C. Vus the Cossack and Strings(异或判断二进制位匹配数奇偶)
Problem - C - Codeforces
题目描述
Vus the Cossack has two binary strings, that is, strings that consist only of "0" and "1". We call these strings aa and bb . It is known that |b| \leq |a|∣b∣≤∣a∣ , that is, the length of bb is at most the length of aa .
The Cossack considers every substring of length |b|∣b∣ in string aa . Let's call this substring cc . He matches the corresponding characters in bb and cc , after which he counts the number of positions where the two strings are different. We call this function f(b, c)f(b,c) .
For example, let b = 00110b=00110 , and c = 11000c=11000 . In these strings, the first, second, third and fourth positions are different.
Vus the Cossack counts the number of such substrings cc such that f(b, c)f(b,c) is even.
For example, let a = 01100010a=01100010 and b = 00110b=00110 . aa has four substrings of the length |b|∣b∣ : 0110001100 , 1100011000 , 1000110001 , 0001000010 .
f(00110, 01100) = 2f(00110,01100)=2 ;
f(00110, 11000) = 4f(00110,11000)=4 ;
f(00110, 10001) = 4f(00110,10001)=4 ;
f(00110, 00010) = 1f(00110,00010)=1 .
Since in three substrings, f(b, c)f(b,c) is even, the answer is 33 .
Vus can not find the answer for big strings. That is why he is asking you to help him.
输入格式
The first line contains a binary string aa ( 1 \leq |a| \leq 10^61≤∣a∣≤106 ) — the first string.
The second line contains a binary string bb ( 1 \leq |b| \leq |a|1≤∣b∣≤∣a∣ ) — the second string.
输出格式
Print one number — the answer.
题意翻译
给定两个由0,10,1构成的字符串aa和bb，其中|b|\leq |a|.∣b∣≤∣a∣.
对于aa的某个长度为|b|∣b∣的字串cc，记对应位不同的字符数为f(b, c).f(b,c).
如：当b=00110,c=11000b=00110,c=11000时，f(b, c) = 4,f(b,c)=4,其中第1,2,3,41,2,3,4位不同。
求所有cc中f(b,c)f(b,c)为偶数的个数。
输入输出样例
输入 #1复制
01100010
00110
输出 #1复制
3
输入 #2复制
1010111110
0110
输出 #2复制
4
题解:
考虑一次匹配的奇偶,
举个例子
1100
0011
不匹配个数是偶数
1100
1100
不匹配个数是偶数
1100
1010
不匹配个数依旧是偶数
所以位置是不用考虑的,因为涉及到变化,如果为2,相当于奇偶不变,奇数就更不用考虑了,相当于数目不变
所以可以利用异或来看一段不匹配的是不是偶数,
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