oj.uz

Submission #956436

# Submission time Handle Problem Language Result Execution time Memory
956436 2024-04-01T23:31:30 Z caterpillow Cats or Dogs (JOI18_catdog) C++17
100 / 100
 263 ms 69744 KB 
#include <bits/stdc++.h>
#include "catdog.h"

using namespace std;

using ll = long long;
using pl = pair<ll, ll>;
#define vt vector
#define f first
#define s second
#define all(x) x.begin(), x.end() 
#define pb push_back
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); i--)
#define F0R(i, b) FOR (i, 0, b)
#define endl '\n'
#define debug(x) do{auto _x = x; cerr << #x << " = " << _x << endl;} while(0)
const ll INF = 1e9;

pl clamp(pl a) {
    return {min(a.f, a.s + 1), min(a.f + 1, a.s)};
}

pl operator+(const pl& a, const pl& b) {
    return {a.f + b.f, a.s + b.s};
}

pl operator-(const pl& a, const pl& b) {
    return {a.f - b.f, a.s - b.s};
}

struct Node {
    pl actual, cat, same, dog; // actual sum, extra cat, same, extra dog
    void build() {
        same = clamp(actual);
        cat = clamp({actual.f + 1, actual.s});
        dog = clamp({actual.f, actual.s + 1});
    }
    inline pl cmb(pl a) const {
        if (a.f == a.s) return {a.f + same.f, a.s + same.s};
        else if (a.f > a.s) return {a.s + cat.f, a.s + cat.s};
        else return {a.f + dog.f, a.f + dog.s};
    }
    Node operator+(const Node& b) const {
        return {
            actual + b.actual,
            b.cmb(cat),
            b.cmb(same),
            b.cmb(dog)
        };
    }
    void operator+=(pl b) {
        actual.f += b.f;
        actual.s += b.s;
    }
    void operator-=(pl b) {
        actual.f -= b.f;
        actual.s -= b.s;
    }
    void print() {
        cerr << '{' << actual.f << ", " << actual.s << ": " << cat.f << ", " << cat.s << ", " << same.f << ", " << same.s << ", " << dog.f << ", " << dog.s << "} \n";
    }
};

const Node NID = {
    {0, 0},
    {1, 0},
    {0, 0},
    {0, 1}
};

// cursed reverse segtree
struct SegTree {
    int n;
    vt<Node> seg; 
    void init(int _n) {
        for (n = 1; n < _n; n *= 2);
        seg.resize(2 * n, NID);
    }
    Node query(int l, int r) {
        Node lhs = NID, rhs = NID;
        for (l += n, r += n + 1; l < r; l /= 2, r /= 2) {
            if (l & 1) lhs = seg[l++] + lhs;
            if (r & 1) rhs = rhs + seg[--r];
        }
        return rhs + lhs;
    }
    void pull(int i) {
        i += n;
        while (i > 1) i /= 2, seg[i] = seg[2 * i + 1] + seg[2 * i];
    }
    void upd(int i, pl val) {
        seg[i += n] += val;
        seg[i].build();
        pull(i - n);
    }
    Node& operator[](int i) {
        return seg[i + n];
    }
};

int n;
vt<int> state;

struct HLD {
    int n, t;
    vt<vt<int>> adj;
    vt<int> pos, root, sz, depth, par, leaf;
    vt<pl> agg;
    SegTree seg;
    void init(int _n) {
        n = _n;
        adj.resize(n);
        agg.resize(n, {-1, -1});
        pos = root = sz = depth = par = leaf = vt<int>(n);
        seg.init(n);
    }
    void ae(int u, int v) {
        adj[u].pb(v);
        adj[v].pb(u);
    }
    int dfs_sz(int u) {
        sz[u] = 1;
        for (int& v : adj[u]) {
            depth[v] = depth[u] + 1;
            par[v] = u;
            adj[v].erase(find(all(adj[v]), u));
            sz[u] += dfs_sz(v);
            if (sz[v] > sz[adj[u][0]]) swap(v, adj[u][0]);
        }
        return sz[u];
    }
    int dfs_hld(int u, int rt) {
        root[u] = rt;
        pos[u] = t++;
        int res = -1;
        for (int v : adj[u]) {
            if (v == adj[u][0]) res = dfs_hld(v, rt);
            else dfs_hld(v, v);
        }
        if (res == -1) leaf[u] = u;
        else leaf[u] = res;
        return leaf[u];
    }
    void gen(int r = 0) {
        t = 0;
        par[r] = -1;
        dfs_sz(r);
        dfs_hld(r, r);
        F0R (u, n) {
            if (root[u] == u) agg[u] = {0, 0};
        }
    }
    void prop(int u) {
        while (true) {
            u = leaf[u]; // go to bottom of heavy path

            // calc updates subtree aggregate
            int rt = root[u];
            Node res = seg.query(pos[rt], pos[u]);

            // update aggregate and its parent
            int p = par[rt];

            if (p >= 0) seg[pos[p]] -= agg[rt];
            agg[rt] = res.same;
            if (p == -1) return;
            
            seg[pos[p]] += res.same;
            seg[pos[p]].build();
            seg.pull(pos[p]);

            u = p; // go to parent
        }
    }  
    ll update(int u, pl v) { // do stuff to update u
        seg.upd(pos[u], v);
        prop(u);
        return min(agg[0].f, agg[0].s);
    }
    void print() {
        F0R (u, n) {
            cerr << u << ": ";
            seg[pos[u]].print();
        }
        cerr << "aggregates\n";
        F0R (u, n) {
            cerr << u << ": " << agg[u].f << " " << agg[u].s << endl;
        }
    }
} hld;

/*

let dp[u] = {min cost to make u's subtree cat safe, min cost to make u's subtree dog safe}
the difference between them is at most 1

keep track of all the cases (extra cat, same, extra dog)
each node stores the sum of everything EXCEPT its heavy path
heavy path roots store its subtree aggregate

when performing an update, modify the current node
walk up from the BASE of each heavy path up to the root, updating subtree aggregates and their parents

*/

void initialize(int N, vt<int> A, vt<int> B) {
    n = N;
    state.resize(n);
    hld.init(n);
    F0R (i, n - 1) {
        int u = A[i] - 1, v = B[i] - 1;
        hld.ae(u, v);
    }
    hld.gen();
}

int cat(int v) {
    v--;
    state[v] = 1;
    return hld.update(v, {INF, 0});
}

int dog(int v) {
    v--;
    state[v] = 2;
    return hld.update(v, {0, INF});
}

int neighbor(int v) {
    v--;
    pl sus;
    if (state[v] == 1) sus = {-INF, 0};
    else sus = {0, -INF};
    state[v] = 0;
    return hld.update(v, sus);
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 500 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 688 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 344 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 500 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 688 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 344 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 2 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 2 ms 500 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 864 KB Output is correct
29 Correct 1 ms 864 KB Output is correct
30 Correct 1 ms 352 KB Output is correct
31 Correct 1 ms 608 KB Output is correct
32 Correct 1 ms 436 KB Output is correct

Subtask #3
62.0 / 62.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 500 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 688 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 344 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 360 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 2 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 2 ms 500 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 864 KB Output is correct
29 Correct 1 ms 864 KB Output is correct
30 Correct 1 ms 352 KB Output is correct
31 Correct 1 ms 608 KB Output is correct
32 Correct 1 ms 436 KB Output is correct
33 Correct 128 ms 16292 KB Output is correct
34 Correct 50 ms 16944 KB Output is correct
35 Correct 106 ms 14496 KB Output is correct
36 Correct 201 ms 29804 KB Output is correct
37 Correct 12 ms 8280 KB Output is correct
38 Correct 212 ms 31044 KB Output is correct
39 Correct 220 ms 31040 KB Output is correct
40 Correct 209 ms 31044 KB Output is correct
41 Correct 216 ms 31056 KB Output is correct
42 Correct 263 ms 31220 KB Output is correct
43 Correct 204 ms 31040 KB Output is correct
44 Correct 236 ms 31212 KB Output is correct
45 Correct 198 ms 31072 KB Output is correct
46 Correct 227 ms 31088 KB Output is correct
47 Correct 211 ms 31140 KB Output is correct
48 Correct 68 ms 27108 KB Output is correct
49 Correct 78 ms 29644 KB Output is correct
50 Correct 25 ms 7260 KB Output is correct
51 Correct 32 ms 13624 KB Output is correct
52 Correct 16 ms 7004 KB Output is correct
53 Correct 97 ms 29776 KB Output is correct
54 Correct 64 ms 14416 KB Output is correct
55 Correct 181 ms 27048 KB Output is correct
56 Correct 108 ms 15584 KB Output is correct
57 Correct 139 ms 29264 KB Output is correct
58 Correct 22 ms 14040 KB Output is correct
59 Correct 33 ms 9052 KB Output is correct
60 Correct 65 ms 28432 KB Output is correct
61 Correct 71 ms 28896 KB Output is correct
62 Correct 45 ms 26584 KB Output is correct
63 Correct 38 ms 28220 KB Output is correct
64 Correct 41 ms 35152 KB Output is correct
65 Correct 62 ms 56876 KB Output is correct
66 Correct 32 ms 12636 KB Output is correct
67 Correct 63 ms 45132 KB Output is correct
68 Correct 97 ms 55232 KB Output is correct
69 Correct 17 ms 4796 KB Output is correct
70 Correct 4 ms 860 KB Output is correct
71 Correct 39 ms 28564 KB Output is correct
72 Correct 62 ms 54096 KB Output is correct
73 Correct 134 ms 69744 KB Output is correct
74 Correct 112 ms 51580 KB Output is correct
75 Correct 102 ms 68944 KB Output is correct
76 Correct 109 ms 62556 KB Output is correct
77 Correct 128 ms 53532 KB Output is correct