oj.uz

답안 #525878

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
525878 2022-02-13T05:35:44 Z koioi.org-koosaga Mountains and Valleys (CCO20_day1problem3) C++17
3 / 25
 108 ms 37836 KB 
#include <bits/stdc++.h>
#define sz(v) ((int)(v).size())
#define all(v) (v).begin(), (v).end()
using namespace std;
typedef long long lint;
typedef pair<lint, lint> pi;
const int MAXN = 500005;

struct edge{
	int s, e, x;
};

int n, m;
vector<int> gph[MAXN];
int par[20][MAXN], dep[MAXN];

int lca(int x, int y){
	if(dep[x] > dep[y]) swap(x, y);
	int dx = dep[y] - dep[x];
	for(int i = 0; dx; i++){
		if(dx & 1) y = par[i][y];
		dx >>= 1;
	}
	for(int i = 19; i >= 0; i--){
		if(par[i][x] != par[i][y]){
			x = par[i][x];
			y = par[i][y];
		}
	}
	if(x != y) return par[0][x];
	return x;
}

struct node{
	int lmax, rmax, opt, len;
	node():
	lmax(-1e9), rmax(-1e9), opt(-1e9), len(0) {}
	node(int x):
	lmax(x), rmax(x), opt(-1e9), len(1) {}

	node(int a, int b, int c, int e):
	lmax(a), rmax(b), opt(c), len(e) {}

	node reverse(){
		return node(rmax, lmax, opt, len);
	}
	node operator+(const node &n)const{
		return node(
			max(lmax - n.len, n.lmax),
			max(rmax, n.rmax - len),
			max({opt, n.opt, lmax + n.rmax - 1}),
			len + n.len);
	};
};

vector<int> ord;
int din[MAXN], dout[MAXN], piv;
int far[MAXN], diam[MAXN], pfar[MAXN], pdiam[MAXN];
int f[20][MAXN], g[MAXN];
vector<pi> fars[MAXN];
vector<pi> subDiams[MAXN];

int fPathMax(int x, int v){
	int ans = -1e9;
	for(int i = 0; v; i++){
		if(v & 1){
			ans = max(ans, f[i][x]);
			x = par[i][x];
		}
		v >>= 1;
	}
	return ans;
}

bool in(int u, int v){
	return din[u] <= din[v] && dout[v] <= dout[u];
}

void dfs(int x, int p = -1){
	ord.push_back(x);
	din[x] = ++piv;
	for(auto &y : gph[x]){
		if(y == p) continue;
		par[0][y] = x;
		dep[y] = dep[x] + 1;
		dfs(y, x);
	}
	dout[x] = piv;
}

bool vis[MAXN];

pi dfsl(int x, int p = -1){
	pi ret(0, x);
	for(auto &y : gph[x]){
		if(y == p || vis[y]) continue;
		auto ans = dfsl(y, x);
		ans.first++;
		ret = max(ret, ans);
	}
	return ret;
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin >> n >> m;
	vector<edge> qry;
	for(int i = 0; i < m; i++){
		int s, e, x; cin >> s >> e >> x;
		if(x == 1){
			gph[s].push_back(e);
			gph[e].push_back(s);
		}
		else{
			qry.push_back({s, e, x});
		}
	}
	dfs(0);
	for(int i = 1; i < 20; i++){
		for(int j = 0; j < n; j++){
			par[i][j] = par[i-1][par[i-1][j]];
		}
	}
	{
		reverse(all(ord));
		for(auto &i : ord){
			for(auto &j : gph[i]){
				if(j == par[0][i]) continue;
				far[i] = max(far[i], far[j] + 1);
				diam[i] = max({diam[i], diam[j], far[j] + 1});
				fars[i].emplace_back(far[j], j);
			}
			sort(all(fars[i]));
			reverse(all(fars[i]));
			if(sz(fars[i]) >= 2) diam[i] = max(diam[i], (int)fars[i][0].first + (int)fars[i][1].first + 2);
		}
		reverse(all(ord));
		for(auto &i : ord){
			if(i == 0) continue;
			for(auto &j : fars[par[0][i]]){
				if(j.second == i) continue;
				pfar[i] = j.first + 1;
				break;
			}
			fars[i].emplace_back(pfar[i], par[0][i]);
			sort(all(fars[i]));
			reverse(all(fars[i]));
		}	
		for(auto &i : ord){
			if(i == 0) continue;
			for(auto &[d, v] : subDiams[par[0][i]]){
				if(v == i) continue;
				pdiam[i] = max(pdiam[i], (int)d);
				break;
			}
			{
				int new_diam = 0;
				int cnt = 0;
				for(auto &[d, v] : fars[par[0][i]]){
					if(v == i) continue;
					new_diam += d + 1;
					cnt += 1;
					if(cnt == 2) break;
				}
				pdiam[i] = max(pdiam[i], new_diam);
			}
			for(auto &j : gph[i]){
				if(j == par[0][i]) subDiams[i].emplace_back(pdiam[i], j);
				else subDiams[i].emplace_back(diam[j], j);
			}
			sort(all(subDiams[i]));
			reverse(all(subDiams[i]));
		}
		for(int i = 0; i < n; i++){
			if(dep[i] >= 2){
				int cnt = 0;
				for(auto &[d, v] : fars[par[0][i]]){
					if(v == i || v == par[1][i]) continue;
					g[i] = max(g[i], (int)d + 1);
					f[0][i] += d + 1;
					cnt++;
					if(cnt == 2) break;
				}
				for(auto &[d, v] : subDiams[par[0][i]]){
					if(v == i || v == par[1][i]) continue;
					f[0][i] = max(f[0][i], (int)d + 1);
					break;
				}
			}
		}
		for(int i = 1; i < 20; i++){
			for(int j = 0; j < n; j++){
				f[i][j] = max(f[i-1][j], f[i-1][par[i-1][j]]);
			}
		}
	}
	int ans = 2 * n - 2 - diam[0];
	for(auto &x : qry){
		int l = lca(x.s, x.e);
		int plen = dep[x.s] + dep[x.e] - 2 * dep[l] + 1;
		int maxPath = -1e9;
		if(dep[x.s] >= dep[l] + 2){
			maxPath = max(maxPath, fPathMax(x.s, dep[x.s] - dep[l] - 1) - 3 + plen);
		}
		if(dep[x.e] >= dep[l] + 2){
			maxPath = max(maxPath, fPathMax(x.e, dep[x.e] - dep[l] - 1) - 3 + plen);
		}
		if(l != x.s){
			maxPath = max(maxPath, diam[x.s] - 3 + plen);
		}
		if(l != x.e){
			maxPath = max(maxPath, diam[x.e] - 3 + plen);
		}
		{
			int new_diam = 0;
			int cnt = 0;
			// passes through l
			for(auto &[d, v] : fars[l]){
				if((in(v, x.s) || in(v, x.e)) && v != par[0][l]) continue;
				new_diam += d + 1;
				cnt += 1;
				if(cnt == 2) break;
			}
			for(auto &[d, v] : subDiams[l]){
				if((in(v, x.s) || in(v, x.e)) && v != par[0][l]) continue;
				new_diam = max(new_diam, (int)d);
				break;
			}
			maxPath = max(maxPath, new_diam - 3 + plen);
		}
		// TODO: qn.
		node valup, valdown;
		if(x.s != l) valup = valup + node(far[x.s]);
		if(x.e != l) valdown = valdown + node(far[x.e]);
		for(int i = x.s; dep[i] >= dep[l] + 2; i = par[0][i]) valup = valup + node(g[i]);
		for(int i = x.e; dep[i] >= dep[l] + 2; i = par[0][i]) valdown = valdown + node(g[i]);
		{
			int dist = 0;
			for(auto &[d, v] : fars[l]){
				if((in(v, x.s) || in(v, x.e)) && v != par[0][l]) continue;
				dist = max(dist, (int)d + 1);
				break;
			}
			valup = valup + node(dist);
		}
		node val = valup + valdown.reverse();
		ans = min(ans, 2 * n - 4 + x.x - (val.opt + val.len - 1));
	}
	cout << ans << endl;
}

Subtask #1
1.0 / 1.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct

Subtask #2
0.0 / 2.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #3
2.0 / 2.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 37732 KB Output is correct
2 Correct 97 ms 37792 KB Output is correct
3 Correct 84 ms 37688 KB Output is correct
4 Correct 57 ms 37636 KB Output is correct
5 Correct 53 ms 37632 KB Output is correct
6 Correct 22 ms 37508 KB Output is correct
7 Correct 108 ms 37716 KB Output is correct
8 Correct 89 ms 37760 KB Output is correct
9 Correct 96 ms 37836 KB Output is correct
10 Correct 52 ms 37564 KB Output is correct
11 Correct 56 ms 37708 KB Output is correct
12 Correct 72 ms 37600 KB Output is correct
13 Correct 58 ms 37576 KB Output is correct
14 Correct 60 ms 37580 KB Output is correct

Subtask #4
0.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #5
0.0 / 2.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #6
0.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #7
0.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0.0 / 4.0

# 결과 실행 시간 메모리 Grader output
1 Correct 20 ms 35788 KB Output is correct
2 Correct 16 ms 35788 KB Output is correct
3 Correct 18 ms 35836 KB Output is correct
4 Correct 16 ms 35916 KB Output is correct
5 Correct 17 ms 35916 KB Output is correct
6 Correct 16 ms 35916 KB Output is correct
7 Correct 19 ms 35832 KB Output is correct
8 Correct 16 ms 35788 KB Output is correct
9 Correct 17 ms 35788 KB Output is correct
10 Correct 16 ms 35916 KB Output is correct
11 Correct 18 ms 35816 KB Output is correct
12 Correct 20 ms 35832 KB Output is correct
13 Correct 17 ms 35876 KB Output is correct
14 Correct 17 ms 35836 KB Output is correct
15 Correct 17 ms 35788 KB Output is correct
16 Correct 16 ms 35788 KB Output is correct
17 Correct 17 ms 35888 KB Output is correct
18 Incorrect 16 ms 35908 KB Output isn't correct
19 Halted 0 ms 0 KB -