oj.uz

Submission #786440

# Submission time Handle Problem Language Result Execution time Memory
786440 2023-07-18T07:48:20 Z 박상훈(#10027) Paths (RMI21_paths) C++17
56 / 100
 600 ms 14080 KB 
#include <bits/stdc++.h>
#define int long long

using namespace std;
typedef long long ll;
// constexpr int INF1 = 1e9 + 100;
constexpr ll INF2 = 4e18;

struct Node{
	int x, p;
	ll d;
	Node(){}
	Node(int _x, int _p, ll _d): x(_x), p(_p), d(_d) {}

	bool operator < (const Node &N) const{
		if (d==N.d) return p < N.p;
		return d < N.d;
	}
};

int n, k;
vector<pair<int, ll>> adj[100100];
ll dp1[100100], dp2[100100], D[100100], dist[100100];
int dp1_idx[100100], par[100100], T[100100];

int valP[100100], col[100100], on[100100], onS[100100];
ll ret1, ret2, onD[100100];
ll ans[100100];

void dfs1(int s, int pa = 0, ll paW = 0, int paT = 0){
	dist[s] = paW;
	dp1[s] = 0;
	dp1_idx[s] = s;

	par[s] = pa;
	T[s] = paT;

	for (auto &[v, w]:adj[s]) if (v!=pa){
		dfs1(v, s, paW + w, (paT?paT:v));

		if (dp1[s] < dp1[v] + w){
			dp1[s] = dp1[v] + w;
			dp1_idx[s] = dp1_idx[v];
		}
	}
}

void dfs2(int s, int pa = 0){
	vector<pair<ll, int>> C;
	D[s] = max(dp1[s], dp2[s]);
	
	if (pa) C.emplace_back(dp2[s], s);
	for (auto &[v, w]:adj[s]) if (v!=pa){
		C.emplace_back(dp1[v] + w, v);
	}

	if (!C.empty()) swap(C[0], *max_element(C.begin(), C.end()));
	if (C.size() > 1) swap(C[1], *max_element(C.begin()+1, C.end()));
	for (auto &[v, w]:adj[s]) if (v!=pa){
		if (C[0].second!=v) dp2[v] = C[0].first + w;
		else if (C.size()==1) dp2[v] = w;
		else dp2[v] = C[1].first + w;

		dfs2(v, s);
	}
}

void run(int root, vector<int> P){ // should call dfs1(root) first
	ret1 = 0;
	ret2 = 0;

	fill(valP+1, valP+n+1, 0);
	fill(col+1, col+n+1, 0);
	fill(on+1, on+n+1, 0);
	for (int i=0;i<(int)P.size();i++) valP[P[i]] = (int)P.size() - i;
	
	priority_queue<Node> pq;
	pq.emplace(dp1_idx[root], valP[dp1_idx[root]], dist[dp1_idx[root]]);

	for (int z=1;z<=k;z++) if (!pq.empty()){
		auto [x, _, d] = pq.top(); pq.pop();
		on[x] = 1;
		if (z <= (int)P.size()) assert(_ == (int)P.size() - z + 1);

		ret1 += d;
		while(true){
			for (auto &[y, w]:adj[x]) if (y!=par[x] && !col[y]){
				int z = dp1_idx[y];
				// printf("ok push %lld %lld\n", z, dist[z] - dist[x]);
				pq.emplace(z, valP[z], dist[z] - dist[x]);
			}

			col[x] = 1;

			if (par[x] && !col[par[x]]){
				x = par[x];
			}

			else break;
		}
	}

	if (!pq.empty()) ret2 = pq.top().d;
}

void dfs3(int s, int pa = 0){
	onS[s] = on[s];
	if (on[s]) onD[s] = 0;
	else onD[s] = INF2;

	for (auto &[v, w]:adj[s]) if (v!=pa){
		dfs3(v, s);
		onS[s] += onS[v];
		onD[s] = min(onD[s], onD[v] + w);
	}
}

void get_optimal(int root){
	dfs1(root);

	vector<pair<ll, int>> C;
	for (auto &[v, w]:adj[root]) C.emplace_back(dp1[v]+w, v);
	assert(C.size() > 1);

	swap(C[0], *max_element(C.begin(), C.end()));
	swap(C[1], *max_element(C.begin()+1, C.end()));

	vector<int> V(2);
	for (int i=1;i<=n;i++) if (i!=root){
		if (dist[i]==C[0].first && T[i]==C[0].second) V[0] = i;
		if (dist[i]==C[1].first && T[i]==C[1].second) V[1] = i;
	}

	assert(V[0] && V[1]);
	run(root, V);
	dfs3(root);
}

void dfs4(int s, ll val, int pa = 0, int flag = 0){
	ans[s] = val;

	for (auto &[v, w]:adj[s]) if (v!=pa){
		if (!col[v] || flag){
			dfs4(v, val+w, s, flag);
		}

		else if (onS[v]==1 && val-onD[v]+ret2 > val){
			dfs4(v, val-onD[v]+ret2, s, 1);
		}

		else{
			dfs4(v, val, s, 0);
		}
	}
}

void naive(){
	for (int i=1;i<=n;i++){
		dfs1(i);
		run(i, vector<int>());

		printf("%lld\n", ret1);
	}
}

signed main(){
	scanf("%lld %lld", &n, &k);

	for (int i=1;i<=n-1;i++){
		int x, y, z;
		scanf("%lld %lld %lld", &x, &y, &z);
		adj[x].emplace_back(y, z);
		adj[y].emplace_back(x, z);
	}

	naive();
	return 0;

	dfs1(1);
	dfs2(1);

	if (k==1){
		for (int i=1;i<=n;i++){
			printf("%lld\n", D[i]);
		}
		return 0;
	}

	if (n==2){
		for (int i=1;i<=n;i++) printf("%lld\n", adj[1][0].second);
		return 0;
	}

	int root = -1;
	ll valD = INF2;

	for (int i=1;i<=n;i++) if (D[i] < valD && adj[i].size() > 1){
		valD = D[i];
		root = i;
	}

	assert(root!=-1);
	get_optimal(root);
	dfs4(root, ret1);

	for (int i=1;i<=n;i++){
		printf("%lld\n", ans[i]);
	}
}

Compilation message

Main.cpp: In function 'int main()':
Main.cpp:167:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  167 |  scanf("%lld %lld", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~~~~~~
Main.cpp:171:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  171 |   scanf("%lld %lld %lld", &x, &y, &z);
      |   ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 3 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 3 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 30 ms 2856 KB Output is correct
9 Correct 25 ms 2900 KB Output is correct
10 Correct 21 ms 2772 KB Output is correct
11 Correct 25 ms 2880 KB Output is correct
12 Correct 20 ms 2856 KB Output is correct

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 3 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 30 ms 2856 KB Output is correct
9 Correct 25 ms 2900 KB Output is correct
10 Correct 21 ms 2772 KB Output is correct
11 Correct 25 ms 2880 KB Output is correct
12 Correct 20 ms 2856 KB Output is correct
13 Correct 219 ms 2992 KB Output is correct
14 Correct 150 ms 3076 KB Output is correct
15 Correct 81 ms 3000 KB Output is correct
16 Correct 162 ms 2988 KB Output is correct
17 Correct 154 ms 2984 KB Output is correct
18 Correct 84 ms 2964 KB Output is correct
19 Correct 228 ms 3000 KB Output is correct

Subtask #5
0 / 12.0

# Verdict Execution time Memory Grader output
1 Execution timed out 1068 ms 14080 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #6
0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 3 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 30 ms 2856 KB Output is correct
9 Correct 25 ms 2900 KB Output is correct
10 Correct 21 ms 2772 KB Output is correct
11 Correct 25 ms 2880 KB Output is correct
12 Correct 20 ms 2856 KB Output is correct
13 Correct 219 ms 2992 KB Output is correct
14 Correct 150 ms 3076 KB Output is correct
15 Correct 81 ms 3000 KB Output is correct
16 Correct 162 ms 2988 KB Output is correct
17 Correct 154 ms 2984 KB Output is correct
18 Correct 84 ms 2964 KB Output is correct
19 Correct 228 ms 3000 KB Output is correct
20 Execution timed out 1068 ms 14080 KB Time limit exceeded
21 Halted 0 ms 0 KB -