LOJ#3093. 「BJOI2019」光线

从下到上把两面镜子合成一个

新的镜子是\((\frac{a_{i}a_{i + 1}}{1 - b_{i}b_{i + 1}},b_{i} + \frac{a_{i}^{2}b_{i}}{1 - b_{i}b_{i + 1}})\)

#include <bits/stdc++.h>

#define fi first

#define se second

#define pii pair<int,int>

#define mp make_pair

#define pb push_back

#define space putchar(' ')

#define enter putchar('\n')

#define eps 1e-10

#define MAXN 500005

#define ba 47

//#define ivorysi

using namespace std;

typedef long long int64;

typedef unsigned int u32;

typedef double db;

template<class T>

void read(T &res) {

    res = 0;T f = 1;char c = getchar();

    while(c < '0' || c > '9') {

	if(c == '-') f = -1;

	c = getchar();

    }

    while(c >= '0' && c <= '9') {

	res = res * 10 +c - '0';

	c = getchar();

    }

    res *= f;

}

template<class T>

void out(T x) {

    if(x < 0) {x = -x;putchar('-');}

    if(x >= 10) {

	out(x / 10);

    }

    putchar('0' + x % 10);

}

const int MOD = 1000000007;

int N;

int a[MAXN],b[MAXN];

int inc(int a,int b) {

    return a + b >= MOD ? a + b - MOD : a + b;

}

int mul(int a,int b) {

    return 1LL * a * b % MOD;

}

int fpow(int x,int c) {

    int res = 1,t = x;

    while(c) {

	if(c & 1) res = mul(res,t);

	t = mul(t,t);

	c >>= 1;

    }

    return res;

}

void Solve() {

    read(N);

    int iv = fpow(100,MOD - 2);

    for(int i = 1 ; i <= N ; ++i) {

	read(a[i]);read(b[i]);

	a[i] = mul(a[i],iv);b[i] = mul(b[i],iv);

    }

    for(int i = N - 1 ; i >= 1 ; --i) {

	int inv = fpow(inc(1,MOD - mul(b[i],b[i + 1])),MOD - 2);

	int na = mul(mul(a[i],a[i + 1]),inv);

	int nb = b[i];

	int t = mul(mul(a[i],a[i]),b[i + 1]);

	nb = inc(nb,mul(t,inv));

	a[i] = na;b[i] = nb;

    }

    out(a[1]);enter;

}

int main() {

#ifdef ivorysi

    freopen("f1.in","r",stdin);

#endif

    Solve();

}