C语言中位运算的巧用.doc

C 2012/3/21 by 1X2N24816.X24816101001000100001010110111011110X2N21int CountNumberOfOne(int number)int counter = 0;while (number)counter+;number &= number - 1 ;return counter;1A1010B1100A&B=1000A|B=1110AB=0110A=11110101 1AA8ababab0A1001B3AB1b2bb2bGNU GCC/G+ A=-1ABB-11xx0 232646410A=1011 0131xx ALL_BITS 1 A|B A&B A& B ALL_BITSAbit A|=1bitbit A=1bitbit A&=1bitbit (A&1bit)!=01swap(a, b)a=b;b=a;a=b;2a111 LowbitBIT0x1Lowbit(x)=x&(x(x-1)Lowbit(x)=x&(x-1)Lowbit(x)=x&-xx1x&x-1 Cx (x-1) x-110101N 0) Pdep= Index(K & -K);g2/Index(a)a2 Dfs(dep+1, mask (K & -K); K = K & -K;O(N!)O(NN)21NNx12N-123128-132484CCPUBSFBSRGNU_builtin_clz0_builtin_ctz0CC+0312xxLowbit(x)01x112Cntx x1Cntx = Cntx 1 + (x & 1)3GNU _builtin_popcount _builtin_ctz4pop(xx) /x3232 x=x-(x1)&0x55555555); x=(x&0x33333333)+(x2)&0x33333333); x=(x+(x4)&0x0f0f0f0f; x=x+(x8); x=x+(x16); returnx&0x0000003f; 4ABAB1NO(2N)2)=O(4N)2N,2N,S,N2S,2N,O(2N)2)=O(4N)11001111SuperSetIterating_All_SubSet(SuperSet) i = SuperSet;while (i 0)i = (i - 1) & SuperSet;NO(3N)1abs( x ) y=x31 ; return(xy)-y;/ (x+y)y x, y 322x=(x&0xaaaaaaaa)1)|(x&0x55555555)2)|(x&0x33333333)4)|(x&0x0f0f0f0f)8)|(x&0x00ff00ff)16)|(x&0x0000ffff)16);32x=311=(100110111)2x=3967811584=(11101100100000000000000000000000)23kN 0,1,2,N-1int s = (1 k) - 1;while (!(s & 1 _builtin_ctz(lo 1) C 1TagsC/C+, , ,0?1614 1X2N24816.X24816101001000100001010110111011110X2N21int CountNumberOfOne(int number)int counter = 0;while (number)counter+;number &= number - 1 ;return counter;1A1010B1100A&B=1000A|B=1110AB=0110A=11110101 1AA8ababab0A1001B3AB1b2bb2bGNU GCC/G+ A=-1ABB-11xx0 232646410A=1011 0131xx ALL_BITS 1 A|B A&B A& B ALL_BITSAbit A|=1bitbit A=1bitbit A&=1bitbit (A&1bit)!=01swap(a, b)a=b;b=a;a=b;2a111LowbitBIT0x1Lowbit(x)=x&(x(x-1)Lowbit(x)=x&(x-1)Lowbit(x)=x&-xx1x&x-1 Cx (x-1) x-110101N 0) Pdep= Index(K & -K);g2/Index(a)a2 Dfs(dep+1, mask (K & -K); K = K & -K;O(N!)O(NN)21NNx12N-123128-132484CCPUBSFBSRGNU_builtin_clz0_builtin_ctz0CC+0312xxLowbit(x)01x112Cntx x1Cntx = Cntx 1 + (x & 1)3GNU _builtin_popcount _builtin_ctz4pop(xx)/x3232) x=x-(x1)&0x55555555); x=(x&0x33333333)+(x2)&0x33333333); x=(x+(x4)&0x0f0f0f0f; x=x+(x8); x=x+(x16); returnx&0x0000003f; 4ABAB1NO(2N)2)=O(4N)2N,2N,S,N2S,2N,O(2N)2)=O(4N)11001111SuperSetIterating_All_SubSet(SuperSet) i = SuperSet; while (i 0) i = (i - 1) & SuperSet;NO(3N)1abs( x ) y=x31 ; return(xy)-y;/ (x+y)y x, y 322x=(x&0xaaaaaaaa)1)|(x&0x55555555)2)|(x&0x33333333)4)|(x&0x0f0f0f0f)8)|(x&0x00ff00ff)16)|(x&0x0000ffff)16);32x=31