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답안 #233626

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
233626 2020-05-21T05:50:57 Z dolphingarlic Islands (IOI08_islands) C++14
80 / 100
 596 ms 131072 KB 
/*
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], on_cycle[1000001], adding = false;

void find_cycle(int node, Edge parent = {0, 0, 0}) {
    if (on_cycle[node]) {
        cycle_start = node;
        cycle.push_back({0, node, 0});
        cycle.push_back(parent);
        adding = true;
        return;
    }
    on_cycle[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);
            else on_cycle[parent.to] = false;
            return;
        }
    }
    on_cycle[node] = false;
}

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();

        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()) {
         ^~~

Subtask #1
33.0 / 33.0

# 결과 실행 시간 메모리 Grader output
1 Correct 18 ms 23936 KB Output is correct
2 Correct 18 ms 23936 KB Output is correct
3 Correct 17 ms 23936 KB Output is correct
4 Correct 17 ms 23936 KB Output is correct
5 Correct 17 ms 23936 KB Output is correct
6 Correct 17 ms 23808 KB Output is correct
7 Correct 17 ms 23808 KB Output is correct
8 Correct 17 ms 23936 KB Output is correct
9 Correct 17 ms 23808 KB Output is correct
10 Correct 17 ms 23936 KB Output is correct
11 Correct 17 ms 23936 KB Output is correct

Subtask #2
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 18 ms 24064 KB Output is correct
2 Correct 18 ms 23936 KB Output is correct

Subtask #3
4.0 / 4.0

# 결과 실행 시간 메모리 Grader output
1 Correct 19 ms 24064 KB Output is correct
2 Correct 25 ms 24424 KB Output is correct

Subtask #4
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 24 ms 25472 KB Output is correct
2 Correct 35 ms 28608 KB Output is correct
3 Correct 29 ms 25600 KB Output is correct
4 Correct 22 ms 24704 KB Output is correct

Subtask #5
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 42 ms 30324 KB Output is correct
2 Correct 60 ms 34036 KB Output is correct

Subtask #6
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 101 ms 42612 KB Output is correct
2 Correct 111 ms 46256 KB Output is correct
3 Correct 145 ms 61160 KB Output is correct

Subtask #7
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 181 ms 57888 KB Output is correct
2 Correct 235 ms 87780 KB Output is correct
3 Correct 264 ms 92584 KB Output is correct
4 Correct 319 ms 118880 KB Output is correct

Subtask #8
0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 388 ms 76440 KB Output is correct
2 Runtime error 596 ms 131072 KB Execution killed with signal 9 (could be triggered by violating memory limits)
3 Halted 0 ms 0 KB -

Subtask #9
0 / 10.0

# 결과 실행 시간 메모리 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 -