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Submission #934775

# Submission time Handle Problem Language Result Execution time Memory
934775 2024-02-28T01:05:24 Z eysbutno Hard route (IZhO17_road) C++17
52 / 100
 391 ms 82452 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
#define all(x) begin(x), end(x)
#define sz(x) (int) (x).size()
#define f first 
#define s second 

template<class T> bool smin(T& a, T b) {
    return b < a ? a = b, 1 : 0;
}
template<class T> bool smax(T& a, T b) {
    return b > a ? a = b, 1 : 0;
}
int main() {
    cin.tie(0) -> sync_with_stdio(0);
    int n; cin >> n;
    vector adj(n, vector<int>());
    for (int i = 1; i < n; i++) {
        int x, y; cin >> x >> y;
        adj[--x].push_back(--y);
        adj[y].push_back(x);
    }
    vector<int> d(n), c(n);
    auto dfs = [&](int u, int p, auto&& dfs) -> void {
        d[u] = 0, c[u] = 1;
        for (int v : adj[u]) if (v != p) {
            dfs(v, u, dfs);
            if (smax(d[u], d[v] + 1)) {
                c[u] = c[v];
            } else if (d[v] + 1 == d[u]) {
                c[u] += c[v];
            }
        }
    }; dfs(0, -1, dfs);
    ll hard = 0, cnt = 1;
    auto dfs2 = [&](int u, int p, int pd, int pc, 
                    auto&& dfs2) -> void {
        vector<pii> opt;
        if (u > 0 || sz(adj[u]) == 1) {
            opt.push_back({pd, pc});
        }
        for (int v : adj[u]) if (v != p) {
            opt.push_back({d[v] + 1, c[v]});
        }
        sort(all(opt), greater<>());
        if (sz(adj[u]) >= 3) { // can form nonzero path
            ll cur = opt[0].f * (opt[1].f + opt[2].f), 
               num = 0;
            int ties = 0; // equal to third element
            for (auto [k, v] : opt) {
                if (k == opt[2].f) ties += v;
            }
            // case 1: all are distinct
            if (opt[0].f != opt[1].f &&
                opt[1].f != opt[2].f) {
                // num = opt[0].s * opt[1].s * ties;
                num = opt[1].s * ties;
            }
            // case 2: all are the same
            else if (opt[0].f == opt[1].f &&
                opt[1].f == opt[2].f) {
                num = ties * ties;
				for (auto [k, v] : opt) {
					if (k == opt[2].f) num -= v * v;
				}
				num /= 2;
            }
            // case 3: first two are the same
            else if (opt[0].f == opt[1].f) {
                num = (opt[0].s + opt[1].s) * ties;
            }
            // case 4: last two are the same
            else {
               	num = ties * ties;
				for (auto [k, v] : opt) {
					if (k == opt[2].f) num -= v * v;
				}
				num /= 2;
            }
            if (smax(hard, cur)) {
                cnt = num;
            } else if (hard == cur) {
                cnt += num;
            }
        }
        // processing parent dist & parent count
        int l1 = 0, l2 = 0, cnt1 = 0, cnt2 = 0;
        for (auto [k, v] : opt) {
            // all paths will increase by len 1
            if (k + 1 > l1) {
                swap(l1, l2), swap(cnt1, cnt2);
                l1 = k + 1, cnt1 = v;
            } else if (k + 1 == l1) {
                cnt1 += v;
            } else if (k + 1 > l2) {
                l2 = k + 1, cnt2 = v;
            } else if (k + 1 == l2) {
                cnt2 += v;
            }
        }
        for (int v : adj[u]) if (v != p) {
            if (d[v] + 2 == l1) {
                (c[v] == cnt1) ? dfs2(v, u, l2, cnt2, dfs2) :
                            	 dfs2(v, u, l1, cnt1 - c[v], dfs2);
            } else {
                dfs2(v, u, l1, cnt1, dfs2);
            }
        }
    }; dfs2(0, -1, 0, 1, dfs2);
    cout << hard << ' ' << cnt << '\n';
}
/**
 * TASK: Hard Route (IZhO).
 * Terminals are (obviously) leaves.
 * Probably will consider all paths 
 * from a given LCA (from which the
 * longest distance lies on).
 * 
 * So, DFS over every root x, where
 * the endpoints and farthest nodes
 * can be chosen. NOTE THAT THE PATH
 * WILL BE THE TWO SHORTER DISTANCES!
 * (Note that using this information,
 * you can prove that no (u, v) pair
 * will be double counted.)
*/

Subtask #1
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 344 KB Output is correct
13 Correct 0 ms 344 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 344 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 344 KB Output is correct
13 Correct 0 ms 344 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 344 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 2 ms 860 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 2 ms 1236 KB Output is correct
28 Correct 2 ms 1236 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 2 ms 1116 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1116 KB Output is correct
34 Correct 2 ms 1028 KB Output is correct
35 Correct 2 ms 1116 KB Output is correct
36 Correct 2 ms 1116 KB Output is correct
37 Correct 3 ms 1148 KB Output is correct
38 Correct 3 ms 1624 KB Output is correct
39 Correct 2 ms 860 KB Output is correct
40 Correct 2 ms 860 KB Output is correct
41 Correct 2 ms 860 KB Output is correct
42 Correct 2 ms 800 KB Output is correct
43 Correct 2 ms 732 KB Output is correct
44 Correct 2 ms 604 KB Output is correct
45 Correct 2 ms 604 KB Output is correct
46 Correct 1 ms 604 KB Output is correct
47 Correct 2 ms 860 KB Output is correct
48 Correct 2 ms 860 KB Output is correct

Subtask #3
0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 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 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 344 KB Output is correct
13 Correct 0 ms 344 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 344 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 2 ms 860 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 2 ms 1236 KB Output is correct
28 Correct 2 ms 1236 KB Output is correct
29 Correct 2 ms 1116 KB Output is correct
30 Correct 2 ms 1116 KB Output is correct
31 Correct 2 ms 1116 KB Output is correct
32 Correct 2 ms 1116 KB Output is correct
33 Correct 2 ms 1116 KB Output is correct
34 Correct 2 ms 1028 KB Output is correct
35 Correct 2 ms 1116 KB Output is correct
36 Correct 2 ms 1116 KB Output is correct
37 Correct 3 ms 1148 KB Output is correct
38 Correct 3 ms 1624 KB Output is correct
39 Correct 2 ms 860 KB Output is correct
40 Correct 2 ms 860 KB Output is correct
41 Correct 2 ms 860 KB Output is correct
42 Correct 2 ms 800 KB Output is correct
43 Correct 2 ms 732 KB Output is correct
44 Correct 2 ms 604 KB Output is correct
45 Correct 2 ms 604 KB Output is correct
46 Correct 1 ms 604 KB Output is correct
47 Correct 2 ms 860 KB Output is correct
48 Correct 2 ms 860 KB Output is correct
49 Correct 366 ms 71252 KB Output is correct
50 Correct 335 ms 77036 KB Output is correct
51 Correct 391 ms 82452 KB Output is correct
52 Correct 335 ms 63824 KB Output is correct
53 Incorrect 280 ms 76988 KB Output isn't correct
54 Halted 0 ms 0 KB -