【Codeforces 608B】Hamming Distance Sum(前缀和)

最新推荐文章于 2021-09-09 22:07:11 发布

Chen_yuazzy

最新推荐文章于 2021-09-09 22:07:11 发布

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分类专栏： Water（水题）文章标签： codeforces 前缀和

本文链接：https://blog.youkuaiyun.com/Chen_yuazzy/article/details/77074410

该博客详细解释了如何利用前缀和方法解决Codeforces上的Hamming Distance Sum问题。通过计算两个二进制字符串间所有长度相等的子串的汉明距离之和，博主介绍了如何避免暴力求解，转而采用前缀和技巧降低复杂度，从而在限制时间内得到答案。

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Hamming Distance Sum

Description
Genos needs your help. He was asked to solve the following programming problem by Saitama:

The length of some string s is denoted |s|. The Hamming distance between two strings s and t of equal length is defined as , where si is the i-th character of s and ti is the i-th character of t. For example, the Hamming distance between string “0011” and string “0110” is |0 - 0| + |0 - 1| + |1 - 1| + |1 - 0| = 0 + 1 + 0 + 1 = 2.

Given two binary strings a and b, find the sum of the Hamming distances between a and all contiguous substrings of b of length |a|.

Input
The first line of the input contains binary string a (1 ≤ |a| ≤ 200 000).

The second line of the input contains binary string b (|a| ≤ |b| ≤ 200 000).

Both strings are guaranteed to consist of characters ‘0’ and ‘1’ only.

Output
Print a single integer — the sum of Hamming distances between a and all contiguous substrings of b of length |a|.

Example
Input
01
00111
Output
3
Input
0011
0110
Output
2

Note
For the first sample case, there are four contiguous