use std::io::{stdin, Read, StdinLock}; use std::str::FromStr; struct Input { n: usize, w: Vec, } fn read_input(cin_lock: &mut StdinLock) -> Input { let n = next_token(cin_lock); let w = (0..n).map(|_| next_token(cin_lock)).collect(); Input { n, w } } fn solve(input: Input) -> bool { let max_w: usize = input.w.iter().sum::(); if max_w % 2 != 0 { return false; } let half_w = max_w / 2; let mut dp = vec![vec![false; half_w + 1]; 2]; dp[0][0] = true; // 合計 0 になる組み合わせは存在する // 全ての重りに対して操作する for i in 0..input.n { let curr_line = i % 2; // 0, 1, 0, ... let next_line = (i + 1) % 2; // 1, 0, 1, ... // 存在しうる重りを考慮する for w in 0..half_w + 1 { dp[next_line][w] = dp[curr_line][w] || (w >= input.w[i] && dp[curr_line][w - input.w[i]]) } } // 指定した重さの組み合わせがあるか判定 return dp[input.n % 2][half_w]; } #[cfg(test)] mod tests { use super::*; #[test] fn test_solve_01() { assert_eq!( solve(Input { n: 3, w: vec![1, 2, 3], }), true ); } #[test] fn test_solve_02() { assert_eq!( solve(Input { n: 5, w: vec![1, 2, 3, 4, 5], }), false ); } #[test] fn test_solve_03() { assert_eq!( solve(Input { n: 15, w: vec![62, 8, 90, 2, 24, 62, 38, 64, 76, 60, 30, 76, 80, 74, 72], }), false ); } #[test] fn test_solve_04() { assert_eq!( solve(Input { n: 10, w: vec![88, 15, 15, 82, 19, 17, 35, 86, 40, 33], }), true ); } } fn next_token(cin_lock: &mut StdinLock) -> T { cin_lock .by_ref() .bytes() .map(|c| c.unwrap() as char) .skip_while(|c| c.is_whitespace()) .take_while(|c| !c.is_whitespace()) .collect::() .parse::() .ok() .unwrap() } fn main() { let cin = stdin(); let mut cin_lock = cin.lock(); let input = read_input(&mut cin_lock); println!( "{}", if solve(input) { "possible" } else { "impossible" } ); }