oj.uz

Submission #534372

# Submission time Handle Problem Language Result Execution time Memory
534372 2022-03-08T06:10:23 Z amunduzbaev Paths (RMI21_paths) C++17
100 / 100
 453 ms 27452 KB 
#include "bits/stdc++.h"
using namespace std;

#define ar array
typedef long long i64;
const int N = 1e5 + 5;
vector<ar<int, 2>> edges[N];
int n, k, par[N][20];
int tin[N], tout[N], t;
i64 d[N];

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];
}

i64 dis(int a, int b){
	return d[a] + d[b] - d[lca(a, b)] * 2;
}

int a[N], vdp[N], vup[N];
i64 dp[N], up[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){
	i64 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]);
	}
}

/*

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*/

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<pair<i64, int>> tot, god;
	i64 sum = 0;
	auto upd = [&](int u, int p){
		long long 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()).first;
				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()).first;
			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];
		upd(i, x);
	}
	
	vector<i64> 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 2 ms 2636 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 2 ms 2636 KB Output is correct
3 Correct 3 ms 2764 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2684 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 2 ms 2636 KB Output is correct
3 Correct 3 ms 2764 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2684 KB Output is correct
8 Correct 4 ms 2892 KB Output is correct
9 Correct 4 ms 2892 KB Output is correct
10 Correct 5 ms 2872 KB Output is correct
11 Correct 3 ms 2892 KB Output is correct
12 Correct 4 ms 2892 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 2 ms 2636 KB Output is correct
3 Correct 3 ms 2764 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2684 KB Output is correct
8 Correct 4 ms 2892 KB Output is correct
9 Correct 4 ms 2892 KB Output is correct
10 Correct 5 ms 2872 KB Output is correct
11 Correct 3 ms 2892 KB Output is correct
12 Correct 4 ms 2892 KB Output is correct
13 Correct 9 ms 3104 KB Output is correct
14 Correct 6 ms 3148 KB Output is correct
15 Correct 6 ms 3064 KB Output is correct
16 Correct 6 ms 3148 KB Output is correct
17 Correct 5 ms 3020 KB Output is correct
18 Correct 5 ms 3020 KB Output is correct
19 Correct 6 ms 3020 KB Output is correct

Subtask #5
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 383 ms 23652 KB Output is correct
2 Correct 395 ms 25292 KB Output is correct
3 Correct 306 ms 20632 KB Output is correct
4 Correct 336 ms 23712 KB Output is correct
5 Correct 387 ms 24512 KB Output is correct
6 Correct 350 ms 23804 KB Output is correct

Subtask #6
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 3 ms 2764 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2684 KB Output is correct
8 Correct 4 ms 2892 KB Output is correct
9 Correct 4 ms 2892 KB Output is correct
10 Correct 5 ms 2872 KB Output is correct
11 Correct 3 ms 2892 KB Output is correct
12 Correct 4 ms 2892 KB Output is correct
13 Correct 9 ms 3104 KB Output is correct
14 Correct 6 ms 3148 KB Output is correct
15 Correct 6 ms 3064 KB Output is correct
16 Correct 6 ms 3148 KB Output is correct
17 Correct 5 ms 3020 KB Output is correct
18 Correct 5 ms 3020 KB Output is correct
19 Correct 6 ms 3020 KB Output is correct
20 Correct 383 ms 23652 KB Output is correct
21 Correct 395 ms 25292 KB Output is correct
22 Correct 306 ms 20632 KB Output is correct
23 Correct 336 ms 23712 KB Output is correct
24 Correct 387 ms 24512 KB Output is correct
25 Correct 350 ms 23804 KB Output is correct
26 Correct 449 ms 23948 KB Output is correct
27 Correct 409 ms 25360 KB Output is correct
28 Correct 428 ms 25720 KB Output is correct
29 Correct 298 ms 20912 KB Output is correct
30 Correct 379 ms 24040 KB Output is correct
31 Correct 388 ms 22532 KB Output is correct
32 Correct 453 ms 24984 KB Output is correct
33 Correct 404 ms 26040 KB Output is correct
34 Correct 254 ms 22408 KB Output is correct
35 Correct 381 ms 26172 KB Output is correct
36 Correct 398 ms 27452 KB Output is correct