Problem:
0-1 Knapsack Problem

You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 1000

1 ≤ wi ≤ 1000

1 ≤ W ≤ 10000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

Solution in Rust (judge verdict: Accepted)

use std::cmp;
use std::collections::HashMap;
use std::io::Read;

fn main() {
    let mut buf = String::new();

    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();

    // 読み込んだStringを空白で分解する
    // println!("buf: {:?}", buf);
    buf = buf.replace("\n", " ");
    buf = buf.replace("\r", " ");
    let mut iter = buf.split_whitespace();

    let n: i32 = iter.next().unwrap().parse().unwrap();
    let w: i32 = iter.next().unwrap().parse().unwrap();

    let wv: Vec<(i32, i32)> = (0..n)
        .map(|_| {
            let v = iter.next().unwrap().parse().unwrap();
            let w = iter.next().unwrap().parse().unwrap();
            (w, v)
        })
        .collect();
    // println!("{:?}", wv);
    println!("{}", solve(&wv, w));
}

fn solve(wv: &Vec<(i32, i32)>, w: i32) -> i32 {
    let mut cache: HashMap<(i32, i32), i32> = HashMap::new();
    solve_iter(0, w, wv, &mut cache)
}

// i 番目移行で重さ j 以下になるような最大値
fn solve_iter(i: i32, j: i32, wv: &Vec<(i32, i32)>, cache: &mut HashMap<(i32, i32), i32>) -> i32 {
    if let Some(v) = cache.get(&(i, j)) {
        return *v;
    }
    let res: i32;
    if i as usize == wv.len() {
        res = 0;
    } else if j < wv[i as usize].0 {
        res = solve_iter(i + 1, j, wv, cache);
    } else {
        res = cmp::max(
            solve_iter(i + 1, j, wv, cache),
            solve_iter(i + 1, j - wv[i as usize].0, wv, cache) + wv[i as usize].1,
        );
    }
    cache.insert((i, j), res);
    res
}