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Submission #938642

# Submission time Handle Problem Language Result Execution time Memory
938642 2024-03-05T11:37:21 Z Gromp15 Graph (BOI20_graph) C++17
100 / 100
 116 ms 37204 KB 
#include <bits/stdc++.h>
#define ll long long
#define ar array
#define db double
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define rint(l, r) uniform_int_distribution<int>(l, r)(rng)
template<typename T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template<typename T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
void test_case() {
	int n, m;
	cin >> n >> m;
	vector<vector<ar<int, 2>>> adj(n+1);
	vector<ar<int, 3>> E;
	for (int i = 0; i < m; i++) {
		int x, y, w;
		cin >> x >> y >> w;
		E.push_back({x, y, w});
		adj[x].push_back({y, 2*w});
		adj[y].push_back({x, 2*w});
	}
	vector<int> ans(n+1);
	vector<bool> vis2(n+1);
	vector<int> depth(n+1), val(n+1);
	for (int v = 1; v <= n; v++) if (!vis2[v]) {
		ll tot_sum = 0;
		vector<ar<int, 3>> edges;
		vector<int> comp;
		auto dfs = [&](auto&& s, int v, int cur) -> void {
			vis2[v] = 1;
			comp.emplace_back(v);
			val[v] = cur;
			tot_sum += cur;
			for (auto [u, w] : adj[v]) {
				edges.push_back({v, u, w});
				if (!vis2[u]) {
					depth[u] = depth[v] + 1;
					s(s, u, w - cur);
				}
			}
		};
		dfs(dfs, v, 0);
		// val[x] + val[y] +/- 2x = 2*w
		// tot_sum + totx = final val
		int need; bool f = 1;
		for (auto [x, y, w] : edges) {
			if ((depth[x] + depth[y]) & 1) { // they must have the same val
				if (val[x] + val[y] != w) {
					cout << "NO\n"; return;
				}
			}
			else {
				// val[x] + val[y] +/- 2x = w
				int other = (w - val[x] - val[y]) * (depth[x] & 1 ? -1 : 1);
				assert(other % 2 == 0);
				other /= 2;
				if (f) {
					need = other, f = 0;
				}
				else {
					if (need != other) {
						cout << "NO\n"; return;
					}
				}
			}
		}
		if (f) {
			// choose x that minimizes tot_sum + tot*x
			int N = sz(comp);
			vector<ll> each(4 * N + 1), each2(4 * N + 1);
			auto add = [&](int L, int R, int X, int del) { // a[L...R] += x + del
				// X + 0
				// X + del
				// X + 2*del
				// X + ...
				each[L+2*N] += X;
				if (L+2*N+1 <= 4*N) {
					each2[L+2*N+1] += del;
				}
				if (R+1 <= 2*N) {
					each[R+2*N+1] -= X;
					each2[R+2*N+1] -= del;
					each[R+2*N+1] -= (R - L) * del;
				}
				/*
				for (int i = L + 2*N; i <= R + 2*N; i++) {
					each[i] += X + (i - (L + 2*N)) * del;
				}
				*/
			};
			for (int u : comp) {
				if (depth[u] & 1) {
					add(-2*N, val[u], val[u] + 2*N, -1);
					if (val[u] + 1 <= 2*N) add(val[u] + 1, 2*N, 1, 1);
				}
				else {
					add(-2*N, -val[u], -val[u] + 2*N, -1);
					if (-val[u] + 1 <= 2*N) add(-val[u] + 1, 2*N, 1, 1);
				}
			}
			for (int i = 1; i <= 4*N; i++) each[i] += each[i-1], each2[i] += each2[i-1];
			for (int i = 1; i <= 4*N; i++) each2[i] += each2[i-1];
			for (int i = 0; i <= 4*N; i++) {
				each[i] += each2[i];
			}
			int who = (min_element(each.begin(), each.end()) - each.begin()) - 2 * N;
			for (int u : comp) {
				ans[u] = val[u] + who * (depth[u] & 1 ? -1 : 1);
			}
		}
		else {
			// x is set
			for (int u : comp) {
				ans[u] = val[u] + need * (depth[u] & 1 ? -1 : 1);
			}
		}
	}
	cout << "YES\n";
	cout << fixed << setprecision(1);

	for (int i = 1; i <= n; i++) cout << (db)ans[i] / 2 << " \n"[i==n];



}
int main() {
    cin.tie(0)->sync_with_stdio(0);
    int t = 1;
//    cin >> t;
    while (t--) test_case();
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB answer = YES
2 Correct 0 ms 460 KB answer = YES
3 Correct 1 ms 348 KB answer = YES
4 Correct 0 ms 348 KB answer = NO
5 Correct 0 ms 348 KB answer = YES
6 Correct 0 ms 348 KB answer = YES
7 Correct 0 ms 348 KB answer = YES
8 Correct 1 ms 456 KB answer = YES
9 Correct 0 ms 460 KB answer = NO
10 Correct 0 ms 348 KB answer = YES
11 Correct 0 ms 348 KB answer = YES
12 Correct 0 ms 348 KB answer = NO
13 Correct 0 ms 348 KB answer = YES
14 Correct 1 ms 348 KB answer = YES
15 Correct 1 ms 348 KB answer = YES
16 Correct 0 ms 348 KB answer = YES
17 Correct 0 ms 344 KB answer = YES
18 Correct 1 ms 344 KB answer = YES
19 Correct 1 ms 348 KB answer = YES
20 Correct 0 ms 348 KB answer = YES
21 Correct 0 ms 348 KB answer = YES
22 Correct 0 ms 348 KB answer = NO
23 Correct 0 ms 348 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB answer = YES
2 Correct 0 ms 460 KB answer = YES
3 Correct 1 ms 348 KB answer = YES
4 Correct 0 ms 348 KB answer = NO
5 Correct 0 ms 348 KB answer = YES
6 Correct 0 ms 348 KB answer = YES
7 Correct 0 ms 348 KB answer = YES
8 Correct 1 ms 456 KB answer = YES
9 Correct 0 ms 460 KB answer = NO
10 Correct 0 ms 348 KB answer = YES
11 Correct 0 ms 348 KB answer = YES
12 Correct 0 ms 348 KB answer = NO
13 Correct 0 ms 348 KB answer = YES
14 Correct 1 ms 348 KB answer = YES
15 Correct 1 ms 348 KB answer = YES
16 Correct 0 ms 348 KB answer = YES
17 Correct 0 ms 344 KB answer = YES
18 Correct 1 ms 344 KB answer = YES
19 Correct 1 ms 348 KB answer = YES
20 Correct 0 ms 348 KB answer = YES
21 Correct 0 ms 348 KB answer = YES
22 Correct 0 ms 348 KB answer = NO
23 Correct 0 ms 348 KB answer = NO
24 Correct 1 ms 348 KB answer = YES
25 Correct 1 ms 600 KB answer = YES
26 Correct 0 ms 344 KB answer = YES
27 Correct 0 ms 388 KB answer = YES
28 Correct 1 ms 348 KB answer = YES
29 Correct 0 ms 348 KB answer = YES
30 Correct 0 ms 348 KB answer = NO
31 Correct 1 ms 348 KB answer = YES
32 Correct 0 ms 460 KB answer = YES
33 Correct 0 ms 348 KB answer = YES
34 Correct 0 ms 344 KB answer = YES
35 Correct 0 ms 348 KB answer = YES
36 Correct 0 ms 344 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB answer = YES
2 Correct 0 ms 460 KB answer = YES
3 Correct 1 ms 348 KB answer = YES
4 Correct 0 ms 348 KB answer = NO
5 Correct 0 ms 348 KB answer = YES
6 Correct 0 ms 348 KB answer = YES
7 Correct 0 ms 348 KB answer = YES
8 Correct 1 ms 456 KB answer = YES
9 Correct 0 ms 460 KB answer = NO
10 Correct 0 ms 348 KB answer = YES
11 Correct 0 ms 348 KB answer = YES
12 Correct 0 ms 348 KB answer = NO
13 Correct 0 ms 348 KB answer = YES
14 Correct 1 ms 348 KB answer = YES
15 Correct 1 ms 348 KB answer = YES
16 Correct 0 ms 348 KB answer = YES
17 Correct 0 ms 344 KB answer = YES
18 Correct 1 ms 344 KB answer = YES
19 Correct 1 ms 348 KB answer = YES
20 Correct 0 ms 348 KB answer = YES
21 Correct 0 ms 348 KB answer = YES
22 Correct 0 ms 348 KB answer = NO
23 Correct 0 ms 348 KB answer = NO
24 Correct 1 ms 348 KB answer = YES
25 Correct 1 ms 600 KB answer = YES
26 Correct 0 ms 344 KB answer = YES
27 Correct 0 ms 388 KB answer = YES
28 Correct 1 ms 348 KB answer = YES
29 Correct 0 ms 348 KB answer = YES
30 Correct 0 ms 348 KB answer = NO
31 Correct 1 ms 348 KB answer = YES
32 Correct 0 ms 460 KB answer = YES
33 Correct 0 ms 348 KB answer = YES
34 Correct 0 ms 344 KB answer = YES
35 Correct 0 ms 348 KB answer = YES
36 Correct 0 ms 344 KB answer = YES
37 Correct 1 ms 348 KB answer = YES
38 Correct 1 ms 600 KB answer = YES
39 Correct 1 ms 344 KB answer = YES
40 Correct 1 ms 604 KB answer = YES
41 Correct 1 ms 604 KB answer = NO
42 Correct 1 ms 604 KB answer = YES
43 Correct 1 ms 604 KB answer = YES
44 Correct 1 ms 348 KB answer = YES
45 Correct 1 ms 604 KB answer = YES
46 Correct 1 ms 344 KB answer = YES
47 Correct 1 ms 604 KB answer = YES
48 Correct 1 ms 604 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB answer = YES
2 Correct 0 ms 460 KB answer = YES
3 Correct 1 ms 348 KB answer = YES
4 Correct 0 ms 348 KB answer = NO
5 Correct 0 ms 348 KB answer = YES
6 Correct 0 ms 348 KB answer = YES
7 Correct 0 ms 348 KB answer = YES
8 Correct 1 ms 456 KB answer = YES
9 Correct 0 ms 460 KB answer = NO
10 Correct 0 ms 348 KB answer = YES
11 Correct 0 ms 348 KB answer = YES
12 Correct 0 ms 348 KB answer = NO
13 Correct 0 ms 348 KB answer = YES
14 Correct 1 ms 348 KB answer = YES
15 Correct 1 ms 348 KB answer = YES
16 Correct 0 ms 348 KB answer = YES
17 Correct 0 ms 344 KB answer = YES
18 Correct 1 ms 344 KB answer = YES
19 Correct 1 ms 348 KB answer = YES
20 Correct 0 ms 348 KB answer = YES
21 Correct 0 ms 348 KB answer = YES
22 Correct 0 ms 348 KB answer = NO
23 Correct 0 ms 348 KB answer = NO
24 Correct 1 ms 348 KB answer = YES
25 Correct 1 ms 600 KB answer = YES
26 Correct 0 ms 344 KB answer = YES
27 Correct 0 ms 388 KB answer = YES
28 Correct 1 ms 348 KB answer = YES
29 Correct 0 ms 348 KB answer = YES
30 Correct 0 ms 348 KB answer = NO
31 Correct 1 ms 348 KB answer = YES
32 Correct 0 ms 460 KB answer = YES
33 Correct 0 ms 348 KB answer = YES
34 Correct 0 ms 344 KB answer = YES
35 Correct 0 ms 348 KB answer = YES
36 Correct 0 ms 344 KB answer = YES
37 Correct 1 ms 348 KB answer = YES
38 Correct 1 ms 600 KB answer = YES
39 Correct 1 ms 344 KB answer = YES
40 Correct 1 ms 604 KB answer = YES
41 Correct 1 ms 604 KB answer = NO
42 Correct 1 ms 604 KB answer = YES
43 Correct 1 ms 604 KB answer = YES
44 Correct 1 ms 348 KB answer = YES
45 Correct 1 ms 604 KB answer = YES
46 Correct 1 ms 344 KB answer = YES
47 Correct 1 ms 604 KB answer = YES
48 Correct 1 ms 604 KB answer = YES
49 Correct 7 ms 2456 KB answer = YES
50 Correct 7 ms 2444 KB answer = YES
51 Correct 7 ms 2956 KB answer = YES
52 Correct 3 ms 2640 KB answer = NO
53 Correct 1 ms 604 KB answer = YES
54 Correct 2 ms 860 KB answer = YES
55 Correct 4 ms 1372 KB answer = YES
56 Correct 7 ms 2448 KB answer = YES
57 Correct 7 ms 1580 KB answer = YES
58 Correct 6 ms 1924 KB answer = YES
59 Correct 6 ms 1604 KB answer = YES
60 Correct 7 ms 2140 KB answer = YES
61 Correct 3 ms 1116 KB answer = YES
62 Correct 52 ms 17864 KB answer = NO
63 Correct 48 ms 18116 KB answer = YES
64 Correct 46 ms 17604 KB answer = NO
65 Correct 51 ms 17600 KB answer = YES
66 Correct 2 ms 852 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB answer = YES
2 Correct 0 ms 460 KB answer = YES
3 Correct 1 ms 348 KB answer = YES
4 Correct 0 ms 348 KB answer = NO
5 Correct 0 ms 348 KB answer = YES
6 Correct 0 ms 348 KB answer = YES
7 Correct 0 ms 348 KB answer = YES
8 Correct 1 ms 456 KB answer = YES
9 Correct 0 ms 460 KB answer = NO
10 Correct 0 ms 348 KB answer = YES
11 Correct 0 ms 348 KB answer = YES
12 Correct 0 ms 348 KB answer = NO
13 Correct 0 ms 348 KB answer = YES
14 Correct 1 ms 348 KB answer = YES
15 Correct 1 ms 348 KB answer = YES
16 Correct 0 ms 348 KB answer = YES
17 Correct 0 ms 344 KB answer = YES
18 Correct 1 ms 344 KB answer = YES
19 Correct 1 ms 348 KB answer = YES
20 Correct 0 ms 348 KB answer = YES
21 Correct 0 ms 348 KB answer = YES
22 Correct 0 ms 348 KB answer = NO
23 Correct 0 ms 348 KB answer = NO
24 Correct 1 ms 348 KB answer = YES
25 Correct 1 ms 600 KB answer = YES
26 Correct 0 ms 344 KB answer = YES
27 Correct 0 ms 388 KB answer = YES
28 Correct 1 ms 348 KB answer = YES
29 Correct 0 ms 348 KB answer = YES
30 Correct 0 ms 348 KB answer = NO
31 Correct 1 ms 348 KB answer = YES
32 Correct 0 ms 460 KB answer = YES
33 Correct 0 ms 348 KB answer = YES
34 Correct 0 ms 344 KB answer = YES
35 Correct 0 ms 348 KB answer = YES
36 Correct 0 ms 344 KB answer = YES
37 Correct 1 ms 348 KB answer = YES
38 Correct 1 ms 600 KB answer = YES
39 Correct 1 ms 344 KB answer = YES
40 Correct 1 ms 604 KB answer = YES
41 Correct 1 ms 604 KB answer = NO
42 Correct 1 ms 604 KB answer = YES
43 Correct 1 ms 604 KB answer = YES
44 Correct 1 ms 348 KB answer = YES
45 Correct 1 ms 604 KB answer = YES
46 Correct 1 ms 344 KB answer = YES
47 Correct 1 ms 604 KB answer = YES
48 Correct 1 ms 604 KB answer = YES
49 Correct 7 ms 2456 KB answer = YES
50 Correct 7 ms 2444 KB answer = YES
51 Correct 7 ms 2956 KB answer = YES
52 Correct 3 ms 2640 KB answer = NO
53 Correct 1 ms 604 KB answer = YES
54 Correct 2 ms 860 KB answer = YES
55 Correct 4 ms 1372 KB answer = YES
56 Correct 7 ms 2448 KB answer = YES
57 Correct 7 ms 1580 KB answer = YES
58 Correct 6 ms 1924 KB answer = YES
59 Correct 6 ms 1604 KB answer = YES
60 Correct 7 ms 2140 KB answer = YES
61 Correct 3 ms 1116 KB answer = YES
62 Correct 52 ms 17864 KB answer = NO
63 Correct 48 ms 18116 KB answer = YES
64 Correct 46 ms 17604 KB answer = NO
65 Correct 51 ms 17600 KB answer = YES
66 Correct 2 ms 852 KB answer = YES
67 Correct 78 ms 31988 KB answer = YES
68 Correct 70 ms 32260 KB answer = YES
69 Correct 64 ms 25860 KB answer = YES
70 Correct 102 ms 37204 KB answer = YES
71 Correct 67 ms 25868 KB answer = YES
72 Correct 74 ms 20228 KB answer = YES
73 Correct 65 ms 16136 KB answer = YES
74 Correct 56 ms 15376 KB answer = YES
75 Correct 33 ms 15112 KB answer = NO
76 Correct 8 ms 2712 KB answer = YES
77 Correct 17 ms 5136 KB answer = YES
78 Correct 30 ms 8976 KB answer = YES
79 Correct 69 ms 17504 KB answer = YES
80 Correct 52 ms 19236 KB answer = YES
81 Correct 39 ms 21528 KB answer = NO
82 Correct 99 ms 25516 KB answer = YES
83 Correct 92 ms 25864 KB answer = YES
84 Correct 89 ms 32544 KB answer = YES
85 Correct 76 ms 32256 KB answer = YES
86 Correct 69 ms 26116 KB answer = YES
87 Correct 32 ms 14520 KB answer = NO
88 Correct 81 ms 17156 KB answer = YES
89 Correct 64 ms 9988 KB answer = YES
90 Correct 73 ms 10008 KB answer = YES
91 Correct 65 ms 9824 KB answer = YES
92 Correct 31 ms 7444 KB answer = YES
93 Correct 31 ms 7444 KB answer = YES
94 Correct 46 ms 26372 KB answer = NO
95 Correct 32 ms 9592 KB answer = NO
96 Correct 116 ms 31888 KB answer = YES
97 Correct 34 ms 26088 KB answer = NO