小学生计算机编程经典算法
1．求两数的最大公约数
if a
function gcd(a,b:qword):qword;
begin
if b=0 then gcd:=a
else gcd:=gcd(b,a mod b);
end;
2．求两数的最小公倍数
function lcm(a,b:qword):qword;
begin
if a
lcm:=a div gcd(a,b)*b;
end;
3．素数的求法
function prime (n: integer): boolean;
var i: integer;
begin
for i:=2 to trunc(sqrt(n)) do
if n mod i=0 then
begin
prime:=false; exit;
end;
prime:=true;
end;
排序算法
1.快速排序：
procedure qsort(l,r:integer);
var i,j,mid:integer;
begin
i:=l;j:=r; mid:=a[(l+r) div 2]; {将当前序列在中间位置的数定义为中间数} repeat
while a while a[j]>mid do dec(j);{在右半部分寻找比中间数小的数} if i<=j then begin {若找到一组与排序目标不一致的数对则交换它们} swap(a[i],a[j]); inc(i);dec(j); {继续找} until i>j; if l end;{sort} 2.选择排序： procedure sort; var i,j,k:integer; begin for i:=1 to n-1 do for j:=i+1 to n do if a[i]>a[j] then swap(a,a[j]); end; 3. 冒泡排序 procedure bubble_sort; var i,j,k:integer; begin for i:=1 to n-1 do for j:=n downto i+1 do if a[j-1] 4.归并排序 procedure merge; var i,j,k:longint; begin i:=1;j:=1;k:=1; while (i<=n)and(j<=m) do if a[i] else begin c[k]:=b[j];inc(j);inc(k); end; while j<=m do begin c[k]:=b[j];inc(j);inc(k); end; while i<=n do begin c[k]:=a[i];inc(i);inc(k); end; end; 闰年 if (y mod 400=0) or((y mod 100<>0) and (y mod 4=0)) then y:=' 闰年'; 高精度计算 1．高精度加法 function plus(a,b:ansistring):ansistring; var m,n:array[1..5000] of integer; i,j:integer; la,lb,len:integer; begin la:=length(a); lb:=length(b); fillchar(m,sizeof(m),0); fillchar(n,sizeof(n),0); for i:=1 to la do m[i]:=ord(a[la-i+1])-ord('0'); for i:=1 to lb do n[i]:=ord(b[lb-i+1])-ord('0'); if la>lb then len:=la else len:=lb; for i:=1 to len do m[i]:=m[i]+n[i]; for i:=1 to len do if m[i]>=10 then begin m[i+1]:=m[i+1]+m[i] div 10; m[i]:=m[i] mod 10; end; plus:=''; j:=4500; while m[j]=0 do dec(j); for i:=j downto 1 do plus:=plus+chr(m[i]+ord('0')); end; 2．高精度减法 function substract(a,b:ansistring):ansistring; var m,n:array[1..5000] of integer; i,j:integer; la,lb,len:integer; begin la:=length(a); lb:=length(b); fillchar(m,sizeof(m),0); fillchar(n,sizeof(n),0); for i:=1 to la do m[i]:=ord(a[la-i+1])-ord('0'); for i:=1 to lb do n[i]:=ord(b[lb-i+1])-ord('0'); if la>lb then len:=la else len:=lb; for i:=1 to len do if m[i]>=n[i] then m[i]:=m[i]-n[i] else begin m[i]:=m[i]+10-n[i]; m[i+1]:=m[i+1]-1; end; substract:=''; j:=4500; while m[j]=0 do dec(j); for i:=j downto 1 do substract:=substract+chr(m[i]+ord('0')); end; 3．高精度乘法 function multiply(a,b:string):string; var m,n,o:array[1..5000] of longint; i,j,la,lb,x:longint; begin la:=length(a); lb:=length(b); fillchar(m,sizeof(m),0); fillchar(n,sizeof(n),0); fillchar(o,sizeof(o),0); for i:=1 to la do m[i]:=ord(a[la-i+1])-48; for i:=1 to lb do n[i]:=ord(b[lb-i+1])-48; for i:=1 to la do begin x:=0; for j:=1 to lb do begin o[i+j-1]:=m[i]*n[j]+x+o[i+j-1]; x:=o[i+j-1] div 10; o[i+j-1]:=o[i+j-1] mod 10; end; o[i+j]:=x; end; multiply:=''; j:=4500; while (o[j]=0) and(j>1) do dec(j); for i:=j downto 1 do multiply:= multiply +chr(o[i]+48); end; 4．高精度除法 var x:longint;//余数 function devide(s:ansistring;n:longint):ansistring; var a,c:array[1..5000] of longint; i,j,la:longint; begin fillchar(a,sizeof(a),0); fillchar(c,sizeof(c),0); la:=length(s); for i:=1 to la do a[i]:=ord(s[i])-48; x:=0; for i:=1 to la do begin c[i]:=(a[i]+x*10) div n; x:=(a[i]+x*10) mod n; end; j:=1; devide:=''; while (c[j]=0)and(j for i:=j to la do devide:= devide +chr(c[i]+48); end; 0-1背包： var n,m,i,x:longint; f:array[0..10000] of longint; w,c:array[1..2000] of longint; begin fillchar(f,sizeof(f),0);//必须要 readln(m,n);//背包容量m物品数n for i:=1 to n do readln(w[i],c[i]);//每个物品的重量w价值c for i:=1 to n do for x:=m downto w[i] do//注意downto if f[x-w[i]]+c[i]>f[x] then f[x]:=f[x-w[i]]+c[i];//f(x)为重量不超过x的最大价值writeln(f[m]);//f(m)为最后的最优解 end. 折半查找 function binsearch(x,l,r:longint):longint; var m:longint; begin m:=(l+r) div 2; if l>r then binsearch:=0 else if a[m]=x then binsearch:=m else if x>a[m] then binsearch:=binsearch(x,m+1,r) else binsearch:=binsearch(x,l,m-1); end;