Untitled

 avatar
unknown
c_cpp
a year ago
3.8 kB
5
Indexable
#include "bits/stdc++.h"
using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x...)
#endif

using ll = long long;

constexpr int N = 2e5;
constexpr int K = 7;
constexpr int M = 2187;

int n, k;
int a[K][N];
vector<int> ids[M];

bool match(int am, int bm) {
    for (int i = 0; i < k; i++) {
        if (am % 3 == bm % 3 && am % 3 != 2) return false;
        am /= 3;
        bm /= 3;
    }
    return true;
}

struct edge {
    int v, c, f, id;
};

vector<edge> g[M + 2];

void addEdge(int u, int v, int st) {
    g[u].emplace_back(v, st, 0, (int)g[v].size());
    g[v].emplace_back(u, 0, 0, (int)g[u].size() - 1);
}

int d[M + 2];

bool bfs() {
    fill(d, d + M + 2, -1);
    queue<int> q;
    q.push(M);
    d[M] = 0;
    while (!q.empty()) {
        int t = q.front();
        q.pop();
        if (t == M + 1) return true;
        for (auto &[v, c, f, id] : g[t]) {
            if (c - f > 0 && d[v] == -1) {
                d[v] = d[t] + 1;
                q.push(v);
            }
        }
    }
    return false;
}

int ptr[M + 2];

int dfs(int u, int flow) {
    if (!flow) return 0;
    if (u == M + 1) return flow;
    for (int &to = ptr[u]; to < (int)g[u].size(); to++) {
        if (d[g[u][to].v] != d[u] + 1) continue;
        int pushed = dfs(g[u][to].v, min(flow, g[u][to].c - g[u][to].f));
        if (pushed) {
            g[u][to].f += pushed;
            g[g[u][to].v][g[u][to].id].f -= pushed;
            return pushed;
        }
    }
    return 0;
}

int dinic() {
    int flow = 0;
    while (bfs()) {
        fill(ptr, ptr + M + 2, 0);
        while (int pushed = dfs(M, INT_MAX)) {
            flow += pushed;
        }
    }
    return flow;
}

void test_case() {
    cin >> n >> k;
    for (int j = 0; j < n; j++) {
        for (int i = 0; i < k; i++) {
            cin >> a[i][j];
        }
    }
    for (int i = 0; i < k; i++) {
        int tmp[n];
        copy(a[i], a[i] + n, tmp);
        sort(tmp, tmp + n);
        int median = (tmp[n / 2 - 1] + tmp[n / 2]) / 2;
        int half = (tmp[n / 2 - 1] + tmp[n / 2]) % 2;
        for (int j = 0; j < n; j++) {
            if (a[i][j] > median + half) {
                a[i][j] = 1;
            } else if (a[i][j] < median) {
                a[i][j] = 0;
            } else {
                a[i][j] = 2;
            }
        }
    }
    for (int i = 0; i < n; i++) {
        int val = 0, mult = 1;
        for (int j = k - 1; j >= 0; j--) {
            val += a[j][i] * mult;
            mult *= 3;
        }
        ids[val].push_back(i);
    }
    int MX = 1;
    for (int i = 0; i < k; i++) {
        MX *= 3;
    }
    for (int am = 0; am < MX / 3; am++) {
        addEdge(M, am, ids[am].size());
    }
    for (int bm = MX / 3; bm < MX; bm++) {
        addEdge(bm, M + 1, ids[bm].size());
    }
    for (int am = 0; am < MX / 3; am++) {
        for (int bm = MX / 3; bm < MX; bm++) {
            if (match(am, bm)) {
                addEdge(am, bm, min(ids[am].size(), ids[bm].size()));
            }
        }
    }
    if (dinic() == n / 2) {
        cout << "YES\n";
        for (int u = 0; u < MX / 3; u++) {
            for (auto &[v, c, f, id] : g[u]) {
                while (f-- > 0) {
                    cout << ids[u].back() + 1 << ' ' << ids[v].back() + 1 << '\n';
                    ids[u].pop_back();
                    ids[v].pop_back();
                }
            }
        }
    } else {
        cout << "NO\n";
    }
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    int tests = 1;
    // cin >> tests;
    while (tests--) {
        test_case();
    }
    return 0;
}
Leave a Comment