n作为2的幂的总和的写法数量 [英] Number of ways to write n as a sum of powers of 2
本文介绍了n作为2的幂的总和的写法数量的处理方法,对大家解决问题具有一定的参考价值,需要的朋友们下面随着小编来一起学习吧!
问题描述
是否有一种算法可以找出用多少种方式写一个数字(例如n),且总和为2?
示例:对于4种方法,有四种方法:
4 = 4
4 = 2 + 2
4 = 1 + 1 + 1 + 1
4 = 2 + 1 + 1
谢谢.
解决方案
假设g(m)是将m乘以2的幂的总和.所有数字的幂小于或等于k的m写为2的幂的和的方式.然后我们可以简化为等式:
if m==0 f(m,k)=1;
if k<0 f(m,k)=0;
if k==0 f(m,k)=1;
if m>=power(2,k) f(m,k)=f(m-power(2,k),k)+f(m,k-1);//we can use power(2,k) as one of the numbers or not.
else f(m,k)=f(m,k-1);
以6为例:
g(6)=f(6,2)
=f(2,2)+f(6,1)
=f(2,1)+f(4,1)+f(6,0)
=f(0,1)+f(2,0)+f(2,1)+f(4,0)+1
=1+1+f(0,1)+f(2,0)+1+1
=1+1+1+1+1+1
=6
这是下面的代码:
#include<iostream>
using namespace std;
int log2(int n)
{
int ret = 0;
while (n>>=1)
{
++ret;
}
return ret;
}
int power(int x,int y)
{
int ret=1,i=0;
while(i<y)
{
ret*=x;
i++;
}
return ret;
}
int getcount(int m,int k)
{
if(m==0)return 1;
if(k<0)return 0;
if(k==0)return 1;
if(m>=power(2,k))return getcount(m-power(2,k),k)+getcount(m,k-1);
else return getcount(m,k-1);
}
int main()
{
int m=0;
while(cin>>m)
{
int k=log2(m);
cout<<getcount(m,k)<<endl;
}
return 0;
}
希望有帮助!
Is there any algorithm to find out that how many ways are there for write a number for example n , with sum of power of 2 ?
example : for 4 there are four ways :
4 = 4
4 = 2 + 2
4 = 1 + 1 + 1 + 1
4 = 2 + 1 + 1
thanks.
解决方案
Suppose g(m) is the number of ways to write m as a sum of powers of 2. We use f(m,k) to represent the number of ways to write m as a sum of powers of 2 with all the numbers' power is less than or equal to k. Then we can reduce to the equation:
if m==0 f(m,k)=1;
if k<0 f(m,k)=0;
if k==0 f(m,k)=1;
if m>=power(2,k) f(m,k)=f(m-power(2,k),k)+f(m,k-1);//we can use power(2,k) as one of the numbers or not.
else f(m,k)=f(m,k-1);
Take 6 as an example:
g(6)=f(6,2)
=f(2,2)+f(6,1)
=f(2,1)+f(4,1)+f(6,0)
=f(0,1)+f(2,0)+f(2,1)+f(4,0)+1
=1+1+f(0,1)+f(2,0)+1+1
=1+1+1+1+1+1
=6
Here is the code below:
#include<iostream>
using namespace std;
int log2(int n)
{
int ret = 0;
while (n>>=1)
{
++ret;
}
return ret;
}
int power(int x,int y)
{
int ret=1,i=0;
while(i<y)
{
ret*=x;
i++;
}
return ret;
}
int getcount(int m,int k)
{
if(m==0)return 1;
if(k<0)return 0;
if(k==0)return 1;
if(m>=power(2,k))return getcount(m-power(2,k),k)+getcount(m,k-1);
else return getcount(m,k-1);
}
int main()
{
int m=0;
while(cin>>m)
{
int k=log2(m);
cout<<getcount(m,k)<<endl;
}
return 0;
}
Hope it helps!
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