/*
IOI 2008 Islands
- to, 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, to, len;
bool operator!=(Edge B) { return idx != B.idx; }
};
vector<Edge> graph[1000001], cycle;
ll ans = 0, cmp_ans, p[5][1000001];
int cycle_start = 0, discarded;
bool processed[1000001], visited[1000001], on_cycle[1000001], 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.to, {i.idx, node, i.len});
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.to != parent && !on_cycle[i.to]) {
calc_tree(i.to, node);
if (p[4][i.to] + i.len > mx) sc = mx, mx = p[4][i.to] + i.len;
else if (p[4][i.to] + i.len > sc) sc = p[4][i.to] + i.len;
}
p[4][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, 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().len;
cycle.pop_back();
for (Edge j : cycle) on_cycle[j.to] = true;
cmp_ans = 0;
FOR(j, 1, cycle.size()) p[0][cycle[j].to] = p[0][cycle[j - 1].to] + cycle[j].len;
for (int j = cycle.size() - 2; j >= 0; j--)
p[1][cycle[j].to] = p[1][cycle[j + 1].to] + cycle[j + 1].len;
ll mx = 0;
FOR(j, 0, cycle.size()) {
calc_tree(cycle[j].to);
p[2][cycle[j].to] = p[4][cycle[j].to] - p[0][cycle[j].to];
p[3][cycle[j].to] = p[4][cycle[j].to] + p[0][cycle[j].to];
p[4][cycle[j].to] = p[4][cycle[j].to] + p[1][cycle[j].to];
cmp_ans = max(cmp_ans, p[3][cycle[j].to] + mx);
mx = max(mx, p[2][cycle[j].to]);
}
mx = p[4][cycle.back().to];
for (int j = cycle.size() - 2; j >= 0; j--) {
cmp_ans = max(cmp_ans, p[3][cycle[j].to] + mx + discarded);
mx = max(mx, p[4][cycle[j].to]);
}
ans += cmp_ans;
}
cout << ans;
return 0;
}
Compilation message
islands.cpp: In function 'int main()':
islands.cpp:17:40: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
#define FOR(i, x, y) for (int i = x; i < y; i++)
islands.cpp:85:13:
FOR(j, 1, cycle.size()) p[0][cycle[j].to] = p[0][cycle[j - 1].to] + cycle[j].len;
~~~~~~~~~~~~~~~~~~
islands.cpp:85:9: note: in expansion of macro 'FOR'
FOR(j, 1, cycle.size()) p[0][cycle[j].to] = p[0][cycle[j - 1].to] + cycle[j].len;
^~~
islands.cpp:17:40: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
#define FOR(i, x, y) for (int i = x; i < y; i++)
islands.cpp:90:13:
FOR(j, 0, cycle.size()) {
~~~~~~~~~~~~~~~~~~
islands.cpp:90:9: note: in expansion of macro 'FOR'
FOR(j, 0, cycle.size()) {
^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
23968 KB |
Output is correct |
| 2 |
Correct |
19 ms |
23936 KB |
Output is correct |
| 3 |
Correct |
18 ms |
23936 KB |
Output is correct |
| 4 |
Correct |
18 ms |
23936 KB |
Output is correct |
| 5 |
Correct |
20 ms |
23808 KB |
Output is correct |
| 6 |
Correct |
17 ms |
23808 KB |
Output is correct |
| 7 |
Correct |
18 ms |
23936 KB |
Output is correct |
| 8 |
Correct |
19 ms |
23936 KB |
Output is correct |
| 9 |
Correct |
19 ms |
23936 KB |
Output is correct |
| 10 |
Correct |
19 ms |
23936 KB |
Output is correct |
| 11 |
Correct |
18 ms |
23936 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
24064 KB |
Output is correct |
| 2 |
Correct |
19 ms |
24064 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
19 ms |
24064 KB |
Output is correct |
| 2 |
Correct |
20 ms |
24448 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
26 ms |
25312 KB |
Output is correct |
| 2 |
Correct |
35 ms |
28480 KB |
Output is correct |
| 3 |
Correct |
28 ms |
25600 KB |
Output is correct |
| 4 |
Correct |
25 ms |
24832 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
44 ms |
30068 KB |
Output is correct |
| 2 |
Correct |
57 ms |
33908 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
110 ms |
42484 KB |
Output is correct |
| 2 |
Correct |
113 ms |
45364 KB |
Output is correct |
| 3 |
Correct |
141 ms |
58988 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
195 ms |
58168 KB |
Output is correct |
| 2 |
Correct |
234 ms |
85224 KB |
Output is correct |
| 3 |
Correct |
259 ms |
89056 KB |
Output is correct |
| 4 |
Correct |
324 ms |
113536 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
376 ms |
76552 KB |
Output is correct |
| 2 |
Runtime error |
642 ms |
131072 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 |
442 ms |
131076 KB |
Execution killed with signal 9 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
