Codeforces-solutions/Codeforces Round 304 (Div. 2)/E. Soldier and Traveling.cpp

/* Problem URL: https://codeforces.com/problemset/problem/546/E */

#include <bits/stdc++.h>

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int tmp, m;
    cin >> tmp >> m;

    int n = tmp * 2 + 2;

    vvi graph(n);
    V<tuple<int, int, int>> edges;

    auto makeedge = [&](int a, int b, int c){
        graph[a].push_back(edges.size());
        edges.emplace_back(b, c, 0);
        graph[b].push_back(edges.size());
        edges.emplace_back(a, 0, 0);
    };

    int inf = INT32_MAX >> 1;

    vi a(tmp);
    vi b(tmp);
    cin >> a >> b;

    int total = accumulate(all(b), 0);
    if (total != accumulate(all(a), 0)) {
        cout << "NO\n";
        return 0;
    }

    int s = 0;
    int t = n - 1;

    rep(i, tmp) {
        makeedge(s, i + 1, a[i]);
        makeedge(i + 1, i + tmp + 1, inf);
        makeedge(i + tmp + 1, t, b[i]);
    }

    while (m--) {
        int a, b;
        cin >> a >> b;

        makeedge(a, b + tmp, inf);
        makeedge(b, a + tmp, inf);
    }

    vi level(n);

    auto bfs = [&](){
        queue<int> q;
        q.push(s);
        level[s] = 0;

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

            for (auto id : graph[u]) {
                auto [v, c, f] = edges[id];
                if (level[v] > level[u] + 1 && c != f) {
                    level[v] = level[u] + 1;
                    q.push(v);
                }
            }
        }

        return level[t] != inf;
    };

    V<bool> vis(n);

    function<int(int, int)> dfs = [&](int i, int f){
        if (f == 0) {
            return 0;
        }

        if (i == t) {
            return f;
        }

        for (auto id : graph[i]) {
            auto &[j, c, fj] = edges[id];
            if (vis[j] || level[j] <= level[i]) {
                continue;
            }

            int ans = dfs(j, min(f, c - fj));
            if (ans == 0) {
                continue;
            }

            auto &[_, __, fc] = edges[id ^ 1];

            fj += ans;
            fc -= ans;

            return ans;
        }

        vis[i] = true;

        return 0;
    };

    int ans = 0;
    while (true) {
        fill(all(level), inf);
        if (!bfs()) {
            break;
        }

        fill(all(vis), false);

        int count = 0;
        while ((count = dfs(s, inf))) {
            ans += count;
        }
    }

    if (ans != total) {
        cout << "NO\n";
        return 0;
    }

    vvi act(tmp, vi(tmp, 0));

    rep(i, tmp) {
        for (auto _ : graph[i + 1]) {
            if ((_ & 1) == 1) {
                continue;
            }

            auto [j, __, f] = edges[_];
            act[i][j - tmp - 1] = f;
        }
    }

    cout << "YES\n" << act;
}