Submission #526669

#	Time	Username	Problem	Language	Result	Execution time	Memory
526669		PurpleCrayon	Comparing Plants (IOI20_plants)	C++17	100 / 100	1706 ms	145012 KiB

plants

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

#define sz(v) int(v.size())
const int INF = 1e9+10;

struct S {
    int n;
    vector<pair<int, int>> t;
    vector<int> lzy;

    void build(int v, int tl, int tr, const vector<int>& a) {
        if (tl == tr) {
            t[v] = make_pair(a[tl], tl);
        } else {
            int tm = (tl + tr) / 2;
            build(2*v, tl, tm, a), build(2*v+1, tm+1, tr, a);
            t[v] = min(t[2*v], t[2*v+1]);
        }
    }

    S() {}
    S(vector<int> a) {
        n = sz(a);
        t.resize(4 * n);
        lzy.assign(4 * n, 0);
        build(1, 0, n-1, a);
    }
    S(int _n): n(_n) {
        vector<int> a(n, INF);
        t.resize(4 * n);
        lzy.assign(4 * n, 0);
        build(1, 0, n-1, a);
    }
    void push(int v, int tl, int tr, int x) {
        if (!x) return;
        t[v].first += x;
        if (tl != tr) {
            lzy[2*v] += x;
            lzy[2*v+1] += x;
        }
    }
    void app(int v, int tl, int tr) {
        push(v, tl, tr, lzy[v]);
        lzy[v] = 0;
    }
    void upd(int v, int tl, int tr, int l, int r, int x) {
        app(v, tl, tr);
        if (l > r || l > tr || r < tl) return;
        if (l <= tl && tr <= r) {
            push(v, tl, tr, x);
            return;
        }
        int tm = (tl + tr) / 2;
        upd(2*v, tl, tm, l, r, x), upd(2*v+1, tm+1, tr, l, r, x);
        t[v] = min(t[2*v], t[2*v+1]);
    }
    void upd(int l, int r, int x) {
        if (l > r) {
            upd(1, 0, n-1, 0, r, +x);
            upd(1, 0, n-1, l, n-1, +x);
        } else {
            upd(1, 0, n-1, l, r, +x);
        }
    }
    pair<int, int> qry(int v, int tl, int tr, int l, int r) {
        app(v, tl, tr);
        if (l > r || l > tr || r < tl) return {INF, INF};
        if (l <= tl && tr <= r) return t[v];
        int tm = (tl + tr) / 2;
        return min(qry(2*v, tl, tm, l, r), qry(2*v+1, tm+1, tr, l, r));
    }
    pair<int, int> qry(int l, int r) {
        if (l > r) {
            return min(qry(1, 0, n-1, 0, r), qry(1, 0, n-1, l, n-1));
        } else {
            return qry(1, 0, n-1, l, r);
        }
    }
    void set(int pos, int x) {
        upd(pos, pos, -qry(pos, pos).first + x);
    }
};

const int L = 19;
vector<vector<int>> build_lift(vector<int> par) {
    int n = sz(par);
    vector<vector<int>> up(L, vector<int>(n, -1));
    up[0] = par;
    for (int k = 1; k < L; k++) {
        for (int i = 0; i < n; i++) {
            up[k][i] = up[k-1][i] == -1 ? -1 : up[k-1][up[k-1][i]];
        }
    }
    return up;
}
int search_lift(const vector<vector<int>>& up, int c, const auto& f) {
    for (int k = L-1; k >= 0; k--) {
        if (f(up[k][c])) {
            c = up[k][c];
        }
    }
    return c;
}

int n, k;
vector<int> a, b;
vector<int> nxt, prv;

vector<vector<int>> up_nxt, up_prv;

void init(int K, vector<int> r) {
    n = sz(r), k = K;
    vector<bool> done(n);

    a.resize(n);
    nxt.assign(2*n, -1), prv.assign(2*n, -1);

    set<int> cand;
    set<int> bad_cand;
    auto prv_cand = [&](int x, bool which) {
        const auto& use = (which ? cand : bad_cand);
        if (!sz(use)) return INF;
        auto it = use.lower_bound(x);
        if (it != use.begin()) return *prev(it);
        return *use.rbegin();
    };
    auto nxt_cand = [&](int x, bool which) {
        const auto& use = (which ? cand : bad_cand);
        if (!sz(use)) return INF;
        auto it = use.upper_bound(x);
        if (it == use.end()) return *use.begin();
        return *it;
    };
    auto forward_dist = [&](int a, int b) {
        if (a == INF || b == INF) return INF;
        if (a < b) return b - a;
        return n - a + b;
    };

    S seg(r);
    vector<bool> has_add(n);
    for (int i = 0; i < n; i++) if (!r[i]) {
        cand.insert(i), has_add[i] = 1;
        seg.upd(i, i, INF);
    }

    vector<set<int>> stop(n);
    vector<int> stopped(n, -1);

    auto add_stop = [&](int x, int y) {
        if (stopped[y] != -1) {
            stop[stopped[y]].erase(y);
        }
        stop[x].insert(y);
        stopped[y] = x;
    };

    for (int i = 0; i < n; i++) if (!r[i]) {
        int p = prv_cand(i, true);
        if (forward_dist(p, i) < k) {
            add_stop(p, i);
            // stop[p].insert(i);
            bad_cand.insert(i);
        }
    }
    for (int x : bad_cand) cand.erase(x);

    auto prv_cand_both = [&](int x) {
        int one = prv_cand(x, true), two = prv_cand(x, false);
        if (forward_dist(one, x) < forward_dist(two, x)) return one;
        return two;
    };
    auto nxt_cand_both = [&](int x) {
        int one = nxt_cand(x, true), two = nxt_cand(x, false);
        if (forward_dist(x, one) < forward_dist(x, two)) return one;
        return two;
    };

    auto add_cand = [&](int x) {
        int p = prv_cand_both(x);
        if (p != INF && forward_dist(p, x) < k) {
            add_stop(p, x);
            // stop[p].push_back(x);
            cand.erase(x);
            bad_cand.insert(x);
        } else {
            bad_cand.erase(x);
            cand.insert(x);
        }
        int q = nxt_cand_both(x);
        if (q != INF && forward_dist(x, q) < k) {
            add_stop(x, q);
            // stop[x].push_back(q);
            cand.erase(q);
            bad_cand.insert(q);
        }
    };

    for (int rep = 0; rep < n; rep++) {
        int me = *cand.begin();

        a[me] = n - 1 - rep;
        done[me] = 1;
        cand.erase(me);

        for (int x : stop[me]) if (!done[x]) {
            add_cand(x);
        }

        int L = ((me - k + 1) + n) % n, R = (me - 1 + n) % n;
        seg.upd(L, R, -1);
        for (auto C = seg.qry(L, R); C.first == 0; C = seg.qry(L, R)) {
            int c = C.second;
            add_cand(c);
            seg.upd(c, c, +INF);
        }
    }
    for (int rep : {0, 1}) for (int x : a) b.push_back(x);

    assert(sz(b) == 2*n);
    vector<vector<int>> loc(n);
    for (int i = 0; i < 2*n; i++) loc[b[i]].push_back(i);

    S b_seg(2*n);
    for (int l = n-1; l >= 0; l--) for (int i : loc[l]) {
        {
            int L = i+1, R = min(2*n, i+k)-1;
            if (L <= R) {
                auto c = b_seg.qry(L, R);
                if (c.first != INF) nxt[i] = c.second;
            }
        }
        {
            int L = max(0, i-k+1), R = i-1;
            if (L <= R) {
                auto c = b_seg.qry(L, R);
                if (c.first != INF) prv[i] = c.second;
            }
        }
        if (nxt[i] == INF) nxt[i] = -1;
        if (prv[i] == INF) prv[i] = -1;

        b_seg.set(i, b[i]);
    }

    // for (int x : b) cerr << x << ' '; cerr << endl;
    // for (int x : nxt) cerr << x << ' '; cerr << endl;
    // for (int x : prv) cerr << x << ' '; cerr << endl;

    /*
    for (int i = 0; i < 2*n; i++) {
        int c_nxt = -1;
        for (int j = i+1; j < min(2*n, i+k); j++) { // range min
            if (b[j] > b[i] && (c_nxt == -1 || b[c_nxt] > b[j]))
                c_nxt = j;
        }
        // cerr << "nxt: " << i << ' ' << c_nxt << ' ' << nxt[i] << endl;
        assert(c_nxt == nxt[i]);
        int c_prv = -1;
        for (int j = max(0, i-k+1); j < i; j++) { // range min
            if (b[j] > b[i] && (c_prv == -1 || b[c_prv] > b[j]))
                c_prv = j;
        }
        // cerr << "prv: " << i << ' ' << c_prv << ' ' << prv[i] << endl;
        assert(c_prv == prv[i]);
    }
    */

    up_nxt = build_lift(nxt);
    up_prv = build_lift(prv);
}

bool can_nxt(int x, int y) { // slow
    int c = x;
    int need = y < x ? y + n : y;
    c = search_lift(up_nxt, c, [&](int v){ return v != -1 && v <= need; });
    /*
    while (nxt[c] != -1 && nxt[c] <= need) {
        assert(b[nxt[c]] > b[c]);
        c = nxt[c];
    }
    */
    assert(b[need] == a[y]);
    return need - c < k && b[need] >= b[c];
}
bool can_prv(int x, int y) { // slow
    int c = x > y ? x : x + n;
    int need = y;
    c = search_lift(up_prv, c, [&](int v){ return v != -1 && v >= need; });
    /*
    while (prv[c] != -1 && prv[c] >= need) {
        assert(b[prv[c]] > b[c]);
        c = prv[c];
    }
    */
    assert(b[need] == a[y]);
    return c - need < k && b[need] >= b[c];
}
bool can_reach(int x, int y) {
    return can_nxt(x, y) || can_prv(x, y);
}

int compare_plants(int x, int y) {
    if (can_reach(x, y)) { // y is greater than x
        assert(a[y] > a[x]);
        return -1;
    }
    if (can_reach(y, x)) { // x is greater than y
        assert(a[x] > a[y]);
        return 1;
    }
    return 0;
}

Compilation message (stderr)

plants.cpp:98:61: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   98 | int search_lift(const vector<vector<int>>& up, int c, const auto& f) {
      |                                                             ^~~~
plants.cpp: In function 'void init(int, std::vector<int>)':
plants.cpp:220:14: warning: unused variable 'rep' [-Wunused-variable]
  220 |     for (int rep : {0, 1}) for (int x : a) b.push_back(x);
      |              ^~~

• Subtask 1: 5 / 5
• Subtask 2: 14 / 14
• Subtask 3: 13 / 13
• Subtask 4: 17 / 17
• Subtask 5: 11 / 11
• Subtask 6: 15 / 15
• Subtask 7: 25 / 25