish[sa[r]].x)/v+fall[l]-fall[r]>zero then exit(false);
exit(true);
end;
//====================
procedure huisu(x:longint);
begin
if g[x]>0 then huisu(g[x]);
inc(tot);
all:=all+fish[sa[x]].w;
step[tot].s:=sa[x];
step[tot].x:=fish[sa[x]].x;
step[tot].t:=fall[x];
end;
//====================
begin
assign(input,'nemo6.in'); reset(input);
assign(output,'nemo6.out'); rewrite(output);
randomize;
read(w0,v,tot_t,x0,y0);
read(n); all:=0;
for i:=1 to n do
begin
read(fish[i].w,fish[i].x,fish[i].y,fish[i].p,fish[i].q);
fall[i]:=abs(fish[i].y-y0)/abs(fish[i].q);
sa[i]:=i;
end;
sort(1,n);
for i:=1 to n do f[i]:=-100000000;
f[0]:=0;
for i:=1 to n do
begin
for j:=0 to i-1 do
if check(j,i) and (f[i]<f[j]+fish[sa[i]].w) then
begin
f[i]:=f[j]+fish[sa[i]].w;
g[i]:=j;
end;
if best<f[i] then
begin
best:=f[i];
t:=i;
end;
end;
huisu(t);
writeln(tot);
writeln(all:0:6);
for i:=1 to tot do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
case 7/8：数字三角形
program nemo2;
{for case7/8}
uses math;
type
ty=record
t,x,y:extended;
s:int64;
end;
var
n,tx,tot,p,q,maxq,ans,wi:int64;
i,j:longint;
w,v,t,x0,y0,time:extended;
fash,id:array[0..2000,0..2000] of int64;
step:array[0..2000] of ty;
f,g:array[0..2000,0..2000] of int64;
//===============================
procedure huisu(x,y:int64);
begin
if x>1 then huisu(x-1,g[x,y]);
inc(tot);
//writeln(x,' ',y);
time:=time+sqrt(sqr(x-y0)+sqr(y-x0))/v;
step[tot].t:=time;
step[tot].x:=y; step[tot].y:=x;
x0:=y; y0:=x;
step[tot].s:=id[x,y];
end;
//===============================
begin
assign(input,'nemo7.in'); reset(input);
assign(output,'nemo7.out'); rewrite(output);
read(w,v,t,x0,y0);
read(n);
fillchar(fash,sizeof(fash),$fe);
for i:=1 to n do
begin
read(wi);
read(p,q); fash[q,p]:=wi;
id[q,p]:=i;
if maxq<q then maxq:=q; read(p,q);
end;
fillchar(f,sizeof(f),$fe);
for i:=0 to 2000 do
f[0,i]:=0;
for i:=1 to maxq do
for j:=0 to 2000 do
if f[i-1,j+1]>f[i-1,j-1] then
begin
f[i,j]:=f[i-1,j+1]+fash[i,j];
g[i,j]:=j+1;
end else
begin
f[i,j]:=f[i-1,j-1]+fash[i,j];
g[i,j]:=j-1;
end;
for i:=0 to 2000 do
if ans<f[maxq,i] then
begin
ans:=f[maxq,i];
tx:=i;
end;
writeln(maxq);
writeln(extended(ans):0:6);
time:=0;
huisu(maxq,tx);
for i:=1 to maxq do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
case 9：贪心：
program nemo;
{for case 9}
const max=10000000;
zero=1e-6;
type
ty1=record
w,x,y,p,q:extended;
end;
ty2=record
t,x,y:extended;
s:longint;
end;
var
w,x,y,v,tot_t,now_t,ans,d:extended;
n,i,j,t,tot:longint;
f:array[0..10000] of ty1;
get:array[0..10000] of boolean;
step:array[0..10000] of ty2;
//============================
function dis(i:longint; x,y:extended):extended;
begin
exit(sqrt(sqr(x-f[i].x)+sqr(y-f[i].y)));
end;
//============================
begin
assign(input,'nemo9.in'); reset(input);
assign(output,'nemo9.out'); rewrite(output);
read(w,v,tot_t,x,y);
read(n); ans:=0; tot:=0; now_t:=0;
fillchar(get,sizeof(get),false);
for i:=1 to n do read(f[i].w,f[i].x,f[i].y,f[i].p,f[i].q);
for i:=1 to n do
begin
d:=max; t:=0;
for j:=1 to n do
if not get[j] and (f[j].w-w<-zero) and (dis(j,x,y)<d) then
begin
t:=j;
d:=dis(j,x,y);
end;
if t=0 then break;
now_t:=now_t+dis(t,x,y)/v;
if now_t-tot_t>zero then break;
get[t]:=true;
w:=w+f[t].w;
ans:=ans+f[t].w;
inc(tot);
step[tot].t:=now_t;
step[tot].s:=t;
step[tot].x:=f[t].x;
step[tot].y:=f[t].y;
x:=f[t].x; y:=f[t].y;
end;
writeln(tot);
writeln(ans:0:6);
for i:=1 to tot do
writeln(step[i].t:0:6,' ',step[i].x:0:6,' ',step[i].y:0:6,' ',step[i].s);
close(input); close(output);
end.
{nemo 100 Evaluate answer files.
101 10 0.000 Correct! Yours = 20.00, Best = 20.00
101 10 0.000 Correct! Yours = 73.00, Best = 73.00
101 10 0.000 Correct! Yours = 1073741823.00, Best = 1073741823.00
101 10 0.000 Correct! Yours = 25905712.00, Best = 25905712.00
101 10 0.000 Correct! Yours = 34258154.00, Best = 34258154.00
101 10 0.000 Correct! Yours = 34189691.00, Best = 34189691.00
101 10 0.000 Correct! Yours = 56452.00, Best = 56452.00
101 10 0.000 Correct! Yours = 174773389722037.00, Best = 174773389722037.00
101 10 0.000 Correct! Yours = 16667039.00, Best = 16667039.00
101 10 0.000 Correct! Yours = 22072761.00, Best = 21848713.00
}102 100
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