Submission #985852

#	Time	Username	Problem	Language	Result	Execution time	Memory
985852		GrindMachine	Fish 2 (JOI22_fish2)	C++17	31 / 100	2379 ms	30636 KiB

fish2

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif

/*

refs:
https://codeforces.com/blog/entry/101003?#comment-898608

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

template<typename T>
struct lazysegtree {
    /*=======================================================*/

    struct data {
        ll mn,cnt;
    };

    struct lazy {
        ll a;
    };

    data d_neutral = {inf2,0};
    lazy l_neutral = {0};

    void merge(data &curr, data &left, data &right) {
        curr.mn = min(left.mn,right.mn);
        curr.cnt = 0;
        if(left.mn == curr.mn) curr.cnt += left.cnt;
        if(right.mn == curr.mn) curr.cnt += right.cnt;
    }

    void create(int x, int lx, int rx, T v) {
        tr[x] = {v,1};
    }

    void modify(int x, int lx, int rx, T v) {
        lz[x].a = v;
    }

    void propagate(int x, int lx, int rx) {
        ll v = lz[x].a;
        if(!v) return;

        tr[x].mn += v;

        if(rx-lx > 1){
            lz[2*x+1].a += v;
            lz[2*x+2].a += v;
        }

        lz[x] = l_neutral;
    }

    /*=======================================================*/

    int siz = 1;
    vector<data> tr;
    vector<lazy> lz;

    lazysegtree() {

    }

    lazysegtree(int n) {
        while (siz < n) siz *= 2;
        tr.assign(2 * siz, d_neutral);
        lz.assign(2 * siz, l_neutral);
    }

    void build(int n, int x, int lx, int rx) {
        if (rx - lx == 1) {
            if (lx < n) {
                create(x, lx, rx, 0);
            }

            return;
        }

        int mid = (lx + rx) / 2;

        build(n, 2 * x + 1, lx, mid);
        build(n, 2 * x + 2, mid, rx);

        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }

    void build(int n) {
        build(n, 0, 0, siz);
    }

    void rupd(int l, int r, T v, int x, int lx, int rx) {
        propagate(x, lx, rx);

        if (lx >= r or rx <= l) return;
        if (lx >= l and rx <= r) {
            modify(x, lx, rx, v);
            propagate(x, lx, rx);
            return;
        }

        int mid = (lx + rx) / 2;

        rupd(l, r, v, 2 * x + 1, lx, mid);
        rupd(l, r, v, 2 * x + 2, mid, rx);

        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }

    void rupd(int l, int r, T v) {
        rupd(l, r + 1, v, 0, 0, siz);
    }

    data query(int l, int r, int x, int lx, int rx) {
        propagate(x, lx, rx);

        if (lx >= r or rx <= l) return d_neutral;
        if (lx >= l and rx <= r) return tr[x];

        int mid = (lx + rx) / 2;

        data curr;
        data left = query(l, r, 2 * x + 1, lx, mid);
        data right = query(l, r, 2 * x + 2, mid, rx);

        merge(curr, left, right);
        return curr;
    }

    data query(int l, int r) {
        return query(l, r + 1, 0, 0, siz);
    }
};

template<typename T>
struct segtree {
    // https://codeforces.com/blog/entry/18051

    /*=======================================================*/

    struct data {
        ll sum,mnp,mns,val1,val2;
    };

    data neutral = {0,0,0,inf2,inf2};

    data merge(data &left, data &right) {
        data curr;

        curr.sum = left.sum+right.sum;
        curr.mnp = min({left.mnp,left.sum+right.mnp});
        curr.mns = min({right.mns,right.sum+left.mns});
        curr.val1 = min({left.val1,curr.mnp});
        curr.val2 = min({right.val2,curr.mns});

        return curr;
    }

    void create(int i, T v) {

    }

    void modify(int i, T v) {
        tr[i] = {v,-v,-v};
    }

    /*=======================================================*/

    int n;
    vector<data> tr;

    segtree() {

    }

    segtree(int siz) {
        init(siz);
    }

    void init(int siz) {
        n = siz;
        tr.assign(2 * n, neutral);
    }

    void build(vector<T> &a, int siz) {
        rep(i, siz) create(i + n, a[i]);
        rev(i, n - 1, 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    void pupd(int i, T v) {
        modify(i + n, v);
        for (i = (i + n) >> 1; i; i >>= 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    data query(int l, int r) {
        data resl = neutral, resr = neutral;

        for (l += n, r += n; l <= r; l >>= 1, r >>= 1) {
            if (l & 1) resl = merge(resl, tr[l++]);
            if (!(r & 1)) resr = merge(tr[r--], resr);
        }

        return merge(resl, resr);
    }
};

ll msb(ll x){
    return 63-__builtin_clzll(x);
}

void solve(int test_case)
{
    ll n; cin >> n;
    vector<ll> a(n+5);
    rep1(i,n) cin >> a[i];
    a[0] = a[n+1] = inf2;
    vector<ll> p(n+5);
    rep1(i,n) p[i] = p[i-1]+a[i];

    vector<ll> ngel(n+5), nger(n+5,n+1);

    {
        stack<ll> stk;

        rep1(i,n){
            while(!stk.empty() and a[i] >= a[stk.top()]){
                nger[stk.top()] = i;
                stk.pop();
            }
            stk.push(i);
        }
    }

    {
        stack<ll> stk;

        rev(i,n,1){
            while(!stk.empty() and a[i] >= a[stk.top()]){
                ngel[stk.top()] = i;
                stk.pop();
            }
            stk.push(i);
        }
    }

    set<pll> pairs;

    auto add_pair = [&](ll l, ll r){
        if(l > r) swap(l,r);
        if(r-l-1 <= 0) return;

        ll sum = p[r-1]-p[l];
        if(min(a[l],a[r]) > sum){
            pairs.insert({l+1,r-1});
        }
    };

    rep1(i,n){
        add_pair(i,ngel[i]);
        add_pair(i,nger[i]);
    }

    lazysegtree<ll> st(n+5);
    st.build(n+1);
    for(auto [l,r] : pairs){
        st.rupd(l,r,1);
    }

    segtree<ll> seg(n+5);
    rep1(i,n) seg.pupd(i,a[i]);

    set<ll> pos[30];
    rep1(i,n) pos[msb(a[i])].insert(i);

    auto get = [&](ll i){
        vector<pll> segs;

        // sum[l..i] < a[l-1]
        vector<ll> points_left;
        rep(bit,30){
            auto it = pos[bit].upper_bound(i);
            if(it != pos[bit].begin()){
                it--;
                points_left.pb(*it);
                if(it != pos[bit].begin()){
                    it--;
                    points_left.pb(*it);
                }
            }
        }

        vector<pll> ok_left;
        
        trav(l,points_left){
            if(i == l) conts;
            ll sum = seg.query(l+1,i).sum;
            if(sum < a[l]){
                ok_left.pb({l+1,sum});
            }
            if(l+1 <= i-1 and sum-a[i] < min(a[l],a[i])){
                segs.pb({l+1,i-1});
            }
        }

        ok_left.pb({1,seg.query(1,i).sum});

        // sum[i..r] < a[r+1]
        vector<ll> points_right;
        rep(bit,30){
            auto it = pos[bit].lower_bound(i);
            if(it != pos[bit].end()){
                points_right.pb(*it);
                if(next(it) != pos[bit].end()){
                    points_right.pb(*next(it));
                }
            }
        }

        vector<pll> ok_right;

        trav(r,points_right){
            if(i == r) conts;
            ll sum = seg.query(i,r-1).sum;
            if(sum < a[r]){
                ok_right.pb({r-1,sum});
            }
            if(i+1 <= r-1 and sum-a[i] < min(a[i],a[r])){
                segs.pb({i+1,r-1});
            }
        }

        ok_right.pb({n,seg.query(i,n).sum});

        // merge ok_left, ok_right

        for(auto [l,sum1] : ok_left){
            for(auto [r,sum2] : ok_right){
                ll sum = sum1+sum2-a[i];
                if(sum < min(a[l-1],a[r+1])){
                    segs.pb({l,r});
                }
            }
        }

        // [l..i-1] and [i+1..r] that were not added
        auto &curr = pos[msb(a[i])];
        auto it = curr.find(i);
        if(it != curr.begin()){
            it--;
            if(it != curr.begin()){
                it--;
                ll l = *it+1;
                if(seg.query(l,i-1).sum < min(a[l-1],a[i])){
                    segs.pb({l,i-1});
                }
            }
        }

        it = curr.find(i);
        it++;
        if(it != curr.end()){
            it++;
            if(it != curr.end()){
                ll r = *it-1;
                if(seg.query(i+1,r).sum < min(a[i],a[r+1])){
                    segs.pb({i+1,r});
                }
            }
        }

        return segs;
    };

    ll q; cin >> q;
    while(q--){
        ll t; cin >> t;
        if(t == 1){
            ll i,v; cin >> i >> v;
            auto del = get(i);

            pos[msb(a[i])].erase(i);
            a[i] = v;
            seg.pupd(i,v);
            pos[msb(v)].insert(i);

            auto ins = get(i);

            // debug(i,v);
            // debug(del);
            // debug(ins);
            // cout << endl;

            for(auto [l,r] : del){
                st.rupd(l,r,-1);
            }
            for(auto [l,r] : ins){
                st.rupd(l,r,1);
            }
        }
        else{
            ll l,r; cin >> l >> r;
            ll pos1 = l, pos2 = r;

            {
                ll lo = l, hi = r;
                while(lo <= hi){
                    ll mid = (lo+hi) >> 1;
                    if(seg.query(l,mid-1).sum+seg.query(mid,r).val1 < 0){
                        pos1 = mid;
                        lo = mid+1;
                    }
                    else{
                        hi = mid-1;
                    }
                }
            }

            {
                ll lo = l, hi = r;
                while(lo <= hi){
                    ll mid = (lo+hi) >> 1;
                    if(seg.query(mid+1,r).sum+seg.query(l,mid).val2 < 0){
                        pos2 = mid;
                        hi = mid-1;
                    }
                    else{
                        lo = mid+1;
                    }
                }
            }

            ll ans = st.query(pos1,pos2).cnt;
            cout << ans << endl;
        }
    }
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

• Subtask 1: 0 / 5
• Subtask 2: 8 / 8
• Subtask 3: 0 / 12
• Subtask 4: 23 / 23
• Subtask 5: 0 / 35
• Subtask 6: 0 / 17