/*
IOI 2008 Islands
- First, split the graph up into its connected components. We want the sum of the longest
paths in each component
- Notice how each component is made of a single cycle with trees appended to each node on the cycle
- Case 1: The longest path lies in one of the trees
- Just use DP to find this length
- Case 2: The longest path goes from one tree to the other and crosses the cycle
- Let dp[i] = The length of the longest path going through node i
- If we flatten the cycle by removing an edge, then notice how
we can use prefix sums to get the answer in this case
- Just handle these 2 cases for each component
- Complexity: O(N)
*/
#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
struct Edge {
int idx, first;
ll second;
bool operator!=(Edge B) { return idx != B.idx; }
};
vector<Edge> graph[1010101], cycle;
ll discarded, ans = 0, cmp_ans, dp[1010101], p[5][1010101];
int cycle_start = 0;
bool processed[1010101], visited[1010101], on_cycle[1010101], adding = false;
void find_cycle(int node, Edge parent = {0, 0, 0}) {
if (visited[node]) {
cycle_start = node;
cycle.push_back({0, node, 0});
cycle.push_back(parent);
adding = true;
return;
}
visited[node] = true;
for (Edge i : graph[node]) if (i != parent) {
find_cycle(i.first, {i.idx, node, i.second});
if (cycle_start) {
if (node == cycle_start) adding = false;
if (adding) cycle.push_back(parent);
return;
}
}
}
void calc_tree(int node, int parent = 0) {
processed[node] = true;
ll mx = 0, sc = 0;
for (Edge i : graph[node]) if (i.first != parent && !on_cycle[i.first]) {
calc_tree(i.first, node);
if (dp[i.first] + i.second > mx) sc = mx, mx = dp[i.first] + i.second;
else if (dp[i.first] + i.second > sc) sc = dp[i.first] + i.second;
}
dp[node] = mx;
cmp_ans = max(cmp_ans, mx + sc);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
FOR(i, 1, n + 1) {
int v;
ll l;
cin >> v >> l;
graph[i].push_back({i, v, l});
graph[v].push_back({i, i, l});
}
FOR(i, 1, n + 1) if (!processed[i]) {
cycle.clear();
cycle_start = 0;
find_cycle(i);
discarded = cycle.back().second;
cycle.pop_back();
for (Edge j : cycle) on_cycle[j.first] = true;
cmp_ans = 0;
int m = cycle.size();
FOR(j, 1, m) p[0][j] = p[0][j - 1] + cycle[j].second;
for (int j = m - 2; j >= 0; j--) p[1][j] = p[1][j + 1] + cycle[j + 1].second;
FOR(j, 0, m) {
calc_tree(cycle[j].first);
p[2][j] = dp[cycle[j].first] - p[0][j];
p[3][j] = dp[cycle[j].first] + p[0][j];
p[4][j] = dp[cycle[j].first] + p[1][j];
}
ll mx = 0;
FOR(j, 0, m) {
cmp_ans = max(cmp_ans, p[3][j] + mx);
mx = max(mx, p[2][j]);
}
mx = p[4][m - 1];
for (int j = m - 2; j >= 0; j--) {
cmp_ans = max(cmp_ans, p[3][j] + mx + discarded);
mx = max(mx, p[4][j]);
}
ans += cmp_ans;
FOR(j, 0, 5) FOR(k, 0, m) p[j][k] = 0;
}
cout << ans;
return 0;
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
18 ms |
24192 KB |
Output is correct |
2 |
Correct |
19 ms |
24192 KB |
Output is correct |
3 |
Correct |
19 ms |
24192 KB |
Output is correct |
4 |
Correct |
17 ms |
24064 KB |
Output is correct |
5 |
Correct |
17 ms |
24192 KB |
Output is correct |
6 |
Correct |
18 ms |
24192 KB |
Output is correct |
7 |
Correct |
17 ms |
24064 KB |
Output is correct |
8 |
Correct |
18 ms |
24064 KB |
Output is correct |
9 |
Correct |
18 ms |
24192 KB |
Output is correct |
10 |
Correct |
18 ms |
24064 KB |
Output is correct |
11 |
Correct |
18 ms |
24192 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
18 ms |
24320 KB |
Output is correct |
2 |
Correct |
19 ms |
24320 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
20 ms |
24320 KB |
Output is correct |
2 |
Correct |
20 ms |
24704 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
26 ms |
25600 KB |
Output is correct |
2 |
Correct |
37 ms |
28920 KB |
Output is correct |
3 |
Correct |
29 ms |
25728 KB |
Output is correct |
4 |
Correct |
23 ms |
24960 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
45 ms |
30704 KB |
Output is correct |
2 |
Correct |
62 ms |
34032 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
111 ms |
41840 KB |
Output is correct |
2 |
Correct |
116 ms |
49768 KB |
Output is correct |
3 |
Correct |
148 ms |
64108 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
189 ms |
56180 KB |
Output is correct |
2 |
Correct |
231 ms |
88160 KB |
Output is correct |
3 |
Correct |
263 ms |
99168 KB |
Output is correct |
4 |
Correct |
339 ms |
124764 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
389 ms |
90428 KB |
Output is correct |
2 |
Runtime error |
636 ms |
131076 KB |
Execution killed with signal 9 (could be triggered by violating memory limits) |
3 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Runtime error |
433 ms |
131072 KB |
Execution killed with signal 9 (could be triggered by violating memory limits) |
2 |
Halted |
0 ms |
0 KB |
- |