原题链接:[编程入门]完数的判断
解题思路:
输入一个数N,循环判断,从i=2到N的每一个数;
如果是完数,则输出;
判断方法,定义j为因子(1到N-1),若i%j==0,则是它的因子;
判断期间把所有因子的和(sum)求出来;
最后和(sum)等于i则是完数;
注意事项:
每次判断完,一个数i后,要把sum置0;
按输出规则输出;
参考代码:
#include <stdio.h>
int main()
{
long double N, sum = 0;
scanf( "%Lf", &N );
for ( int i = 2; i <= N; i++ )
{
for ( int j = 1; j <i; j++ )
{
if ( i % j == 0 )
{
sum = sum + j;
}
}
if ( sum == i )
{
printf( "%d its factors are ", i );
for ( int k = 1; k < i; k++ )
{
if ( i % k == 0 )
{
printf( "%d ", k );
}
}
printf( "\n" );
}
sum = 0;
}
return(0);
}上述代码已被淘汰,现在提交会时间超限;
根据一个数的最大因子(除去他本身)不会大于它的一半,改进得到下面代码(注意:一个数 n 如果是合数,那么它的所有的因子不超过sqrt(n)是错误的;比如16的一个因子8,大于4;)
改进代码:
#include <stdio.h>
int main()
{
long double N, sum = 0;
scanf( "%Lf", &N );
for ( int i = 2; i <= N; i++ )
{
for ( int j = 1; j <=i/2; j++ )
{
if ( i % j == 0 )
{
sum = sum + j;
}
}
if ( sum == i )
{
printf( "%d its factors are ", i );
for ( int k = 1; k <=i/2; k++ )
{
if ( i % k == 0 )
{
printf( "%d ", k );
}
}
printf( "\n" );
}
sum = 0;
}
return(0);
}改进代码2:(观察前面12 个完数,个位数都是6 或者8,所以个位不是6 或8的就不判断了,并且在判断过程中,直接记录它的因子)
#include <stdio.h>
int main()
{
long double N, sum = 0;
int factor[100], x = 0;
scanf( "%Lf", &N );
for ( int i = 6; i <= N; i++ )
{
if ( i % 10 == 6 || i % 10 == 8 )
{
for ( int j = 1; j <= i / 2; j++ )
{
if ( i % j == 0 )
{
factor[x] = j;
x++;
sum = sum + j;
}
}
if ( sum == i )
{
printf( "%d its factors are ", i );
for ( int k = 0; k < x; k++ )
{
printf( "%d ", factor[k] );
}
printf( "\n" );
}
sum = 0;
x = 0;
}
}
return(0);
}0.0分
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