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Submission #534351

# Submission time Handle Problem Language Result Execution time Memory
534351 2022-03-08T05:58:48 Z amunduzbaev Paths (RMI21_paths) C++17
68 / 100
 532 ms 38976 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
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34
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39

28
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32
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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; 
		}
	}
	
	//~ cout<<rot<<endl;
	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;
			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 2 ms 2636 KB Output is correct
2 Correct 3 ms 2660 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 3 ms 2660 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 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 2 ms 2636 KB Output is correct
2 Correct 3 ms 2660 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 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 6 ms 3020 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 6 ms 2936 KB Output is correct
11 Correct 4 ms 3040 KB Output is correct
12 Correct 4 ms 3020 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 3 ms 2660 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 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 6 ms 3020 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 6 ms 2936 KB Output is correct
11 Correct 4 ms 3040 KB Output is correct
12 Correct 4 ms 3020 KB Output is correct
13 Correct 7 ms 3268 KB Output is correct
14 Correct 6 ms 3404 KB Output is correct
15 Correct 6 ms 3276 KB Output is correct
16 Correct 7 ms 3316 KB Output is correct
17 Correct 7 ms 3276 KB Output is correct
18 Correct 6 ms 3276 KB Output is correct
19 Correct 8 ms 3404 KB Output is correct

Subtask #5
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 412 ms 34728 KB Output is correct
2 Correct 459 ms 38708 KB Output is correct
3 Correct 311 ms 34160 KB Output is correct
4 Correct 386 ms 36800 KB Output is correct
5 Correct 464 ms 37688 KB Output is correct
6 Correct 388 ms 36948 KB Output is correct

Subtask #6
0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 3 ms 2660 KB Output is correct
3 Correct 2 ms 2764 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 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 6 ms 3020 KB Output is correct
9 Correct 6 ms 3020 KB Output is correct
10 Correct 6 ms 2936 KB Output is correct
11 Correct 4 ms 3040 KB Output is correct
12 Correct 4 ms 3020 KB Output is correct
13 Correct 7 ms 3268 KB Output is correct
14 Correct 6 ms 3404 KB Output is correct
15 Correct 6 ms 3276 KB Output is correct
16 Correct 7 ms 3316 KB Output is correct
17 Correct 7 ms 3276 KB Output is correct
18 Correct 6 ms 3276 KB Output is correct
19 Correct 8 ms 3404 KB Output is correct
20 Correct 412 ms 34728 KB Output is correct
21 Correct 459 ms 38708 KB Output is correct
22 Correct 311 ms 34160 KB Output is correct
23 Correct 386 ms 36800 KB Output is correct
24 Correct 464 ms 37688 KB Output is correct
25 Correct 388 ms 36948 KB Output is correct
26 Correct 502 ms 37200 KB Output is correct
27 Correct 499 ms 38680 KB Output is correct
28 Correct 532 ms 38976 KB Output is correct
29 Correct 337 ms 34328 KB Output is correct
30 Incorrect 482 ms 37260 KB Output isn't correct
31 Halted 0 ms 0 KB -