假设我们有lexicographicaly整数 3,5,6,9,10,12或0011,0101,0110,1001,1010,1100
每两个位设置
Say we have the lexicographicaly integers 3,5,6,9,10,12 or 0011,0101,0110,1001,1010,1100
Each with two bits set.
我要的是找到距离(有多少间辞书排列,而不做实际工作的排列)之间的发言权 3
和 5
用尽可能少的操作成为可能。
What I want is to find the distance(how many lexicographical permutations between them, without doing the actuall permutations) between say 3
and 5
using as few operations as possible.
的距离表如下
3->5 = 1 or 0011->0101 = 0001
3->6 = 2 or 0011->0110 = 0010
3->9 = 3 or 0011->1001 = 0011
3->10 = 4 or 0011->1010 = 0100
3->12 = 5 or 0011->1100 = 0101
因此,一个函数f(3,5)将返回1;
So a function f(3,5) would return 1;
该功能将始终以相同的汉明权(组位相同数量)的参数。
The function will always take arguments of same Hamming weight (same amount of set bits).
没有阵列应该被使用。
任何想法将是巨大的。
修改
忘了提,任何设置位大小(汉明权重),我会一直使用第辞书置换(基础
)作为第一个参数。
Forgot to mention, for any set bit size(the hamming weight) I will always use the first lexicographical permutation(base
) as the first argument.
例如。
hamming weight 1 base = 1
hamming weight 2 base = 3
hamming weight 3 base = 7
...
编辑2
该解决方案应该适用于任何汉明权重,对不起,我是不够具体。
The solution should work for any hamming weight, sorry I was not specific enough.
推荐答案
具有数 X = 2 K 1 +2 K 2 + ... + 2 K 米 其中k 1 < k 2 < ...< k M 它可以被要求保护的数x的该位置中具有相同汉明的所有数字的字典顺序有序序列重量是 lex_order(X)= C(K 1 ,1)+ C(K 2 ,2)+ ... + C(K M ,M) 其中,C(N,M)= N!/ M!/(N-M)!或者0,如果M> N
Having a number x = 2k1+2k2+...+2km where k1<k2<...<km it could be claimed that position of number x in lexicographically ordered sequence of all numbers with the same hamming weight is lex_order(x) = C(k1,1)+C(k2,2)+...+C(km,m) where C(n,m) = n!/m!/(n-m)! or 0 if m>n
例如:
3 = 2 0 + 2 1 lex_order(3)= C(0,1)+ C(1,2)= 0 + 0 = 0
3 = 20 + 21 lex_order(3) = C(0,1)+C(1,2) = 0+0 = 0
5 = 2 0 + 2 2 lex_order(5)= C(0,1)+ C(2,2)= 0 + 1 = 1
5 = 20 + 22 lex_order(5) = C(0,1)+C(2,2) = 0+1 = 1
6 = 2 1 + 2 2 lex_order(6)= C(1,1)+ C(2,2)= 1 + 1 = 2
6 = 21 + 22 lex_order(6) = C(1,1)+C(2,2) = 1+1 = 2
9 = 2 0 + 2 3 lex_order(9)= C(0,1)+ C(3,2)= 0 + 3 = 3
9 = 20 + 23 lex_order(9) = C(0,1)+C(3,2) = 0+3 = 3
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