Submission #1056422

#	Time	Username	Problem	Language	Result	Execution time	Memory
1056422		Forested	Radio Towers (IOI22_towers)	C++17	58 / 100	4040 ms	7668 KiB

towers

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

using i32 = int;
using i64 = long long;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

#define OVERRIDE4(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, l, r) for (i32 i = (i32)(l); i < (i32)(r); ++i)
#define REP(...) OVERRIDE4(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, l, r) for (i32 i = (i32)(r)-1; i >= (i32)(l); --i)
#define PER(...) OVERRIDE4(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32) size(x)

void dbg(i32 x) { cerr << x; }
void dbg(i64 x) { cerr << x; }
template <typename T, typename U>
void dbg(pair<T, U> p) {
    cerr << '(' << p.first << ", " << p.second << ')';
}
template <typename T>
void dbg(V<T> arr) {
    cerr << '[';
    REP(i, LEN(arr)) {
        if (i) {
            cerr << ", ";
        }
        dbg(arr[i]);
    }
    cerr << ']';
}
void debug() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug(Head head, Tail... tail) {
    dbg(head);
    cerr << ", ";
    debug(tail...);
}
#ifdef DEBUGF
#define DBG(...)                       \
    do {                               \
        cerr << #__VA_ARGS__ << " : "; \
        debug(__VA_ARGS__);            \
    } while (false)
#else
#define DBG(...) (void)0
#endif

#include "towers.h"

constexpr i32 INF = 1001001001;

template <typename T>
i32 lob(const V<T> &arr, T v) {
    return (i32)(lower_bound(ALL(arr), v) - begin(arr));
}
template <typename T>
i32 upb(const V<T> &arr, T v) {
    return (i32)(upper_bound(ALL(arr), v) - begin(arr));
}


struct RMQ {
    i32 n;
    V<i32> dat;
    
    RMQ(i32 n) : n(n), dat(2 * n, -INF) {}
    
    void update(i32 idx, i32 val) {
        idx += n;
        dat[idx] = val;
        while ((idx /= 2) >= 1) {
            dat[idx] = max(dat[2 * idx], dat[2 * idx + 1]);
        }
    }
    
    i32 rmq(i32 l, i32 r) const {
        l += n;
        r += n;
        i32 m = -INF;
        while (l < r) {
            if (l & 1) {
                chmax(m, dat[l++]);
            }
            if (r & 1) {
                chmax(m, dat[--r]);
            }
            l /= 2;
            r /= 2;
        }
        return m;
    }
    
    void trc() const {
        V<i32> arr(n + ALL(dat));
        DBG(arr);
    }
};

template <typename T>
class RemovableQueue {
    priority_queue<T, V<T>, greater<>> pq, rm;
    
public:
    RemovableQueue() : pq(), rm() {}
    void add(T x) {
        pq.push(x);
    }
    void remove(T x) {
        rm.push(x);
    }
    T getmin() {
        while (!rm.empty() && rm.top() == pq.top()) {
            rm.pop();
            pq.pop();
        }
        return pq.top();
    }
    i32 size() const {
        return (i32)pq.size() - (i32)rm.size();
    }
};

V<pair<i32, i32>> calc_all_ans(i32 n, V<i32> h) {
    V<pair<i32, i32>> ret;
    V<i32> down(n, 0), up(n, 0);
    REP(i, 1, n - 1) {
        if (h[i - 1] < h[i] && h[i] > h[i + 1]) {
            up[i] = 1;
        }
        if (h[i - 1] > h[i] && h[i] < h[i + 1]) {
            down[i] = 1;
        }
    }
    if (accumulate(ALL(up), 0) == 0) {
        ret.emplace_back(1, 1);
        return ret;
    }
    i32 l = 0;
    while (h[l] > h[l + 1]) {
        ++l;
    }
    i32 r = n;
    while (h[r - 2] < h[r - 1]) {
        --r;
    }
    down[l] = down[r - 1] = 1;
    V<i32> imp;
    REP(i, n) {
        if (down[i] || up[i]) {
            imp.push_back(i);
        }
    }
    DBG(imp);
    RemovableQueue<tuple<i32, i32, i32>> pq;
    V<i32> lft(LEN(imp), -1), rgt(LEN(imp), -1);
    REP(i, LEN(imp) - 1) {
        pq.add(make_tuple(abs(h[imp[i]] - h[imp[i + 1]]), i, i + 1));
        lft[i + 1] = i;
        rgt[i] = i + 1;
    }
    ret.emplace_back(1, LEN(pq) / 2 + 1);
    while (LEN(pq) >= 2) {
        auto [d, l, r] = pq.getmin();
        ret.emplace_back(d + 1, LEN(pq) / 2);
        pq.remove(make_tuple(d, l, r));
        i32 ll = lft[l], rr = rgt[r];
        DBG(d, l, r, ll, rr);
        if (ll != -1) {
            pq.remove(make_tuple(abs(h[imp[ll]] - h[imp[l]]), ll, l));
            rgt[ll] = rr;
        }
        if (rr != -1) {
            pq.remove(make_tuple(abs(h[imp[r]] - h[imp[rr]]), r, rr));
            lft[rr] = ll;
        }
        if (ll != -1 && rr != -1) {
            pq.add(make_tuple(abs(h[imp[ll]] - h[imp[rr]]), ll, rr));
        }
    }
    V<pair<i32, i32>> simp;
    REP(i, LEN(ret)) {
        if (i == LEN(ret) - 1 || ret[i].first != ret[i + 1].first) {
            simp.push_back(ret[i]);
        }
    }
    ret = simp;
    DBG(ret);
    return ret;
}

i32 n;
V<i32> h;
V<i32> psum;
i32 peak;
V<pair<i32, i32>> allans;

void init(i32 _n, V<i32> _h) {
    n = _n;
    h = _h;
    
    psum.resize(n + 1, 0);
    REP(i, n) {
        psum[i + 1] = psum[i] + (0 < i && i < n - 1 && h[i - 1] < h[i] && h[i] > h[i + 1]);
    }
    
    {
        i32 mi = (i32)(max_element(ALL(h)) - begin(h));
        peak = mi;
        REP(i, mi) {
            if (h[i] > h[i + 1]) {
                peak = -1;
            }
        }
        REP(i, mi, n - 1) {
            if (h[i] < h[i + 1]) {
                peak = -1;
            }
        }
    }
    
    allans = calc_all_ans(n, h);
}

i32 max_towers(i32 l, i32 r, i32 delta) {
    ++r;
    if (r - l == 1) {
        return 1;
    }
    
    if (delta == 1) {
        i32 ans = psum[r - 1] - psum[l + 1] + 1;
        return ans;
    }
    
    if (peak != -1) {
        if (l <= peak && peak < r && max(h[l], h[r - 1]) + delta <= h[peak]) {
            return 2;
        } else {
            return 1;
        }
    }
    
    if (l == 0 && r == n) {
        auto itr = lower_bound(ALL(allans), pair<i32, i32>(delta + 1, 0));
        --itr;
        return itr->second;
    }
    
    V<i32> g(begin(h) + l, begin(h) + r);
    i32 m = r - l;
    
    V<i32> hs;
    hs.reserve(3 * m);
    REP(i, m) {
        hs.push_back(g[i] - delta);
        hs.push_back(g[i]);
        hs.push_back(g[i] + delta);
    }
    sort(ALL(hs));
    hs.erase(unique(ALL(hs)), end(hs));
    i32 k = LEN(hs);
    RMQ down(k);
    RMQ up(k);
    
    REP(i, m) {
        i32 d = max(1, up.rmq(lob(hs, g[i] + delta), k) + 1);
        i32 u = down.rmq(0, lob(hs, g[i] - delta) + 1);
        i32 idx = lob(hs, g[i]);
        down.update(idx, d);
        up.update(idx, u);
    }
    i32 ans = down.rmq(0, k);
    return ans;
}

• Subtask 1: 4 / 4
• Subtask 2: 11 / 11
• Subtask 3: 12 / 12
• Subtask 4: 14 / 14
• Subtask 5: 17 / 17
• Subtask 6: 0 / 19
• Subtask 7: 0 / 23