【题目】把自然数Ｎ分解为若干个自然数之积。

【参考程序】

var  path :array[1..1000] of integer;

     total,n:integer;

procedure find(k,sum,dep:integer);     {K:}

var b,d:Integer;

begin

     if sum=n then                       {积等于N}

      begin

               write(n,'=',path[1]);

               for d:=2 to dep-1 do write('*',path[d]);

               writeln;inc(total);

               exit;

      end;

    if sum>n then exit;                         {累积大于N}

    for b:= trunc(n/sum)+1 downto k do               {每一种可能都去试}

               begin

                      path[dep]:=b;

                      find(b,sum*b,dep+1);

               end;

end;

begin

readln(n); total:=0;

find(2,1,1);writeln('total:',total);

readln;

end.

【题目】把自然数Ｎ分解为若干个自然数之和。

【参考答案】

                         n     │ total  

                         5     │   7

                         6     │  11

                         7     │  15

                              10     │  42

                              100    │  190569291

 【参考程序】

var n:byte; num:array[0..255] of byte;               total:word;

 procedure output(dep:byte);

var j:byte;

begin

     for j:=1 to dep do write(num[j]:3);writeln;    inc(total);

end;

 procedure find(n,dep:byte);  {N:待分解的数,DEP:深度}

  var i,j,rest:byte;

  begin

     for i:=1 to n do              {每一位从N到1去试}

      if num[dep-1]<=i then   {保证选用的数大于前一位}

       begin

                num[dep]:=i;

                rest:=n - i;               {剩余的数进行下一次递归调用}

                if (rest>0) then begin   find(rest,dep+1);end

                             else if rest=0 then output(dep);{刚好相等则输出}

                num[dep]:=0;

       end;

  end;

begin  {主程序}

   writeln('input n:');readln(n);

   fillchar(num,sizeof(num),0);

   total:=0; num[0]:=0;

   find(n,1);

   writeln('sum=',total);

end.