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 C++11 (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;

const int MAX_N = 100010;

const int inf = 2147483647;
int dat[MAX_N * 4];
int n;

void init(int n_){
    n = 1;
    while(n < n_) n *= 2; // 2のn乗に切り上げる
    // 全て inf で初期化したいとき
    for(int i = 0; i < n*2; i++){
        dat[i] = inf;
    }
    // 配列 a の要素で初期化したいとき
    // for(int i = n; i < n+n; i++){
    //     dat[i] = a[i-n];
    // }
    // for(int i=n-1; i>=1; i--){
    //     dat[i] = min(dat[i*2], dat[i*2+1]);
    // }
}

void update(int i, int x){
    i += n;
    dat[i] = x;
    while(i > 0){
        dat[i/2] = min(dat[i], dat[i^1]);
        i /= 2;
    }
}

int find(int a, int b, int i, int l, int r){
    if(r <= a || b <= l) return inf;
    if(a <= l && r <= b) return dat[i];
    return min(find(a,b,i*2,l,(l+r)/2), find(a,b,i*2+1,(l+r)/2,r));
}

int find(int a, int b){
    return find(a,b,1,0,n);
}

int main(){
    int n, q;
    while(cin >> n >> q){
        init(n);
        for(int i = 0; i < q; i++){
            char c;
            int x, y;
            cin >> c >> x >> y;
            if(c == '0'){
                update(x,y);
            } else {
                cout << find(x,y+1) << endl;
            }
        }
    }
}