Example Usage.cpp

// Problem: C. First element at least X
// Contest: Codeforces - ITMO Academy: pilot course - Segment Tree, part 1 - Step 2
// URL: https://codeforces.com/edu/course/2/lesson/4/2/practice/contest/273278/problem/C
// Memory Limit: 1024 MB
// Time Limit: 1000 ms
// Parsed on: 14-10-2021 15:10:54 IST (UTC+05:30)
// Author: Kapil Choudhary
// ********************************************************************
// कर्मण्येवाधिकारस्ते मा फलेषु कदाचन |
// मा कर्मफलहेतुर्भूर्मा ते सङ्गोऽस्त्वकर्मणि || १.४७ ||
// ********************************************************************

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

#define ll long long
#define ld long double
#define ull unsigned long long
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define mp make_pair
#define F first
#define S second
#define PI 3.1415926535897932384626
#define sz(x) ((int)(x).size())
#define vset(v, n, val) v.clear(); v.resize(n, val)

typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef vector<vull> vvull;
typedef vector<vb> vvb;
typedef vector<vc> vvc;
typedef vector<vs> vvs;

/************************************************** DEBUGGER *******************************************************************************************************/

#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif

void _print(ll t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(ld t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(ull t) { cerr << t; }

template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(vector <vector<T>> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(multimap <T, V> v);
template <class T> void _print(queue <T> v);
template <class T> void _print(priority_queue <T> v);
template <class T> void _print(stack <T> s);

// modify it's definition below as per need such as it can be used for STL containers with custom args passed
template <class T> void _print(T v);

template <class T, class V> void _print(pair <T, V> p) { cerr << "{"; _print(p.F); cerr << ","; _print(p.S); cerr << "}"; }
template <class T> void _print(vector <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T> void _print(vector <vector<T>> v) { cerr << "==>" << endl; for (vector<T> vec : v) { for(T i : vec) {_print(i); cerr << " "; } cerr << endl; } }
template <class T> void _print(set <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T, class V> void _print(map <T, V> v) { cerr << "[ "; for (auto i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T> void _print(multiset <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T, class V> void _print(multimap <T, V> v) { cerr << "[ "; for (auto i : v) {_print(i); cerr << " "; } cerr << "]"; }
template <class T> void _print(queue <T> v) { cerr << "[ "; while(!v.empty()) {_print(v.front()); v.pop(); cerr << " "; } cerr << "]"; }
template <class T> void _print(priority_queue <T> v) { cerr << "[ "; while(!v.empty()) {_print(v.top()); v.pop(); cerr << " "; } cerr << "]"; }
template <class T> void _print(stack <T> v) { cerr << "[ "; while(!v.empty()) {_print(v.top()); v.pop(); cerr << " "; } cerr << "]"; }
template <class T> void _print(T v) {  }

/*******************************************************************************************************************************************************************/

mt19937_64 rang(chrono::high_resolution_clock::now().time_since_epoch().count());
int rng(int lim) {
    uniform_int_distribution<int> uid(0,lim-1);
    return uid(rang);
}

const int INF = 0x3f3f3f3f;
const int mod = 1e9+7;

ll mod_exp(ll a, ll b) { a %= mod; if(a == 0) return 0LL; ll res = 1LL;
                         while(b > 0) { if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; }

ll mod_inv(ll a) { return mod_exp(a, mod - 2); } // works only for prime value of "mod"
ll GCD(ll a, ll b) { return (b == 0) ? a : GCD(b, a % b); }

/******************************************************************************************************************************/

/*
KEYNOTES:
------------------------------------------------------------------------------------------
merge(X,identity_element) = X
------------------------------------------------------------------------------------------
// (i.e no transformation at all or if we combine any new update with the identity update
// it should give the newer update)
identity_transformation.combine(X) = X
------------------------------------------------------------------------------------------
ALWAYS: older_update.combine(newer_update)
------------------------------------------------------------------------------------------
*/

// this structure depends on the nature of query
struct node {
    // 1. change(s) required
    // use more variables if you want more information
    // these default values should be identity_element
    int mx = -INF;

    node() {}
    node(int val) {
        // 2. change(s) required
        mx = val;
    }

    // associative merging function, store the thing you wanna query
    void merge(const node &l, const node &r){
        // 3. change(s) required
        mx = max(l.mx, r.mx);
    }
};

// this structure depends on the nature of update
struct update {
    // 4. change(s) required
    // use more variables if you want more information
    // these default values should be identity_transformation or identity_update
    int y = 0;

    update() {}
    update(int val) {
        // 5. change(s) required
        y = val;
    }

    // combine the current update with the other update (see keynotes)
    // basically combine older lazy value(s) (if exist) with newer one(s).
    // for this function, you can be sure that the "other" is newer than current
    void combine(update &other, const int32_t &tl, const int32_t &tr) {
        // 6. change(s) required
        y = other.y;
    }

    // store the correct information in the node x
    void apply(node &x, const int32_t &tl, const int32_t &tr) {
        // 7. change(s) required
        x.mx = y;
    }
};

template<typename node, typename update>
struct segtree {
    int len;
    vector<node> t;
    vector<update> u;
    vector<bool> lazy;
    node identity_element;
    update identity_transformation;

    segtree(int l) {
        len = l;
        t.clear(); t.resize(4 * len);
        u.clear(); u.resize(4 * len);
        lazy.clear(); lazy.resize(4 * len);
        identity_element = node();
        identity_transformation = update();
    }

    void pushdown(const int32_t &v, const int32_t &tl, const int32_t &tr) {
        if(!lazy[v]) return;
        int32_t tm = (tl + tr) >> 1;
        apply(v << 1, tl, tm, u[v]);
        apply((v << 1) | 1, tm + 1, tr, u[v]);
        u[v] = identity_transformation;
        lazy[v] = 0;
    }

    void apply(const int32_t &v, const int32_t &tl, const int32_t &tr, update upd) {
        if(tl != tr) {
            lazy[v] = 1;
            u[v].combine(upd, tl, tr);
        }

        upd.apply(t[v], tl, tr);
    }

    template<typename T>
    void build(const T &arr, const int32_t &v, const int32_t &tl, const int32_t &tr) {
        if(tl == tr) {
            t[v] = arr[tl];
            return;
        }

        int32_t tm = (tl + tr) >> 1;
        build(arr, v << 1, tl, tm);
        build(arr, (v << 1) | 1, tm + 1, tr);
        t[v].merge(t[v << 1],t[(v << 1) | 1]);
    }

    node query(const int32_t &v, const int32_t &tl, const int32_t &tr, const int32_t &l, const int32_t &r) {
        if(l > tr || r < tl) {
            return identity_element;
        }

        if(tl >= l && tr <= r){
            return t[v];
        }

        pushdown(v, tl, tr);
        int32_t tm = (tl + tr) >> 1;
        node a = query(v << 1, tl, tm, l, r), b = query((v << 1) | 1, tm + 1, tr, l, r), ans;
        ans.merge(a, b);
        return ans;
    }

    void rupd(const int32_t &v, const int32_t &tl, const int32_t &tr, const int32_t &l, const int32_t &r, const update &upd) {
        if(l > tr || r < tl){
            return;
        }

        if(tl >= l && tr <= r){
            apply(v,tl,tr,upd);
            return;
        }

        pushdown(v, tl, tr);
        int32_t tm = (tl + tr) >> 1;
        rupd(v << 1, tl, tm, l, r, upd);
        rupd((v << 1) | 1, tm + 1, tr, l, r, upd);
        t[v].merge(t[v << 1], t[(v << 1) | 1]);
    }

    public:
    template<typename T>
    void build(const T &arr) {
        build(arr, 1, 0, len - 1);
    }

    node query(const int32_t &l,const int32_t &r) {
        return query(1, 0, len - 1, l, r);
    }

    void rupd(const int32_t &l, const int32_t &r, const update &upd) {
        rupd(1, 0, len - 1, l, r, upd);
    }
};

// https://www.youtube.com/watch?v=Hooe5ORdFsc
void solve()
{
    int n, m; cin >> n >> m;
    vi v(n);
    for(int i = 0; i < n; i++) cin >> v[i];

    struct segtree<node, update> s(n);
    s.build(v);

    while(m--) {
        int tp; cin >> tp;

        if(tp == 1) {
            int idx, val; cin >> idx >> val;
            s.rupd(idx, idx, val);
        }

        else {
            int x; cin >> x;

            int L = 0, R = n - 1;
            int ans = INF;

            while(L <= R) {
                int mid = L + ((R - L) >> 1);
                if(s.query(L, mid).mx < x) L = mid + 1;
                else ans = min(ans, mid), R = mid - 1;
            }

            if(ans == INF) ans = -1;
            cout << ans << "\n";
        }
    }
}

int main()
{
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    srand(chrono::high_resolution_clock::now().time_since_epoch().count());

    // #ifndef ONLINE_JUDGE
    //     freopen("input.txt", "r", stdin);
    //     freopen("output.txt", "w", stdout);
    // #endif

    // #ifndef ONLINE_JUDGE
    //      freopen("error.txt", "w", stderr);
    // #endif

    int t = 1;
    // int test = 1;
    // cin >> t;
    while(t--) {
        // cout << "Case #" << test++ << ": ";
        solve();
    }

    return 0;
}