Cf1066ebinary Numbers and Sum (prefix and, binary)

Source: Internet
Author: User

Main topic

Now, give you two digits forn and m two binary numbers a,b Now, let's do the following:

    • Calculate a&b
    • The answer accumulates the value of the previous action
    • BBB, move right one, the last one to abandon directly

Now, please figure out the final answer, and output the answer to 998244353 modulo

Input and output format: input format:

First row, two integers n , m , (1≤n,m≤2x105)

First line, a binary number a with a length of n

First line, a binary number b with a length of M

Output format:

A line, a number, that represents the answer


Because the first binary number is not moving, the second one is moving, so we can get the answer by preprocessing the first number.

Because it is with, so only two of them are only 1 o'clock will have the answer to the contribution

So, let's say this example:


He's going to have some of the following.






We will find that the first 1 differences and the first 1 above and the last 1 XOR each other and contribute to the answer.

So the 1 contribution to the answer is 8+1=9 .

Let's spread this rule.

Each of the 1 in Y is done as above

You can come up with answers

However, we will find that the complexity of the answer is O (nxm) .

So we're going to preprocess

Use the prefix and run x again

Complexity optimization to O (m+n)


#include <iostream>#include<cstdio>#include<cstring>#include<algorithm>#defineRii Register int i#defineRij Register Int J#defineP 998244353#defineint long Longusing namespacestd;intb;intx[200005],y[200005],bs[200005],qzh[200005];voidYcl () {bs[0]=1;  for(rii=1; i<=200002; i++) {Bs[i]=bs[i-1]*2; Bs[i]%=p; }}signed Main () {scanf ("%lld%lld\n",&a,&b);  for(rii=1; i<=a;i++) {X[i]=getchar ()-'0';    } getchar ();  for(rii=1; i<=b;i++) {Y[i]=getchar ()-'0';    } YCL ();  for(rii=a;i>=1; i--) {Qzh[a-i+1]=qzh[a-i]; Qzh[a-i+1]+=x[i]*bs[a-i]; Qzh[a-i+1]%=p; }    if(b>a) { for(rii=a+1; i<=b;i++) {Qzh[i]=qzh[i-1]; }    }//For (rii=1;i<=b;i++)//  {//printf ("%d", Qzh[i]);//  }    intans=0;  for(rii=1; i<=b;i++) {ans+=y[i]*qzh[b-i+1]; Ans%=p; } cout<<ans%p;}

Cf1066ebinary Numbers and Sum (prefix and, binary)

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