实现pow(int x, int y),即x的y次方 ; 异或交换两个数;

问题1:实现pow(int x, int y) ,即x的y次方

x的y次方就是有y个x连续乘机,代码如下:

#include <stdio.h>
#include <stdlib.h> int my_pow(int x,int y){
if(x==) return ;
int ret=x,i=;
for(;i<y;i++){
ret=ret*x;
printf("y=%d;ret=%d\n",i+,ret);
}
return ret;
} int main(){
int tmp = my_pow(,);
printf("====%d\n",tmp);
return ;
}

结果

[root@admin Desktop]# ./a.out
y=;ret=
y=;ret=
y=;ret=
y=;ret=
y=;ret=
y=;ret=
y=;ret=
y=;ret=
y=;ret=
====
[root@admin Desktop]#

改进:

1.我们发现上面的方法,如果y=100,则乘法计算要进行100次,复杂度较高;

2.我们能否利用上次的计算结果,来简化计算?

比如2^4,用2*2*2*2=4*2*2=8*2=16;

上式*进行了三次乘法;

把所有重复计算剔除:2^4=2^2*2^2=4*4=16,该过程共计算两次乘法2^2,4*4;

乘法次数由3次降为2次;

3.幂运算往往容易越界,比如int最大能表示2147483647,如果算出结果超出这个范围就出错了。

1.对越界做判断和检查;

2.用合适的数据类型表示结果,貌似C里最大的整形数应该是long double;

以下通过递归方式实现以上思想:

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h> long double fun(long double x,long double y)
{
printf("ret is x=%Lf ; y=%Lf\n",x,y);//long double输出用%Lf
assert(x != && y >= );
if( == y) return ;
if( == y) return x;
if( == y) return x*x;
long double tmp = ;
if(y/ != ) tmp = x*fun(x,y-);
else tmp = fun(x*x,y/);
if(tmp>){ //如果越界可能出现负数,至于如何更合理判断越界情况,现在还没想好
printf("TMP > 0 IS: %Lf\n",tmp);
return tmp;
}
else{
printf("TMP < 0 IS: %Lf\n",tmp);
return ;
}
} int main(){
long double ret = fun(,);
printf("result = %Lf\n",ret);
return ;
}

看看洋气的输出结果:

[root@admin Desktop]# ./a.out
ret is x=10.000000 ; y=30.000000
ret is x=10.000000 ; y=29.000000
ret is x=10.000000 ; y=28.000000
ret is x=10.000000 ; y=27.000000
ret is x=10.000000 ; y=26.000000
ret is x=10.000000 ; y=25.000000
ret is x=10.000000 ; y=24.000000
ret is x=10.000000 ; y=23.000000
ret is x=10.000000 ; y=22.000000
ret is x=10.000000 ; y=21.000000
ret is x=10.000000 ; y=20.000000
ret is x=10.000000 ; y=19.000000
ret is x=10.000000 ; y=18.000000
ret is x=10.000000 ; y=17.000000
ret is x=10.000000 ; y=16.000000
ret is x=10.000000 ; y=15.000000
ret is x=10.000000 ; y=14.000000
ret is x=10.000000 ; y=13.000000
ret is x=10.000000 ; y=12.000000
ret is x=10.000000 ; y=11.000000
ret is x=10.000000 ; y=10.000000
ret is x=10.000000 ; y=9.000000
ret is x=10.000000 ; y=8.000000
ret is x=10.000000 ; y=7.000000
ret is x=10.000000 ; y=6.000000
ret is x=10.000000 ; y=5.000000
ret is x=10.000000 ; y=4.000000
ret is x=10.000000 ; y=3.000000
ret is x=10.000000 ; y=2.000000
TMP > IS: 1000.000000
TMP > IS: 10000.000000
TMP > IS: 100000.000000
TMP > IS: 1000000.000000
TMP > IS: 10000000.000000
TMP > IS: 100000000.000000
TMP > IS: 1000000000.000000
TMP > IS: 10000000000.000000
TMP > IS: 100000000000.000000
TMP > IS: 1000000000000.000000
TMP > IS: 10000000000000.000000
TMP > IS: 100000000000000.000000
TMP > IS: 1000000000000000.000000
TMP > IS: 10000000000000000.000000
TMP > IS: 100000000000000000.000000
TMP > IS: 1000000000000000000.000000
TMP > IS: 10000000000000000000.000000
TMP > IS: 100000000000000000000.000000
TMP > IS: 1000000000000000000000.000000
TMP > IS: 10000000000000000000000.000000
TMP > IS: 100000000000000000000000.000000
TMP > IS: 1000000000000000000000000.000000
TMP > IS: 10000000000000000000000000.000000
TMP > IS: 100000000000000000000000000.000000
TMP > IS: 1000000000000000000000000000.000000
TMP > IS: 9999999999999999999731564544.000000
TMP > IS: 99999999999999999997315645440.000000
TMP > IS: 999999999999999999955976585216.000000
result = 999999999999999999955976585216.000000
[root@admin Desktop]#

显然后面的结果不对,但是没有出现负数的情况。疑惑,烦请高人指点一二。

问题2:异或交换两个数

假设x=2;y=3,我们的目标是(没有蛀牙!!)交换x,y的值;

利用异或的特殊性:x^x=0

即两个相同数字异或后值为0;

解决:

令x=x^y=2^3

令y=x^y=x^y^y=2^3^3=2(此时x=x^y)

令x=x^y=x^y^2=2^3^2=3(此时x=x^y;y=2)

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