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++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

const int INF = (1LL<<31)-1;

class RMQ{
private:
    int N;
    vector<int> data;
    
    int find(int a, int b, int k, int l, int r){
        if(r <= a || b <= l)
            return INF;
        if(a <= l && r <= b)
            return data[k];
        int x1 = find(a, b, 2*k+1, l, (l+r)/2);
        int x2 = find(a, b, 2*k+2, (l+r)/2, r);
        return min(x1, x2);
    }

public:
    RMQ(int N_){
        N = 1;
        while(N < N_)
            N <<= 1;
        data.assign(2*N-1, INF);
    }
    
    void update(int x, int a){
        x += N-1;
        data[x] = a;
        while(x){
            x = (x-1)/2;
            data[x] = min(data[2*x+1], data[2*x+2]);
        }
    }
    int find(int a, int b){
        return find(a, b, 0, 0, N);
    }
};

int main(){
    int N, Q;
    cin >> N >> Q;
    
    RMQ rmq(N);
    
    for(int i=0; i<Q; i++){
        int com, x, y;
        cin >> com >> x >> y;
        if(com == 0){
            rmq.update(x, y);
        }
        if(com == 1){
            cout << rmq.find(x, y+1) << endl;
        }
    }
    
    return 0;
}