dynamicRangeMinimumQueries.cpp

//Solution of dynamic range minimum query problem 
//Using segment tree query & update methods

//There are two types of queries, 
//Type 1: Find the minimum element in the given range
//Type 2: Given index of the array, update the element

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

#define pii pair<int, int>
#define F first
#define S second
typedef long long int ll;
const int mod = 1e9+7;

void FAST(){
	ios_base::sync_with_stdio(0);
	cin.tie(nullptr);
	cout.tie(nullptr);
}

void fileIO(){
	#ifndef ONLINE_JUDGE
		freopen("input.txt", "r", stdin);
		freopen("output.txt", "w", stdout);
	#endif
}

ll binpow(ll x, ll y){
	x%=mod;
	ll res=1;
	while(y>0){
		if(y&1){
			res = ((res%mod)*(x%mod))%mod;
		}
		x = ((x%mod)*(x%mod))%mod;
		y >>=1;
	}
	return res;
}

vector<ll> prime;
void sieve(){
	vector<bool> v(1e6+1, 1);
	for(ll i=2 ; i<=1e6 ; i++){
		if(v[i]){
			for(ll j=i*i ; j<=1e6 ; j+=i){
				v[j] = 0;
			}
			prime.push_back(i);
		}
	}
}

ll query(vector<ll>&st, ll tl, ll tr, ll tv, ll l, ll r){
// completely outside the given range
	if(tl > r || tr < l){
		return 1e9;
	}
// completely inside the given range
	if(tl >= l && tr <= r){
		return st[tv];
	}
// Partially inside and partially outside
	ll tm = (tl+tr)/2;
	ll ans1 = query(st, tl, tm, 2*tv, l, r);
	ll ans2 = query(st, tm+1, tr, 2*tv+1, l, r);
	return min(ans1,ans2);
}

void updateTree(vector<ll>&arr, vector<ll>&st, ll tl, ll tr, ll tv, ll idx, ll value){
	if(tl==tr){
		arr[idx] = value;
		st[tv] = arr[idx];
		return;
	}
	ll tm = (tl+tr)/2;
	if(idx > tm){
		updateTree(arr, st, tm+1, tr, 2*tv+1, idx, value);
	} else {
		updateTree(arr, st, tl, tm, 2*tv, idx, value);
	}
	st[tv] = min(st[2*tv],st[2*tv+1]);
}

void buildTree(vector<ll>&arr, vector<ll>&st, ll tl, ll tr, ll tv){
// BASE CASE
	if(tl == tr){
		st[tv] = arr[tl];
		return;
	}

	ll tm =(tl+tr)/2;
	// two recursive calls to build the left half and
	// right half respectively
	buildTree(arr, st, tl, tm, 2*tv);
	buildTree(arr, st, tm+1, tr, 2*tv+1);
	// the answer to the recursive calls gets stored in
	// the tv
	st[tv] = min(st[2*tv],st[2*tv + 1]);
}



int main(){
	FAST();
	fileIO();
	ll n,q,x, a,b,k,u,qt;
	cin>>n>>q;
	vector<ll> arr(n);
	vector<ll> st(4*n);
	for(ll i=0 ; i<n ; i++){
		cin>>arr[i];
	}

	buildTree(arr, st, 0,n-1,1);

	for(ll i=0 ; i<q ; i++){
		cin>>qt;
		if(qt==1){
			cin>>k>>u;
			updateTree(arr, st, 0, n-1, 1, k-1, u);
		}
		if(qt==2){
			cin>>a>>b;
			cout<<query(st, 0, n-1, 1, a-1, b-1)<<"\n";
		}
	}
	return 0;
}