CF935D Fafa and Ancient Alphabet

CF935D Fafa and Ancient Alphabet

Description

链接

Solutuon

最开始想着正着推，后来发现太复杂了

注意到末尾到末尾的情况显然更容易讨论，相当于越后放的优先级更高，不用考虑前面放的数的影响

分类转移即可

#include<bits/stdc++.h>

using namespace std;

#define LL long long

inline LL read()
{
    LL f = 1,x = 0;
    char ch;
    do
    {
        ch = getchar();
        if(ch == '-') f = -1;
    }while(ch < '0'||ch > '9');
    do
    {
        x = (x<<3) + (x<<1) + ch - '0';
        ch = getchar();
    }while(ch >= '0'&&ch <= '9');
    return f*x;
} 

const int MAXN = 1e5 + 10;
const int MOD = 1e9 + 7;

inline LL Pow(LL x,LL y)
{
    LL res = 1 ,mul = x;
    while(y)
    {
        if(y&1) res = (res * mul)%MOD;
        mul = (mul * mul) % MOD;
        y>>=1;
    }
    return res;
}

inline LL inv(LL x)
{
    return Pow(x,MOD-2);
} 

LL n,m;
LL a[MAXN];
LL b[MAXN];
LL dp[MAXN];
LL cnta[MAXN],cntb[MAXN];
LL Inv;
 
int main()
{
    n = read(),m = read();
    Inv = inv(m);
    for(int i=1;i<=n;i++) a[i] = read();
    for(int i=1;i<=n;i++) b[i] = read();
    for(int i=1;i<=n;i++) if(!a[i]) cnta[i]++; 
    for(int i=1;i<=n;i++) if(!b[i]) cntb[i]++;
    for(int i=1;i<=n;i++) cnta[i]=cnta[i-1]+cnta[i],cntb[i]=cntb[i-1]+cntb[i];
    for(int i=n;i>=1;i--)
    {
    //    cout << i << " " << a[i] << " " << b[i] << endl;
        if(a[i]&&b[i])
        { 
        //    cout << "1" << endl; 
            if(a[i] > b[i]) dp[i] = 1;
            else if(a[i] == b[i]) dp[i] = dp[i+1];
            else dp[i] = 0;
        }
        else if(!a[i]&&b[i]) 
        {
    //        cout << "2" << endl;
            dp[i] = ((dp[i+1] + (m - b[i]))%MOD * Inv)%MOD;
        }
        else if(!b[i]&&a[i])
        {
    //        cout << "3" << endl;
            dp[i] = ((dp[i+1] + a[i] - 1)%MOD * Inv)%MOD;
        } 
        else
        {
            //cout << "4" <<endl;
            dp[i] = (((m * dp[i+1]%MOD + (m * (m-1)/2)%MOD)%MOD * Inv)%MOD)*Inv%MOD;
        }
    }
    cout << dp[1] << endl;
}