/*
尋找與一個給定的數目有相同數目的1位的下一個大數的問題
它在使用位串來表示子集是有用。把一個集合的所有可能元素列成一個線性序列，
使用字或字的序列來表示子集，當集合的成員i屬于該子集時設置字或字序列的第i位為1

R. W. Gosper [HAK, item 175]
?
? 按32位無符號數算 33 = 32 + 1

? s = x & -x
? r = s + x
? y = r | ((x^r) >> 2)/s)

? 或

? y = r | ((x^r) >> (2+ntz(x)))
? y = r | ((x^r) >> (33-nlz(s)))
? y = r | ((1 << (pop(x^r)-2))-1)
*/

?

#include "iostream"
#include "bitset"
#include "limits"

using namespace std;

?

?

#define out2(T) cout<<bitset<numeric_limits<unsigned short>::digits>(T)<<endl
#define SIZE(T) (numeric_limits<unsigned T>::digits)

?

?

unsigned short snoob(unsigned short x)
{
?unsigned short smallest, ripple, ones;
????????????????????????????????????????????????????? // XXX 表示任意
?????????????????????????????????????????????????// x = XXX0 1111 0000
?smallest = x & -x;????????????????????????? // 0000 0001 0000
?ripple = x + smallest;??????????????????? // XXX1 0000 0000
?ones = x ^ ripple;???????????????????????? // 0001 1111 0000
?ones = (ones >> 2)/smallest;?????? // 0000 0000 0111
?return ripple | ones;????????????????????? // XXX1 0000 0111
}

?

?

unsigned short snoob1(unsigned short x)
{ unsigned short ntz(unsigned short x);
?unsigned short smallest, ripple, ones;
??????????????????????????????????????????????? ?// XXX 表示任意
?????????????????????????????????????????????????? // x = XXX0 1111 0000
?smallest = x & -x;?????????????????????????? ?// 0000 0001 0000
?ripple = x + smallest;????????????????????? // XXX1 0000 0000
?ones = x ^ ripple;?????????????????????????? // 0001 1111 0000
?return ripple | (ones >> (2 + ntz(x)));
}

?

?

unsigned short snoob2(unsigned short x)
{ unsigned short nlz(unsigned short x);
?unsigned short smallest, ripple, ones;
?int t = SIZE(short)+1;
?????????????????????????????????????????????? // XXX 表示任意
??????????????????????????????????????????????? // x = XXX0 1111 0000
?smallest = x & -x;????????????????????????? // 0000 0001 0000
?ripple = x + smallest;??????????????????? // XXX1 0000 0000
?ones = x ^ ripple;??????????????????????? ?// 0001 1111 0000
?return ripple | (ones >> (t-nlz(smallest)));
}

?

?

unsigned short snoob3(unsigned short x)
{ unsigned short pop(unsigned short x);
?unsigned short smallest, ripple, ones;
????????????????????????????????????????????? // XXX 表示任意
??????????????????????????????????????????????? ?// x = XXX0 1111 0000
?smallest = x & -x;?????????????????????? ??? // 0000 0001 0000
?ripple = x + smallest;???????????????????? // XXX1 0000 0000
?ones = x ^ ripple;????????????????????????? // 0001 1111 0000
?return ripple | ( (1<<(pop(ones)-2)) - 1 );
}

?

?

unsigned short ntz(unsigned short x) //計算后綴0數目
{
?int s = SIZE(short);
?int i = 0; while ( !(x&(unsigned short)(1)) && i < s) { x>>=1; i++; }
?return i;
}

?

unsigned short nlz(unsigned short x) //計算前導0數目
{
?int s = SIZE(short);
?int L = (unsigned short)(1) << (s-1);
?int i = 0; while ( !(x&L) && i < s) {x<<=1; i++;}
?return i;
}

?

?

unsigned short pop(unsigned short x) //種群計數函數
{
?int s = SIZE(short);
?int i = 0; while(s--) { (x&(unsigned short)(1)) ? ++i : 0; x>>=1; }
?return i;
}

?

?

void main()
{
?out2( snoob(0xF0) );
?out2( snoob1(0xF0) );
?out2( snoob2(0xF0) );
?out2( snoob3(0xF0) );

?cout << ntz(0x17A0) <<endl;
?cout << nlz(0x17F0) <<endl;
?cout << pop(0x359D) <<endl;
}

總結

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