Codeforces 608 B. Hamming Distance Sum-前缀和
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|.
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.
Print a single integer — the sum of Hamming distances between a and all contiguous substrings of b of length |a|.
01
00111
3
0011
0110
2
For the first sample case, there are four contiguous substrings of b of length |a|: "00", "01", "11", and "11". The distance between "01" and "00" is |0 - 0| + |1 - 0| = 1. The distance between "01" and "01" is |0 - 0| + |1 - 1| = 0. The distance between "01" and "11" is |0 - 1| + |1 - 1| = 1. Last distance counts twice, as there are two occurrences of string "11". The sum of these edit distances is 1 + 0 + 1 + 1 = 3.
The second sample case is described in the statement.
题意就是计算距离,拿数据来说,01和00111,就是01和00,01和01,01和11,01和11,就是下面的依次划取和第一组等长的串来计算,划一次就往后走一个数,反正差不多这个意思,而且!!!第二组的长度一定是>=第一组的长度
代码:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=2*1e5+10;
ll sum[N][2];
char s1[N],s2[N];
int a[N],b[N];
int main(){
scanf("%s%s",s1+1,s2+1);
int len1=strlen(s1+1);
int len2=strlen(s2+1);
for(int i=1;i<=len1;i++)
a[i]=s1[i]-'0';
for(int i=1;i<=len2;i++)
b[i]=s2[i]-'0';
for(int i=1;i<=len2;i++){
for(int j=0;j<2;j++)
sum[i][j]+=sum[i-1][j];
sum[i][b[i]]++;
}
ll ans=0;
for(int i=1;i<=len1;i++){
ans+=sum[len2-len1+i][1-a[i]];
ans-=sum[i-1][1-a[i]];
}
printf("%I64d\n",ans);
return 0;
}