Problem:
Range Minimum Query (RMQ)

Write a program which manipulates a sequence A = {a0, a1, . . . , an-1} with the following operations:

find(s, t): report the minimum element in as, as+1, . . . ,at.

update(i, x): change ai to x.

Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Input

n q
com0 x0 y0
com1 x1 y1
...
comq−1 xq−1 yq−1

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(xi, yi) and '1' denotes find(xi, yi).

Output

For each find operation, print the minimum element.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 0 ≤ xi < n, 0 ≤ yi < 231-1.

If comi is 1, then 0 ≤ xi < n, 0 ≤ yi < n.

Sample Input 1

3 5
0 0 1
0 1 2
0 2 3
1 0 2
1 1 2

Sample Output 1

1
2

Sample Input 2

1 3
1 0 0
0 0 5
1 0 0

Sample Output 2

2147483647
5

Solution in Rust (judge verdict: Accepted)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(dead_code)]
pub trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}
#[allow(dead_code)]
#[doc = " Segment Tree"]
pub struct SEG<M: Monoid> {
    n: usize,
    buf: Vec<M::T>,
}
impl<M: Monoid> SEG<M> {
    #[allow(dead_code)]
    pub fn new(n: usize) -> SEG<M> {
        SEG {
            n: n,
            buf: vec![M::id().clone(); 2 * n],
        }
    }
    #[allow(dead_code)]
    pub fn update(&mut self, k: usize, a: M::T) {
        let mut k = k + self.n;
        self.buf[k] = a;
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    pub fn add(&mut self, k: usize, a: &M::T) {
        let mut k = k + self.n;
        self.buf[k] = M::op(&self.buf[k], a);
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    pub fn get(&self, i: usize) -> M::T {
        self.query(i, i + 1)
    }
    #[allow(dead_code)]
    pub fn query(&self, l: usize, r: usize) -> M::T {
        let mut vl = M::id();
        let mut vr = M::id();
        let mut l = l + self.n;
        let mut r = r + self.n;
        while l < r {
            if l & 1 == 1 {
                vl = M::op(&vl, &self.buf[l]);
                l += 1;
            }
            if r & 1 == 1 {
                r -= 1;
                vr = M::op(&self.buf[r], &vr);
            }
            l >>= 1;
            r >>= 1;
        }
        M::op(&vl, &vr)
    }
}
struct MIN;
impl Monoid for MIN {
    type T = usize;
    fn id() -> Self::T {
        (1 << 31) - 1
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        std::cmp::min(*a, *b)
    }
}
fn solve() {
    input! {
        n: usize, q: usize,
        qs: [(usize, usize, usize); q],
    }
    let mut seg: SEG<MIN> = SEG::new(n);

    for q in &qs {
        if q.0 == 0 { // update
            seg.update(q.1, q.2);
        } else { // find
            let v = seg.query(q.1, q.2+1);
            println!("{}", v);
        }
    }
}