제출 #1247358

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1247358		madamadam3	Financial Report (JOI21_financial)	C++20	100 / 100	975 ms	46336 KiB

Main

#include <bits/stdc++.h>

using namespace std;

int bitmask(int n, int d, vector<int> a) {
    int ans = 0;
    for (int mask = 1; mask < (1 << n); mask++) {
        vector<int> active; for (int i = 0; i < n; i++) if (mask & (1 << i)) active.push_back(i);
        int calc = 1, cmax = a[active[0]];
        for (int i = 1; i < active.size(); i++) {
            if (active[i] - active[i-1] > d) {
                calc = 0; break;
            }
            if (a[active[i]] > cmax) {
                cmax = a[active[i]];
                calc++;
            }
        }

        ans = max(ans, calc);
    }

    return ans;
}

// because reachability is monotone forwards, we could do range chmax for all the nodes i can reach
// could get 12 pts for N = 1 as follows: (1) use binary search to find largest array starting at i where max(arr) <= a[i]
//                                            this gives reachable[i]
//                                        (2) ...

struct SegTree {
    int n; vector<int> st;

    SegTree() {};
    SegTree(int N) {
        n = N; st.resize(4*n);
    }

    int update(int i, int l, int r, int k, int v) {
        if (!(l <= k && k < r)) return st[i];
        if (l + 1 == r) return st[i] = v;

        int m = l + (r - l) / 2;
        return st[i] = max(update(2*i+1, l, m, k, v), update(2*i+2, m, r, k, v));
    }

    int query(int i, int l, int r, int ql, int qr) {
        if (r <= ql || qr <= l) return 0;
        if (ql <= l && r <= qr) return st[i];

        int m = l + (r - l) / 2;
        return max(query(2*i+1, l, m, ql, qr), query(2*i+2, m, r, ql, qr));
    }

    void update(int k, int v) {
        update(0, 0, n, k, v);
    }

    int query(int l, int r) {
        return query(0, 0, n, l, r);
    }

    void trace() {
        for (int i = 0; i < n; i++) cout << query(i, i+1) << " "; cout << "\n";
    }
};

/*
    solution so far:
    (1) the problem is very similar to longest increasing subsequence, infact when D = n, it is LIS
    (2) if we process indices in ascending order of a[idx], we still get the answer. ⇒ DP[i] depends only on j < i and a[j] < a[i]
    (3) the set of nodes which can be reached from index i using only nodes where a[j] <= a[i] form a contiguous subarray
    (4) DP[i] = max(all nodes that can reach i, and have a[j] < a[i]). slight restrictioning on (2). we can use a segment tree to do
        2 things at once here. first, sort all indices by a[idx]. we can now query [0, sorted_pos[i]], and get the maximum value of all
        DP[i] where j < i. the second part is we initialise and disable values when needed. so when the contiguous subarray of reachable[j]
        ends, we set DP[i] to 0 inside of the segtree, this way we only query active nodes. the final step is now to efficiently find the 
        value of end[j] (first index j cannot reach)
    (5) if D = N, end[j] = n for all j. if D = 1, we can binary search to find the first index where max(a[i:j]) is > a[i] (n log^2 n with segtree)
    (6) maybe we can use a segtree to compute it for all D?
*/
                                              
int dp(int n, int d, vector<int> a) {
    vector<int> indices(n); iota(indices.begin(), indices.end(), 0);
    sort(indices.begin(), indices.end(), [&](int i, int j) {return a[i] == a[j] ? i > j : a[i] < a[j];});
    vector<int> ridx(n); for (int i = 0; i < n; i++) ridx[indices[i]] = i;

    vector<vector<int>> ends(n+2, vector<int>()), ends2(n+2, vector<int>());
    vector<int> M(n, INT_MAX);
    multiset<int> window;
    int l = 0, r = 0;

    for (; r < n; r++) {
        if (r <= d) {
            M[r] = INT_MIN;
            window.insert(a[r]);
            continue;
        }
        
        window.erase(window.find(a[l++]));
        M[r] = *window.begin();

        window.insert(a[r]);
    }

    auto rmq = SegTree(n); for (int i = 0; i < n; i++) rmq.update(i, M[i]);

    for (int i = 0; i < n; i++) {
        int lo = i+1, hi = n - 1, av = n;
        while (lo <= hi) {
            int mid = (lo + hi) / 2;
            bool check = rmq.query(i+1, mid + 1) > a[i];

            if (check) {
                hi = mid - 1;
                av = mid;
            } else {
                lo = mid + 1;
            }
        }

        ends[av].push_back(i);
        // for (int j = i+1; j < n; j++) {
        //     if (M[j] > a[i]) {
        //         ends[j].push_back(i);
        //         break;
        //     }
        // }
    }

    // for (int i = 0; i < n; i++) {
    //     int max_dist = 0, prev_se = i;

    //     for (int j = i; j < n; j++) {
    //         max_dist = max(max_dist, j - prev_se);
    //         if (a[j] <= a[i]) prev_se = j;
    //         if (max_dist > d) {
    //             ends2[j].push_back(i);
    //             break;
    //         }
    //     }
    // }

    // for (int i = 0; i < n; i++) {
    //     cout << "i: " << i << "\n";
    //     for (auto &el : ends2[i]) cout << el << " "; cout << "\n";
    //     for (auto &el : ends[i]) cout << el << " "; cout << "\n";
    // }

    vector<int> DP(n, 0);
    auto st = SegTree(n);

    for (int i = 0; i < n; i++) {
        for (auto &el : ends[i]) {
            st.update(ridx[el], 0);
        }

        DP[i] = st.query(0, ridx[i]) + 1;

        st.update(ridx[i], DP[i]);
    }

    return *max_element(DP.begin(), DP.end());
}

void debug() {
    mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
    uniform_int_distribution dist(0, 5);

    for (int TRIAL = 0; TRIAL < 1'000; TRIAL++) {
        int N = 6; vector<int> INPUT; for (int i = 0; i < N; i++) INPUT.push_back(dist(rng));
        for (int D = 1; D <= N; D++) {
            int bm = bitmask(N, D, INPUT);
            int dpa = dp(N, D, INPUT);

            if (bm != dpa) {
                cout << "Failure on N: " << N << " D: " << D << " and array:"; for (auto &el : INPUT) cout << " " << el; cout << "\n";
                cout << "Bitmask: " << bm << " DP: " << dpa << "\n";
                break; 
            }
        }
    }
}

int main() {
    // debug();

    cin.tie(0)->sync_with_stdio(0);

    int n, d; cin >> n >> d;
    vector<int> a(n); for (int i = 0; i < n; i++) cin >> a[i];

    cout << dp(n, d, a) << "\n";
    return 0;
}

• Subtask 1: 14 / 14
• Subtask 2: 14 / 14
• Subtask 3: 20 / 20
• Subtask 4: 12 / 12
• Subtask 5: 5 / 5
• Subtask 6: 35 / 35