Description

https://loj.ac/problem/6225

Solution

跟深海机器人类似地建边。
注意输出方案时有点坑，找到一条路径后必须退回终点，再继续找，不然会出bug。

Code

/************************************************
 * Au: Hany01
 * Date: Jul 13th, 2018
 * Prob: LOJ6225 火星探险
 * Inst: Yali High School
************************************************/

#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
#define File(a) freopen(a".in", "r", stdin), freopen(a".out", "w", stdout)
#define rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i)
#define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i)
#define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i)
#define Set(a, b) memset(a, b, sizeof(a))
#define Cpy(a, b) memcpy(a, b, sizeof(a))
#define x first
#define y second
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) ((int)(a).size())
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define y1 wozenmezhemecaia

template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }

inline int read() {
    static int _, __; static char c_;
    for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1;
    for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
    return _ * __;
}

const int maxn = 37 * 37 * 2, maxm = maxn << 4;

int P, Q, beg[maxn], nex[maxm], v[maxm], w[maxm], f[maxm], S, T, vis[maxn], dis[maxn], e = 1, cost, tot, pt[maxn], cnt, tt;

inline void add(int uu, int vv, int ff, int ww, int fl = 1) {
    v[++ e] = vv, f[e] = ff, w[e] = ww, nex[e] = beg[uu], beg[uu] = e;
    if (fl) add(vv, uu, 0, -ww, 0);
}

#define idx(i, j, k) (((i) - 1) * Q + (j) + (k) * P * Q)

inline bool BFS()
{
    static queue<int> q;
    For(i, 1, T) dis[i] = INF;
    Set(vis, 0), dis[S] = 0, q.push(S);
    while (!q.empty()) {
        int u = q.front(); q.pop(), vis[u] = 0;
        for (register int i = beg[u]; i; i = nex[i])
            if (f[i] && chkmin(dis[v[i]], dis[u] + w[i]))
                if (!vis[v[i]]) vis[v[i]] = 1, q.push(v[i]);
    }
    return dis[T] != INF;
}

int DFS(int u, int flow)
{
    if (u == T) return flow;
    int t, res = flow;
    vis[u] = 1;
    for (register int i = beg[u]; i; i = nex[i])
        if (f[i] && dis[v[i]] == dis[u] + w[i] && !vis[v[i]]) {
            f[i] -= (t = DFS(v[i], min(res, f[i]))), f[i ^ 1] += t, cost += t * w[i];
            if (!(res -= t)) return flow;
        }
    return flow - res;
}

void getPath(int u, int now) {
    if (u == T) {
        ++ cnt;
        For(i, 1, tot) printf("%d %d\n", cnt, pt[i]);
        return;
    }
    for (register int i = beg[u]; i; i = nex[i]) {
        if (!(i & 1) && f[i ^ 1] > 0) {
            -- f[i ^ 1];
            int A = u % (P * Q), B = v[i] % (P * Q);
            if (!B) B = P * Q;
            if (!A) A = P * Q;
            if (A != B) {
                if (u != S && v[i] != T) {
                    if (B - A == 1) pt[++ tot] = 0;
                    else assert(B == A + Q), pt[++ tot] = 1;
                    getPath(v[i], now), -- tot;
                } else getPath(v[i], now);
            } else getPath(v[i], now);
            if (cnt == now) return;
        }
    }
}

int main()
{
#ifdef hany01
    File("loj6225");
#endif

    tot = read(), P = read(), Q = read(), T = (S = ((P * Q) << 1) + 1) + 1;
    add(S, idx(1, 1, 0), tot, 0), add(idx(P, Q, 1), T, tot, 0);
    For(j, 1, Q) For(i, 1, P) {
        int t = read();
        if (!(t & 1)) add(idx(i, j, 0), idx(i, j, 1), INF, 0);
        if (t == 2) add(idx(i, j, 0), idx(i, j, 1), 1, -1);
        if (j + 1 <= Q) add(idx(i, j, 1), idx(i, j + 1, 0), INF, 0);
        if (i + 1 <= P) add(idx(i, j, 1), idx(i + 1, j, 0), INF, 0);
    }

    while (BFS()) do Set(vis, 0), tt += DFS(S, INF); while (vis[T]);
    tot = 0;
    For(Cas, 1, tt) getPath(S, Cas);

    return 0;
}
//至今商女，时时犹唱，后庭遗曲。
//    -- 王安石《桂枝香·登临送目》