Write a recursive function that returns the number of 1's in the binary representation of N? I am not looking for code but what is the math equation or a hint of what I am trying to do mathmatically?
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Write a recursive function that returns the number of 1's in the binary representation of N? I am not looking for code but what is the math equation or a hint of what I am trying to do mathmatically?
[Hint]
consider a function that checks a specified bit. That function can recursivley check all bits.
[/Hint]
How does this code work? Especially this line return (x & 1) + Power(x/2); What does this character do &?
#include<iostream>
using namespace std;
int Power(int);
int main()
{
int number;
cin>> number;
cout<< Power(number);
return 0;
}
int Power(int x)
{
if(x == 0)
return 0;
else
return (x & 1) + Power(x/2);
}[CODE]
>> What does this character do &?
& is the bitwise 'and', it will 'and' every bit individually...
ex)
1001 & 0011 == 0001
>> Especially this line return (x & 1) + Power(x/2)
this will return x & 1 (as described above) plus the result of calling Power(x/2). At some point x/2 will equal 0 and 0 will be returned to end the recursive cycle.
the code using Iteration is:
Code:/*assume the binary representation of the number will take M bits so we have an array called unsigned num[M]*/ #include <iostream.h> #define M 10 unsigned num[M]; void convert(unsigned) { for(int i=0;i<M;i++) { num[i]=(My_Number%2==1); My_Number/=2; } } int count(unsigned *a) { int x=0; for(int i=0;i<M;i++) if(num[i]==1) x++; return x; } int main() { unsigned r; cin >>r; for(i=0;i<M;i++) num[i]=0; convert(r); int xcount=count(num); cout <<xcount<<endl; return 0; }
There is some good information on bitwise operators in the Programming FAQ.
BITWISE HINTS:
Programmers will usually use hexadecimal when dealing with binary numbers / bit patterns. It's easier (for humans) to do binary-hex conversions than binary-decimal. C++ can use hex natively... binary takes a few more steps. And, it gets difficult (for humans) to read binary numbers when they get longer than 8-bits.
You can use the built-in Windows calculator to do decimal, binary, octal, and hex conversions.
Start -> Programs -> Accessories -> Calculator -> View -> Scientific