#[allow(unused_imports)] use std::cmp::*; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } fn find(rem: &[i32]) -> usize { let c = rem.len(); let mut vis = 0; let mut que = vec![]; for i in 0..c { if rem[i] <= 0 { que.push(i); } } while let Some(v) = que.pop() { if (vis & 1 << v) != 0 { continue; } let adj = ((vis << 1) & (5 << v)) >> v; let x = match adj { 0 => 0, 1 | 4 => 1, 5 => 2, _ => panic!(), }; if rem[v] <= x { vis |= 1 << v; if v + 1 < c { que.push(v + 1); } if v > 0 { que.push(v - 1); } } } vis } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn solve() { input! { r: usize, c: usize, p: [[f64; c]; r], s: [[i32; c]; r], } let mut dp = vec![0.0; 1 << c]; let mut dpx = vec![0.0; 1 << c]; dp[0] = 1.0; for i in 0..r { let mut ep = vec![0.0; 1 << c]; let mut epx = vec![0.0; 1 << c]; for bits in 0..1 << c { let mut rem = vec![4; c]; let mut pr = 1.0; for j in 0..c { if (bits & 1 << j) != 0 { rem[j] = s[i][j]; pr *= p[i][j] / 100.0; } else { pr *= 1.0 - p[i][j] / 100.0; } } for pre in 0..1 << c { let mut rem = rem.clone(); for j in 0..c { if (pre & 1 << j) != 0 { rem[j] -= 1; } } let to = find(&rem); ep[to] += dp[pre] * pr; epx[to] += dpx[pre] * pr + dp[pre] * pr * to.count_ones() as f64; } } dp = ep; dpx = epx; } let s: f64 = dpx.iter().sum(); println!("{}", s); }