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답안 #221315

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
221315 2020-04-09T21:13:24 Z Sorting Transport (COCI19_transport) C++14
117 / 130
 1000 ms 41944 KB 
#include <bits/stdc++.h>

using namespace std;

const int kN = 1e5 + 7;
const int kBIT = 2e5 + 7;

class BinaryIndexedTree{
private:
	int tr[kBIT];

	long long query(int idx){
		long long ans = 0;
		for(; idx >= 1; idx -= idx & -idx)
			ans += tr[idx];
		return ans;
	}
public:
	BinaryIndexedTree(){}
	void update(int idx, int delta){
		for(; idx < kBIT; idx += idx & -idx)
			tr[idx] += delta;
	}
	long long query(int l, int r){
		return query(r) - query(l - 1);
	}
};

struct Edge{
	int to, weight;

	Edge(){}
	Edge(int to, int weight){
		this->to = to;
		this->weight = weight;
	}
};


int a[kN], subtree_size[kN], n;
vector<Edge> adjacent[kN];
bool visited[kN];
int centroid_decomposition_root;

pair<long long, long long> prefix[kN], suffix[kN];
map<long long, int> prefix_cnt[kN], suffix_cnt[kN];

vector<int> centroid_decomposition[kN];

set<long long> numbers;
map<long long, int> idx;
BinaryIndexedTree fenwick_prefix, fenwick_suffix;

void read_input(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);

	cin >> n;

	for(int i = 1; i <= n; ++i)
		cin >> a[i];

	for(int i = 0; i < n - 1; ++i){
		int u, v, w;
		cin >> u >> v >> w;

		adjacent[u].push_back(Edge{v, w});
		adjacent[v].push_back(Edge{u, w});
	}
}

void build_subtree_size(int node = 1, int parent = -1){
	subtree_size[node] = 1;
	for(auto [to, weight]: adjacent[node]){
		if(to == parent || visited[to])
			continue;

		build_subtree_size(to, node);
		subtree_size[node] += subtree_size[to];
	}
}

int get_centroid(int node, int parent, const int &component_size){
	for(auto [to, weight]: adjacent[node]){
		if(!visited[to] && to != parent && subtree_size[to] > component_size / 2){
			return get_centroid(to, node, component_size);
		}
	}
	return node;
}

void build_centroid_decomposition(int node = 1, int parent = -1){
	build_subtree_size(node);
	int centroid = get_centroid(node, -1, subtree_size[node]);

	if(parent != -1)
		centroid_decomposition[parent].push_back(centroid);
	else
		centroid_decomposition_root = centroid;

	visited[centroid] = true;
	for(auto [to, weight]: adjacent[centroid]){
		if(!visited[to]){
			build_centroid_decomposition(to, centroid);
		}
	}
	visited[centroid] = false;
}

void build_prefix_and_suffix(int node, int weight_to_parent, int parent){
	suffix[node].first = suffix[parent].first - weight_to_parent + a[node];
	suffix[node].second = min(suffix[parent].first - weight_to_parent, suffix[parent].second);
	prefix[node].first = prefix[parent].first - weight_to_parent + a[node];
	prefix[node].second = min((long long)a[node] - weight_to_parent, a[node] - weight_to_parent + prefix[parent].second);
	prefix[node].second = min(prefix[node].second, 0ll);

	array<long long, 2> v{prefix[node].first, -suffix[node].second};
	for(auto x: v)
		numbers.insert(x);

	for(auto [to, weight]: adjacent[node]){
		if(to == parent || visited[to])
			continue;

		build_prefix_and_suffix(to, weight, node);
	}
}

long long get_answer_for_subtree(int node, int parent){
	long long ans = 0;

	ans += prefix[node].second >= 0;
	//if prefix can reach to root, adding the a[root] is not necessary
	ans += suffix[node].second >= 0;
	
	if(prefix[node].second >= 0)
		ans += fenwick_suffix.query(1, idx[ prefix[node].first ]);
	ans += fenwick_prefix.query(idx[ -suffix[node].second ], kBIT - 1);

	for(auto [to, weight]: adjacent[node]){
		if(to == parent || visited[to])
			continue;
		ans += get_answer_for_subtree(to, node);
	}

	return ans;
}

void add_to_fenwick(int node, int parent, int delta){
	if(prefix[node].second >= 0)
		fenwick_prefix.update(idx[ prefix[node].first ], delta);
	fenwick_suffix.update(idx[ -suffix[node].second ], delta);

	for(auto [to, weight]: adjacent[node]){
		if(to == parent || visited[to])
			continue;

		add_to_fenwick(to, node, delta);
	}
}

long long get_answer(int node){
	visited[node] = true;
	prefix[node] = {0, 0};
	suffix[node] = {a[node], 0};

	numbers.clear();
	idx.clear();
	for(auto [to, weight]: adjacent[node]){
		if(visited[to])
			continue;
		build_prefix_and_suffix(to, weight, node);
	}

	int cnt = 1;
	for(long long x: numbers)
		idx[x] = cnt++;

	long long ans = 0;
	for(auto [to, weight]: adjacent[node]){
		if(visited[to])
			continue;
		ans += get_answer_for_subtree(to, node);
		add_to_fenwick(to, node, 1);
	}

	for(auto [to, weight]: adjacent[node]){
		if(visited[to])
			continue;
		add_to_fenwick(to, node, -1);
	}

	for(int to: centroid_decomposition[node])
		ans += get_answer(to);
 
	return ans;
}

int main(){
	read_input();
	build_centroid_decomposition();
	cout << get_answer(centroid_decomposition_root) << "\n";
}

Compilation message

transport.cpp: In function 'void build_subtree_size(int, int)':
transport.cpp:74:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:74:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^
transport.cpp: In function 'int get_centroid(int, int, const int&)':
transport.cpp:84:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:84:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^
transport.cpp: In function 'void build_centroid_decomposition(int, int)':
transport.cpp:102:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[centroid]){
           ^
transport.cpp:102:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[centroid]){
                      ^
transport.cpp: In function 'void build_prefix_and_suffix(int, int, int)':
transport.cpp:121:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp: In function 'long long int get_answer_for_subtree(int, int)':
transport.cpp:140:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:140:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^
transport.cpp: In function 'void add_to_fenwick(int, int, int)':
transport.cpp:154:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:154:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^
transport.cpp: In function 'long long int get_answer(int)':
transport.cpp:169:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:180:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:180:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^
transport.cpp:187:11: warning: decomposition declaration only available with -std=c++1z or -std=gnu++1z
  for(auto [to, weight]: adjacent[node]){
           ^
transport.cpp:187:22: warning: unused variable 'weight' [-Wunused-variable]
  for(auto [to, weight]: adjacent[node]){
                      ^

Subtask #1
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 29 ms 15104 KB Output is correct
2 Correct 28 ms 15488 KB Output is correct

Subtask #2
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 36 ms 15616 KB Output is correct
2 Correct 43 ms 15872 KB Output is correct

Subtask #3
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 378 ms 26104 KB Output is correct
2 Correct 347 ms 25080 KB Output is correct

Subtask #4
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 520 ms 30328 KB Output is correct
2 Correct 636 ms 32320 KB Output is correct

Subtask #5
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 765 ms 36112 KB Output is correct
2 Correct 996 ms 41944 KB Output is correct

Subtask #6
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 251 ms 20088 KB Output is correct
2 Correct 142 ms 19832 KB Output is correct

Subtask #7
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 264 ms 24440 KB Output is correct
2 Correct 379 ms 23416 KB Output is correct

Subtask #8
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 601 ms 27896 KB Output is correct
2 Correct 629 ms 30072 KB Output is correct

Subtask #9
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 835 ms 31608 KB Output is correct
2 Correct 880 ms 33784 KB Output is correct

Subtask #10
0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Execution timed out 1090 ms 35192 KB Time limit exceeded
2 Halted 0 ms 0 KB -