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++ (judge verdict: Accepted)

#include <cstdio>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
using namespace std;
const int MAX=2147483647;
int n,q;
int d[600000];
void init(){
  int n_=1;
  while(n_<n) n_*=2;
  n=n_;
  for(int i=0;i<2*n-1;i++)d[i]=MAX;
}
void update(int k,int x){
  k+=n-1;
  d[k]=x;
  while(k>0){
    k=(k-1)/2;
    d[k]=min(d[k*2+1],d[k*2+2]);
  }
}
int find(int a,int b,int k,int l,int r){
  if(r<=a || b<=l)return MAX;

  if(a<=l && r<=b)return d[k];
  else{
    int vl=find(a,b,k*2+1,l,(l+r)/2);
    int vr=find(a,b,k*2+2,(l+r)/2,r);
    return min(vl,vr);
  }
}
int main(){
  scanf("%d %d",&n,&q);
  init();
  for(int i=0;i<q;i++){
    int c,x,y;
    scanf("%d %d %d",&c,&x,&y);
    if(c==0)update(x,y);
    else printf("%d\n",find(x,y+1,0,0,n));
    // for(int j=0;j<2*n-1;j++)printf("%d ",d[j]);
    //printf("\n");
  }
  return 0;
}