oj.uz

Submission #534362

# Submission time Handle Problem Language Result Execution time Memory
534362 2022-03-08T06:04:55 Z amunduzbaev Paths (RMI21_paths) C++17
56 / 100
 600 ms 36596 KB 
#include "bits/stdc++.h"
using namespace std;

#define ar array
#define int long long
const int N = 1e5 + 5;
vector<ar<int, 2>> edges[N];
int n, k, par[N][20], d[N];
int tin[N], tout[N], t;

void dfs(int u, int p = -1){
	tin[u] = ++t;
	if(p == -1) par[u][0] = u;
	for(int i=1;i<20;i++) par[u][i] = par[par[u][i-1]][i-1];
	for(auto x : edges[u]){
		if(x[0] == p) continue;
		d[x[0]] = d[u] + x[1];
		par[x[0]][0] = u;
		dfs(x[0], u);
	} tout[u] = t;
}

bool is(int a, int b) { return (tin[a] <= tin[b] && tout[b] <= tout[a]); }
int lca(int a, int b){
	if(is(a, b)) return a;
	if(is(b, a)) return b;
	for(int j=19;~j;j--){
		if(!is(par[a][j], b)) a = par[a][j];
	} return par[a][0];
}

int dis(int a, int b){
	return d[a] + d[b] - d[lca(a, b)] * 2;
}

int a[N], dp[N], up[N];
int vdp[N], vup[N];
void Dp(int u){
	vdp[u] = u;
	for(auto x : edges[u]){
		if(x[0] == par[u][0]) continue;
		Dp(x[0]);
		if(dp[x[0]] + x[1] >= dp[u]){
			dp[u] = dp[x[0]] + x[1];
			vdp[u] = vdp[x[0]];
		}
	}
}

void redp(int u){
	int tt = up[u];
	int v = vup[u];
	for(auto x : edges[u]){
		if(x[0] == par[u][0]) continue;
		if(up[x[0]] <= tt + x[1]){
			up[x[0]] = tt + x[1];
			vup[x[0]] = v;
		}
		if(tt <= dp[x[0]] + x[1]){
			tt = dp[x[0]] + x[1];
			v = vdp[x[0]];
		}
	}
	
	reverse(edges[u].begin(), edges[u].end());
	tt = 0;
	v = u;
	for(auto x : edges[u]){
		if(x[0] == par[u][0]) continue;
		if(up[x[0]] <= tt + x[1]){
			up[x[0]] = tt + x[1];
			vup[x[0]] = v;
		}
		if(tt <= dp[x[0]] + x[1]){
			tt = dp[x[0]] + x[1];
			v = vdp[x[0]];
		}
		
		redp(x[0]);
	}
}

/*

34
34
35
39
37
39
34
38
39
38
39

28
28
28
32
30
32
28
32
32
29
30

*/

signed main(){
	ios::sync_with_stdio(0); cin.tie(0);
	
	cin>>n>>k;
	for(int i=1;i<n;i++){
		int a, b, c; cin>>a>>b>>c;
		edges[a].push_back({b, c});
		edges[b].push_back({a, c});
	}
	
	if(n <= 2){
		int res = (n == 2 ? edges[1].back()[1] : 0);
		for(int i=1;i<=n;i++) cout<<res<<"\n";
		return 0;
	}
	
	int rot = -1;
	for(int i=1;i<=n;i++){
		if((int)edges[i].size() > 1){
			rot = i;
			break; 
		}
	}
	
	assert(~rot);
	dfs(rot);
	Dp(rot);
	vup[rot] = rot;
	redp(rot);
	
	multiset<ar<int, 2>> tot, god;
	int sum = 0;
	auto upd = [&](int u, int p){
		int v = dis(a[u], u);
		if(god.count({v, u})){
			god.erase({v, u});
			sum -= v;
			if(!tot.empty()){
				god.insert(*tot.rbegin()), 
				sum += (*tot.rbegin())[0];
				tot.erase(--tot.end());
			}
		} tot.erase({v, u});
		
		a[u] = p, v = dis(p, u);
		god.insert({v, u});
		sum += v;
		if((int)god.size() > k){
			tot.insert(*god.begin());
			sum -= (*god.begin())[0];
			god.erase(god.begin());
		}
	};
	
	for(int i=1;i<=n;i++){
		if((int)edges[i].size() > 1) continue;
		int x = i; a[i] = i;
		for(int j=19;~j;j--){
			if(vdp[par[x][j]] == i) x = par[x][j];
		}
		
		x = par[x][0];
		//~ cout<<i<<" "<<lca(x, i)<<" "<<d[i]<<" "<<dis(x, i)<<"\n";
		upd(i, x);
	}
	
	vector<int> res(n + 1);
	function<void(int)> dfs = [&](int u){
		res[u] = sum;
		for(auto x : edges[u]){
			if(x[0] == par[u][0]) continue;
			assert(a[vdp[x[0]]] == u);
			assert(a[vup[x[0]]] == u);
			upd(vdp[x[0]], x[0]);
			upd(vup[x[0]], x[0]);
			dfs(x[0]);
			upd(vdp[x[0]], u);
			upd(vup[x[0]], u);
		}
	};
	
	dfs(rot);
	for(int i=1;i<=n;i++) cout<<res[i]<<"\n";
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2764 KB Output is correct
5 Correct 4 ms 2764 KB Output is correct
6 Correct 2 ms 2764 KB Output is correct
7 Correct 2 ms 2764 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2764 KB Output is correct
5 Correct 4 ms 2764 KB Output is correct
6 Correct 2 ms 2764 KB Output is correct
7 Correct 2 ms 2764 KB Output is correct
8 Correct 4 ms 3032 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 4 ms 3020 KB Output is correct
11 Correct 5 ms 3020 KB Output is correct
12 Correct 6 ms 3028 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2764 KB Output is correct
5 Correct 4 ms 2764 KB Output is correct
6 Correct 2 ms 2764 KB Output is correct
7 Correct 2 ms 2764 KB Output is correct
8 Correct 4 ms 3032 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 4 ms 3020 KB Output is correct
11 Correct 5 ms 3020 KB Output is correct
12 Correct 6 ms 3028 KB Output is correct
13 Correct 10 ms 3332 KB Output is correct
14 Correct 8 ms 3404 KB Output is correct
15 Correct 7 ms 3228 KB Output is correct
16 Correct 8 ms 3276 KB Output is correct
17 Correct 7 ms 3276 KB Output is correct
18 Correct 8 ms 3148 KB Output is correct
19 Correct 11 ms 3352 KB Output is correct

Subtask #5
0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 543 ms 34728 KB Output is correct
2 Execution timed out 615 ms 36596 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #6
0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2764 KB Output is correct
5 Correct 4 ms 2764 KB Output is correct
6 Correct 2 ms 2764 KB Output is correct
7 Correct 2 ms 2764 KB Output is correct
8 Correct 4 ms 3032 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 4 ms 3020 KB Output is correct
11 Correct 5 ms 3020 KB Output is correct
12 Correct 6 ms 3028 KB Output is correct
13 Correct 10 ms 3332 KB Output is correct
14 Correct 8 ms 3404 KB Output is correct
15 Correct 7 ms 3228 KB Output is correct
16 Correct 8 ms 3276 KB Output is correct
17 Correct 7 ms 3276 KB Output is correct
18 Correct 8 ms 3148 KB Output is correct
19 Correct 11 ms 3352 KB Output is correct
20 Correct 543 ms 34728 KB Output is correct
21 Execution timed out 615 ms 36596 KB Time limit exceeded
22 Halted 0 ms 0 KB -