oj.uz

Submission #786443

# Submission time Handle Problem Language Result Execution time Memory
786443 2023-07-18T07:49:52 Z 박상훈(#10027) Paths (RMI21_paths) C++17
100 / 100
 130 ms 24644 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){ // 점이 없음
			dfs4(v, val+w, s, flag);
		}

		else if (onS[v]==1 && val-onD[v]+ret2 > val){ // 옮기는게 이득
			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 1 ms 2644 KB Output is correct
4 Correct 1 ms 2772 KB Output is correct
5 Correct 1 ms 2772 KB Output is correct
6 Correct 1 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 1 ms 2644 KB Output is correct
4 Correct 1 ms 2772 KB Output is correct
5 Correct 1 ms 2772 KB Output is correct
6 Correct 1 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 2 ms 2900 KB Output is correct
9 Correct 2 ms 2900 KB Output is correct
10 Correct 3 ms 2820 KB Output is correct
11 Correct 2 ms 2900 KB Output is correct
12 Correct 2 ms 2900 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 1 ms 2644 KB Output is correct
4 Correct 1 ms 2772 KB Output is correct
5 Correct 1 ms 2772 KB Output is correct
6 Correct 1 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 2 ms 2900 KB Output is correct
9 Correct 2 ms 2900 KB Output is correct
10 Correct 3 ms 2820 KB Output is correct
11 Correct 2 ms 2900 KB Output is correct
12 Correct 2 ms 2900 KB Output is correct
13 Correct 3 ms 3028 KB Output is correct
14 Correct 3 ms 3228 KB Output is correct
15 Correct 3 ms 3028 KB Output is correct
16 Correct 3 ms 3028 KB Output is correct
17 Correct 3 ms 3028 KB Output is correct
18 Correct 2 ms 3028 KB Output is correct
19 Correct 3 ms 3028 KB Output is correct

Subtask #5
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 58 ms 14384 KB Output is correct
2 Correct 88 ms 18504 KB Output is correct
3 Correct 60 ms 14176 KB Output is correct
4 Correct 74 ms 14456 KB Output is correct
5 Correct 75 ms 16036 KB Output is correct
6 Correct 55 ms 14240 KB Output is correct

Subtask #6
32.0 / 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 1 ms 2644 KB Output is correct
4 Correct 1 ms 2772 KB Output is correct
5 Correct 1 ms 2772 KB Output is correct
6 Correct 1 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 2 ms 2900 KB Output is correct
9 Correct 2 ms 2900 KB Output is correct
10 Correct 3 ms 2820 KB Output is correct
11 Correct 2 ms 2900 KB Output is correct
12 Correct 2 ms 2900 KB Output is correct
13 Correct 3 ms 3028 KB Output is correct
14 Correct 3 ms 3228 KB Output is correct
15 Correct 3 ms 3028 KB Output is correct
16 Correct 3 ms 3028 KB Output is correct
17 Correct 3 ms 3028 KB Output is correct
18 Correct 2 ms 3028 KB Output is correct
19 Correct 3 ms 3028 KB Output is correct
20 Correct 58 ms 14384 KB Output is correct
21 Correct 88 ms 18504 KB Output is correct
22 Correct 60 ms 14176 KB Output is correct
23 Correct 74 ms 14456 KB Output is correct
24 Correct 75 ms 16036 KB Output is correct
25 Correct 55 ms 14240 KB Output is correct
26 Correct 105 ms 19612 KB Output is correct
27 Correct 130 ms 23340 KB Output is correct
28 Correct 94 ms 24168 KB Output is correct
29 Correct 65 ms 19248 KB Output is correct
30 Correct 78 ms 20024 KB Output is correct
31 Correct 75 ms 19408 KB Output is correct
32 Correct 109 ms 21304 KB Output is correct
33 Correct 102 ms 19608 KB Output is correct
34 Correct 82 ms 19260 KB Output is correct
35 Correct 109 ms 20516 KB Output is correct
36 Correct 117 ms 24644 KB Output is correct