基本算法(用 PASCAL 描述)
上一篇 / 下一篇 2007-11-16 12:14:31 / 个人分类:Delphi编程
51Testing软件测试网Tvx0[7o4z0F&f
转:http://www.cnblogs.com/dingjie/archive/2005/07/15/193216.html
}:\ `2]D&l:ye051Testing软件测试网(SsYd!kA)lhS基本算法(用 PASCAL 描述)51Testing软件测试网4l(u&c lV b-D
1.数论算法
M co b9T ];wlR0求两数的最大公约数51Testing软件测试网ei$@v(]2t:uc
function gcd(a,b:integer):integer;51Testing软件测试网YMsy;O8@M ~
begin51Testing软件测试网9G;S1l9wl4v-]
if b=0 then gcd:=a
e:[*ZO'P#q0else gcd:=gcd (b,a mod B);
+eJH(T.nn0end;51Testing软件测试网x g I}U`6~ h"M:P
$JT!zkm6~z0求两数的最小公倍数
[t7F){xZZ3|@l0function lcm(a,b:integer):integer;51Testing软件测试网#icnsz
begin
/Eags3b3B0if a< b then swap(a,B);
)tNP we CV AY0lcm:=a;51Testing软件测试网,L\+C ah
while lcm mod b >0 do inc(lcm,a);51Testing软件测试网4j"`_;|JOQ
end;51Testing软件测试网tUV nS
51Testing软件测试网3am@%_*[/tOY
素数的求法
@}5X3Tl:c0A.小范围内判断一个数是否为质数:
!_,?h i9vB}0function prime (n: integer): Boolean;51Testing软件测试网:S#U i!G(i:]I-I l
var I: integer;
4ceJ1[+\0begin51Testing软件测试网IvyO8m(Mq2B
for I:=2 to trunc(sqrt(n)) do
c#FN~;R2G]4k0if n mod I=0 then begin51Testing软件测试网'Cj6j,M%D7Jb
prime:=false; exit;51Testing软件测试网"s Vnyq5_+LN v
end;
%R_j+k:Z ibCh2O9{0prime:=true;51Testing软件测试网!F5bA8@u
end;
6s#V'zlIm ?051Testing软件测试网T7t)_ HV[P&_V
B.判断longint范围内的数是否为素数(包含求50000以内的素数表):51Testing软件测试网*|d J'Hss
procedure getprime;
:s)IOBR'S0var
C:`Z8NM:QE%BN0i,j:longint;51Testing软件测试网n*g+ztV,qI
p:array[1..50000] of boolean;51Testing软件测试网-LSxS$K\
begin
}6C9Bm%oR!mD4Y#l0fillchar(p,sizeof(p),true);51Testing软件测试网A a^l(MM)T1P {$|-d
p[1]:=false;51Testing软件测试网M^/JNc ^}
i:=2;
)M vJ:T'W6K4_U0while i< 50000 do begin51Testing软件测试网Gm,xWn/Ad
if p[i] then begin51Testing软件测试网v!m#IpjuoI*T
j:=i*2;51Testing软件测试网n8bt3EzHF2tw
while j< 50000 do begin51Testing软件测试网:Mne8M#x{y
p[j]:=false;51Testing软件测试网}(Of RkuY.q
inc(j,i);51Testing软件测试网JJ;M)~/x ]e
end;
`$@dETp)e3x0end;51Testing软件测试网nlC%~ gk
inc(i);51Testing软件测试网z3y/?*iE#jN
end;51Testing软件测试网$\,N3odAwt e [[P,Y
l:=0;
1i(v6x$[ }/D0w(EW0for i:=1 to 50000 do
;KdGLU0if p[i] then begin
'g.U;|*{~$_9hVh0inc(l);pr[l]:=i;51Testing软件测试网R`U Da
end;51Testing软件测试网c6]YY7]rd
end;{getprime}
!Bmg8g je0
C1a6V/K;[/Z{ }9lu0function prime(x:longint):integer;
Z7s%O/jIy!r(O0var i:integer;
&B;j!Q@o[0begin51Testing软件测试网0T-}#p~,@&od
prime:=false;
K2T,G6Wm;r0for i:=1 to l do
N7_/j"e"t4m&Ta0if pr[i] >=x then break51Testing软件测试网R)v"P.u0y{4]a1?4z!F
else if x mod pr[i]=0 then exit;51Testing软件测试网K,c;r7s,u:c ^0i!j
prime:=true;
y&EO$d3iF\\0end;{prime}
5b9`"|1b ia0
'd FRj%J+\02.51Testing软件测试网Z-[S9u1~dB#w#a
+`2c[yN {"w A:@03.
.q9]r\v7s_051Testing软件测试网u l G9~ecs
51Testing软件测试网6J `@4WQ9`Mr~.\0W G
4.求最小生成树
j%Z&^6inqn0A.Prim算法:51Testing软件测试网EZ0c|#L9[T.{^m
procedure prim(v0:integer);
%cf bW9yx;G7l.}0var
-Kt[y/G$M`0lowcost,closest:array[1..maxn] of integer;51Testing软件测试网] XL]ez[#U$f
i,j,k,min:integer;51Testing软件测试网;?/amYR Jxg{Q
begin
h!\0}@"O+P)W&RM,t0for i:=1 to n do begin
,xD0ZVv z0lowcost[i]:=cost[v0,i];
%B,qw9\4Vge3d3^0closest[i]:=v0;51Testing软件测试网e$?:@? T~(YI
end;
$NG VWS8k8N0for i:=1 to n-1 do begin
\Xo"^k^ Ao&j0{寻找离生成树最近的未加入顶点k}
c\ @2~ O @A"x0min:=maxlongint;
fjzm1u2lG0for j:=1 to n do51Testing软件测试网lK6O4sLsL%Q
if (lowcost[j]< min) and (lowcost[j]< >0) then begin
.I%]7I_3eH,^0min:=lowcost[j];
Dp/J]4~2lZ*Q0k:=j;51Testing软件测试网Z3`?*l#|^L
end;51Testing软件测试网}#r+b6NI|
lowcost[k]:=0; {将顶点k加入生成树}51Testing软件测试网KOl)Ff9H/uN8yd1d%K
{生成树中增加一条新的边k到closest[k]}51Testing软件测试网4Fn@0^%uU
{修正各点的lowcost和closest值}
A_~Z8gvf1?0for j:=1 to n do51Testing软件测试网 VBH$?"j,m3w
if cost[k,j]< lwocost[j] then begin
W c:S ^4e@zQy0lowcost[j]:=cost[k,j];51Testing软件测试网Xu/vb`+o r$IU5Dp {
closest[j]:=k;
k8C3T@%E6vD0end;
c7Z8B#W Ri"T Z0end;
g8v9aHF0end;{prim}51Testing软件测试网!Qe'd\5X"C!~OT
|dZ Po!JvV0B.Kruskal算法:(贪心)
0i!^jn;P0按权值递增顺序删去图中的边,若不形成回路则将此边加入最小生成树。51Testing软件测试网C`+X\s Ep
function find(v:integer):integer; {返回顶点v所在的集合}51Testing软件测试网ZOv/V umZ
var i:integer;
@D+R(arZn0begin51Testing软件测试网 bI+F}$Vh%W
i:=1;
-|HGU'qOV|l ]{0while (i< =n) and (not v in vset[i]) do inc(i);
k j x8tI@,V5\0if i< =n then find:=i else find:=0;
q lVY?SI0end;51Testing软件测试网*[5E3o"cr1m
51Testing软件测试网*S-^J8S6XP
procedure kruskal;
9F9k|7v"jM}k T8^znM0var
8K-Rpi;]z5e0tot,i,j:integer;
"F,Z3o|G\T`8~1{Z0begin
O-}Z-txnf$aj.V1B RY0for i:=1 to n do vset[i]:=[i];{初始化定义n个集合,第I个集合包含一个元素I}
M co b9T ];wlR0求两数的最大公约数51Testing软件测试网ei$@v(]2t:uc
function gcd(a,b:integer):integer;51Testing软件测试网YMsy;O8@M ~
begin51Testing软件测试网9G;S1l9wl4v-]
if b=0 then gcd:=a
e:[*ZO'P#q0else gcd:=gcd (b,a mod B);
+eJH(T.nn0end;51Testing软件测试网x g I}U`6~ h"M:P
$JT!zkm6~z0求两数的最小公倍数
[t7F){xZZ3|@l0function lcm(a,b:integer):integer;51Testing软件测试网#icnsz
begin
/Eags3b3B0if a< b then swap(a,B);
)tNP we CV AY0lcm:=a;51Testing软件测试网,L\+C ah
while lcm mod b >0 do inc(lcm,a);51Testing软件测试网4j"`_;|JOQ
end;51Testing软件测试网tUV nS
51Testing软件测试网3am@%_*[/tOY
素数的求法
@}5X3Tl:c0A.小范围内判断一个数是否为质数:
!_,?h i9vB}0function prime (n: integer): Boolean;51Testing软件测试网:S#U i!G(i:]I-I l
var I: integer;
4ceJ1[+\0begin51Testing软件测试网IvyO8m(Mq2B
for I:=2 to trunc(sqrt(n)) do
c#FN~;R2G]4k0if n mod I=0 then begin51Testing软件测试网'Cj6j,M%D7Jb
prime:=false; exit;51Testing软件测试网"s Vnyq5_+LN v
end;
%R_j+k:Z ibCh2O9{0prime:=true;51Testing软件测试网!F5bA8@u
end;
6s#V'zlIm ?051Testing软件测试网T7t)_ HV[P&_V
B.判断longint范围内的数是否为素数(包含求50000以内的素数表):51Testing软件测试网*|d J'Hss
procedure getprime;
:s)IOBR'S0var
C:`Z8NM:QE%BN0i,j:longint;51Testing软件测试网n*g+ztV,qI
p:array[1..50000] of boolean;51Testing软件测试网-LSxS$K\
begin
}6C9Bm%oR!mD4Y#l0fillchar(p,sizeof(p),true);51Testing软件测试网A a^l(MM)T1P {$|-d
p[1]:=false;51Testing软件测试网M^/JNc ^}
i:=2;
)M vJ:T'W6K4_U0while i< 50000 do begin51Testing软件测试网Gm,xWn/Ad
if p[i] then begin51Testing软件测试网v!m#IpjuoI*T
j:=i*2;51Testing软件测试网n8bt3EzHF2tw
while j< 50000 do begin51Testing软件测试网:Mne8M#x{y
p[j]:=false;51Testing软件测试网}(Of RkuY.q
inc(j,i);51Testing软件测试网JJ;M)~/x ]e
end;
`$@dETp)e3x0end;51Testing软件测试网nlC%~ gk
inc(i);51Testing软件测试网z3y/?*iE#jN
end;51Testing软件测试网$\,N3odAwt e [[P,Y
l:=0;
1i(v6x$[ }/D0w(EW0for i:=1 to 50000 do
;KdGLU0if p[i] then begin
'g.U;|*{~$_9hVh0inc(l);pr[l]:=i;51Testing软件测试网R`U Da
end;51Testing软件测试网c6]YY7]rd
end;{getprime}
!Bmg8g je0
C1a6V/K;[/Z{ }9lu0function prime(x:longint):integer;
Z7s%O/jIy!r(O0var i:integer;
&B;j!Q@o[0begin51Testing软件测试网0T-}#p~,@&od
prime:=false;
K2T,G6Wm;r0for i:=1 to l do
N7_/j"e"t4m&Ta0if pr[i] >=x then break51Testing软件测试网R)v"P.u0y{4]a1?4z!F
else if x mod pr[i]=0 then exit;51Testing软件测试网K,c;r7s,u:c ^0i!j
prime:=true;
y&EO$d3iF\\0end;{prime}
5b9`"|1b ia0
'd FRj%J+\02.51Testing软件测试网Z-[S9u1~dB#w#a
+`2c[yN {"w A:@03.
.q9]r\v7s_051Testing软件测试网u l G9~ecs
51Testing软件测试网6J `@4WQ9`Mr~.\0W G
4.求最小生成树
j%Z&^6inqn0A.Prim算法:51Testing软件测试网EZ0c|#L9[T.{^m
procedure prim(v0:integer);
%cf bW9yx;G7l.}0var
-Kt[y/G$M`0lowcost,closest:array[1..maxn] of integer;51Testing软件测试网] XL]ez[#U$f
i,j,k,min:integer;51Testing软件测试网;?/amYR Jxg{Q
begin
h!\0}@"O+P)W&RM,t0for i:=1 to n do begin
,xD0ZVv z0lowcost[i]:=cost[v0,i];
%B,qw9\4Vge3d3^0closest[i]:=v0;51Testing软件测试网e$?:@? T~(YI
end;
$NG VWS8k8N0for i:=1 to n-1 do begin
\Xo"^k^ Ao&j0{寻找离生成树最近的未加入顶点k}
c\ @2~ O @A"x0min:=maxlongint;
fjzm1u2lG0for j:=1 to n do51Testing软件测试网lK6O4sLsL%Q
if (lowcost[j]< min) and (lowcost[j]< >0) then begin
.I%]7I_3eH,^0min:=lowcost[j];
Dp/J]4~2lZ*Q0k:=j;51Testing软件测试网Z3`?*l#|^L
end;51Testing软件测试网}#r+b6NI|
lowcost[k]:=0; {将顶点k加入生成树}51Testing软件测试网KOl)Ff9H/uN8yd1d%K
{生成树中增加一条新的边k到closest[k]}51Testing软件测试网4Fn@0^%uU
{修正各点的lowcost和closest值}
A_~Z8gvf1?0for j:=1 to n do51Testing软件测试网 VBH$?"j,m3w
if cost[k,j]< lwocost[j] then begin
W c:S ^4e@zQy0lowcost[j]:=cost[k,j];51Testing软件测试网Xu/vb`+o r$IU5Dp {
closest[j]:=k;
k8C3T@%E6vD0end;
c7Z8B#W Ri"T Z0end;
g8v9aHF0end;{prim}51Testing软件测试网!Qe'd\5X"C!~OT
|dZ Po!JvV0B.Kruskal算法:(贪心)
0i!^jn;P0按权值递增顺序删去图中的边,若不形成回路则将此边加入最小生成树。51Testing软件测试网C`+X\s Ep
function find(v:integer):integer; {返回顶点v所在的集合}51Testing软件测试网ZOv/V umZ
var i:integer;
@D+R(arZn0begin51Testing软件测试网 bI+F}$Vh%W
i:=1;
-|HGU'qOV|l ]{0while (i< =n) and (not v in vset[i]) do inc(i);
k j x8tI@,V5\0if i< =n then find:=i else find:=0;
q lVY?SI0end;51Testing软件测试网*[5E3o"cr1m
51Testing软件测试网*S-^J8S6XP
procedure kruskal;
9F9k|7v"jM}k T8^znM0var
8K-Rpi;]z5e0tot,i,j:integer;
"F,Z3o|G\T`8~1{Z0begin
O-}Z-txnf$aj.V1B RY0for i:=1 to n do vset[i]:=[i];{初始化定义n个集合,第I个集合包含一个元素I}