QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#106459#5423. Perfect MatchingcokleML 2ms3412kbC++112.5kb2023-05-17 20:39:062023-05-17 20:39:09

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-05-17 20:39:09]
  • 评测
  • 测评结果:ML
  • 用时:2ms
  • 内存:3412kb
  • [2023-05-17 20:39:06]
  • 提交

answer

#include <iostream>
#include <vector>
#include <queue>
#include <limits>

using namespace std;

const int INF = numeric_limits<int>::max();
const int NIL = 0;

vector<vector<int>> adjList;
vector<int> dist, match;

bool bfs() {
    queue<int> q;
    for (int u = 1; u < adjList.size(); u++) {
        if (match[u] == NIL) {
            dist[u] = 0;
            q.push(u);
        } else {
            dist[u] = INF;
        }
    }

    dist[NIL] = INF;

    while (!q.empty()) {
        int u = q.front();
        q.pop();

        if (dist[u] < dist[NIL]) {
            for (int v : adjList[u]) {
                if (dist[match[v]] == INF) {
                    dist[match[v]] = dist[u] + 1;
                    q.push(match[v]);
                }
            }
        }
    }

    return dist[NIL] != INF;
}

bool dfs(int u) {
    if (u == NIL) {
        return true;
    }

    for (int v : adjList[u]) {
        if (dist[match[v]] == dist[u] + 1 && dfs(match[v])) {
            match[u] = v;
            match[v] = u;
            return true;
        }
    }

    dist[u] = INF;
    return false;
}

int hopcroftKarp(int n) {
    dist.resize(n + 1);
    match.resize(n + 1);

    int matching = 0;

    while (bfs()) {
        for (int u = 1; u <= n; u++) {
            if (match[u] == NIL && dfs(u)) {
                matching++;
            }
        }
    }

    return matching;
}

int main() {
    int T;
    cin >> T;

    while (T--) {
        int n;
        cin >> n;

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

        // 构建图的邻接表表示
        adjList.clear();
        adjList.resize(n + 1);
        dist.clear();
        dist.resize(n + 1);
        match.clear();
        match.resize(n + 1);

        for (int i = 1; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                if (abs(i - j) == abs(a[i] - a[j])) {
                    adjList[i].push_back(j);
                    adjList[j].push_back(i);
                }
            }
        }

        // 使用Hopcroft-Karp算法求解完美匹配
        int matching = hopcroftKarp(n);

        if (matching == n / 2) {
            cout << "Yes" << endl;

            for (int u = 1; u <= n; u++) {
                if (u < match[u]) {
                    cout << u << " " << match[u] << endl;
                }
            }
        } else {
            cout << "No" << endl;
        }
    }

    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 3412kb

input:

3
6
14 22 33 11 25 36
4
100 10 98 12
4
1 3 5 7

output:

Yes
1 4
2 5
3 6
Yes
1 3
2 4
No

result:

ok 3 Cases (3 test cases)

Test #2:

score: -100
Memory Limit Exceeded

input:

10
100000
0 -1 -2 -3 -4 -5 -2 -7 -8 -9 -10 -9 -12 13 14 15 -16 -17 -18 19 20 19 -22 -21 -20 -25 -26 -27 -28 -27 -26 31 30 29 -34 -35 -34 39 38 37 42 41 42 47 44 45 46 49 48 -53 -52 -51 -56 -55 -54 55 56 57 -58 -59 -60 61 62 63 64 65 64 67 66 69 70 73 72 73 74 73 76 75 74 79 80 81 -84 -83 -84 89 86 8...

output:


result: