专题2024.03.21

xiaruize's Blog / 2024-03-21 / 原文

2024.03.21专题

T1 Bombs

答案显然具有单调性，多删一定比少删更优，这是明显的

一个数 \(a_i=x\) 不被删掉的充要条件为:

\[\sum\limits_{j=1}^{i-1}[a_j < x] \leq k \]

其中 \(k\) 为 \(i\) 之前的炸弹数量

由单调性，考虑每次加一个炸弹后怎么快速的检查一个数合不合法，可以用线段树维护全局的 \(max\) 和区间加

时间复杂度为 \(\mathcal{O}(nlogn)\)

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
#define debug(x) cerr << "On Line:" << __LINE__ << #x << "=" << x << endl
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)

{
    if (a > b)
        return a;
    return b;
}
int min(int a, int b)
{
    if (a < b)
        return a;
    return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 3e5 + 10;

struct segment_tree
{
#define ls p << 1
#define rs p << 1 | 1
    struct node
    {
        int mx, lz;

        void tag(int x)
        {
            mx += x;
            lz += x;
        }
    } tr[N << 2];

    void pushdown(int p)
    {
        tr[ls].tag(tr[p].lz);
        tr[rs].tag(tr[p].lz);
        tr[p].lz = 0;
    }

    void pushup(int p)
    {
        tr[p].mx = max(tr[ls].mx, tr[rs].mx);
    }

    void update(int p, int l, int r, int ll, int rr, int v)
    {
        if (ll <= l && r <= rr)
        {
            tr[p].tag(v);
            return;
        }
        pushdown(p);
        int mid = l + r >> 1;
        if (mid >= ll)
            update(ls, l, mid, ll, rr, v);
        if (mid < rr)
            update(rs, mid + 1, r, ll, rr, v);
        pushup(p);
    }
} seg;

int n;
int p[N], q[N], pos[N];

void solve()
{
    cin >> n;
    rep(i, 1, n)
    {
        cin >> p[i];
        pos[p[i]] = i;
    }
    rep(i, 1, n) cin >> q[i];
    seg.update(1, 1, n, 1, pos[n], 1);
    int res = n;
    cout << n << ' ';
    rep(i, 1, n - 1)
    {
        seg.update(1, 1, n, 1, q[i], -1);
        while (seg.tr[1].mx <= 0)
        {
            res--;
            seg.update(1, 1, n, 1, pos[res], 1);
        }
        cout << res << ' ';
    }
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
    // freopen(".in","r",stdin);
    // freopen(".out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int testcase = 1;
    // cin >> testcase;
    while (testcase--)
        solve();
#ifndef ONLINE_JUDGE
    cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
    cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
    return 0;
}

T2 P1484 种树

\(dp\) 是 \(\mathcal{O}(nk)\) 的，且不太好优化，故考虑贪心

假设当前选择了 \(a_x\)，且 \(a_x\) 周围2格都是空，那么下一步有两种情况

  1. 选择 \(a_{x-1},a_{x+1}\) 并删除 \(a_x\)
  2. 选择不与 \(a_x\) 相邻的数 \(a_y\)
对于第一种情况的证明

考虑删除 \(a_x\) 后不选择 \(a_{x-1},a_{x+1}\)

那么，选择 \(a_x\) 和新增的一个数必然覆盖的区间更小且价值更大

所以是不优的

所以如果删除 \(a_x\) 则必然选择 \(a_{x-1},a_{x+1}\)

用链表和优先队列维护，每次选择一个，将两侧的删掉，当前的的权值改为 \(a_x\leftarrow a_{x-1}+a_{x+1}-a_x\) 并重新压入优先队列

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
#define debug(x) cerr << "On Line:" << __LINE__ << #x << "=" << x << endl
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)

{
    if (a > b)
        return a;
    return b;
}
int min(int a, int b)
{
    if (a < b)
        return a;
    return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 3e5 + 10;

int n, k;
int a[N << 1], pre[N], nxt[N];
priority_queue<pii> q;
bool vis[N];

void del(int x)
{
    nxt[pre[x]] = nxt[x];
    pre[nxt[x]] = pre[x];
}

void solve()
{
    cin >> n >> k;
    rep(i, 1, n)
    {
        cin >> a[i];
        pre[i] = i - 1;
        nxt[i] = i + 1;
        q.push({a[i], i});
    }
    int res = 0;
    int ans = 0;
    while (k--)
    {
        while (vis[q.top().second])
            q.pop();
        int x = q.top().second;
        q.pop();
        res += a[x];
        ans = max(ans, res);
        a[x] = a[pre[x]] + a[nxt[x]] - a[x];
        q.push({a[x], x});
        vis[pre[x]] = vis[nxt[x]] = true;
        del(pre[x]);
        del(nxt[x]);
    }
    cout << ans << endl;
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
    // freopen(".in","r",stdin);
    // freopen(".out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int testcase = 1;
    // cin >> testcase;
    while (testcase--)
        solve();
#ifndef ONLINE_JUDGE
    cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
    cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
    return 0;
}

T3 Square Root of Permutation

从 \(i\rightarrow p_i\) 建图

注意到一定形成若干个环，按照环长度的奇偶性分类

  • 对于长度为奇数的环，令长度为 \(len, mid=\lfloor\frac{len}{2}\rfloor\) 考虑如下答案 \(\forall i < mid,res_i=res_{i+mid+1},res_{i+mid+1}=i+1\) 这里的 \(i\) 为点在环上的下标

  • 对于长度为偶数的环，发现只可以通过等长的两两匹配

模拟即可

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
namespace __DEBUG_UTIL__
{
    using namespace std;
    /* Primitive Datatypes Print */
    void print(const char *x) { cerr << x; }
    void print(bool x) { cerr << (x ? "T" : "F"); }
    void print(char x) { cerr << '\'' << x << '\''; }
    void print(signed short int x) { cerr << x; }
    void print(unsigned short int x) { cerr << x; }
    void print(signed int x) { cerr << x; }
    void print(unsigned int x) { cerr << x; }
    void print(signed long int x) { cerr << x; }
    void print(unsigned long int x) { cerr << x; }
    void print(signed long long int x) { cerr << x; }
    void print(unsigned long long int x) { cerr << x; }
    void print(float x) { cerr << x; }
    void print(double x) { cerr << x; }
    void print(long double x) { cerr << x; }
    void print(string x) { cerr << '\"' << x << '\"'; }
    template <size_t N>
    void print(bitset<N> x) { cerr << x; }
    void print(vector<bool> v)
    { /* Overloaded this because stl optimizes vector<bool> by using
          _Bit_reference instead of bool to conserve space. */
        int f = 0;
        cerr << '{';
        for (auto &&i : v)
            cerr << (f++ ? "," : "") << (i ? "T" : "F");
        cerr << "}";
    }
    /* Templates Declarations to support nested datatypes */
    template <typename T>
    void print(T &&x);
    template <typename T>
    void print(vector<vector<T>> mat);
    template <typename T, size_t N, size_t M>
    void print(T (&mat)[N][M]);
    template <typename F, typename S>
    void print(pair<F, S> x);
    template <typename T, size_t N>
    struct Tuple;
    template <typename T>
    struct Tuple<T, 1>;
    template <typename... Args>
    void print(tuple<Args...> t);
    template <typename... T>
    void print(priority_queue<T...> pq);
    template <typename T>
    void print(stack<T> st);
    template <typename T>
    void print(queue<T> q);
    /* Template Datatypes Definitions */
    template <typename T>
    void print(T &&x)
    {
        /*  This works for every container that supports range-based loop
            i.e. vector, set, map, oset, omap, dequeue */
        int f = 0;
        cerr << '{';
        for (auto &&i : x)
            cerr << (f++ ? "," : ""), print(i);
        cerr << "}";
    }
    template <typename T>
    void print(vector<vector<T>> mat)
    {
        int f = 0;
        cerr << "\n~~~~~\n";
        for (auto &&i : mat)
        {
            cerr << setw(2) << left << f++, print(i), cerr << "\n";
        }
        cerr << "~~~~~\n";
    }
    template <typename T, size_t N, size_t M>
    void print(T (&mat)[N][M])
    {
        int f = 0;
        cerr << "\n~~~~~\n";
        for (auto &&i : mat)
        {
            cerr << setw(2) << left << f++, print(i), cerr << "\n";
        }
        cerr << "~~~~~\n";
    }
    template <typename F, typename S>
    void print(pair<F, S> x)
    {
        cerr << '(';
        print(x.first);
        cerr << ',';
        print(x.second);
        cerr << ')';
    }
    template <typename T, size_t N>
    struct Tuple
    {
        static void printTuple(T t)
        {
            Tuple<T, N - 1>::printTuple(t);
            cerr << ",", print(get<N - 1>(t));
        }
    };
    template <typename T>
    struct Tuple<T, 1>
    {
        static void printTuple(T t) { print(get<0>(t)); }
    };
    template <typename... Args>
    void print(tuple<Args...> t)
    {
        cerr << "(";
        Tuple<decltype(t), sizeof...(Args)>::printTuple(t);
        cerr << ")";
    }
    template <typename... T>
    void print(priority_queue<T...> pq)
    {
        int f = 0;
        cerr << '{';
        while (!pq.empty())
            cerr << (f++ ? "," : ""), print(pq.top()), pq.pop();
        cerr << "}";
    }
    template <typename T>
    void print(stack<T> st)
    {
        int f = 0;
        cerr << '{';
        while (!st.empty())
            cerr << (f++ ? "," : ""), print(st.top()), st.pop();
        cerr << "}";
    }
    template <typename T>
    void print(queue<T> q)
    {
        int f = 0;
        cerr << '{';
        while (!q.empty())
            cerr << (f++ ? "," : ""), print(q.front()), q.pop();
        cerr << "}";
    }
    /* Printer functions */
    void printer(const char *) {} /* Base Recursive */
    template <typename T, typename... V>
    void printer(const char *names, T &&head, V &&...tail)
    {
        /* Using && to capture both lvalues and rvalues */
        int i = 0;
        for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
            if (names[i] == '(' or names[i] == '<' or names[i] == '{')
                bracket++;
            else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
                bracket--;
        cerr.write(names, i) << " = ";
        print(head);
        if (sizeof...(tail))
            cerr << " ||", printer(names + i + 1, tail...);
        else
            cerr << "]\n";
    }
    /* PrinterArr */
    void printerArr(const char *) {} /* Base Recursive */
    template <typename T, typename... V>
    void printerArr(const char *names, T arr[], size_t N, V... tail)
    {
        size_t ind = 0;
        for (; names[ind] and names[ind] != ','; ind++)
            cerr << names[ind];
        for (ind++; names[ind] and names[ind] != ','; ind++)
            ;
        cerr << " = {";
        for (size_t i = 0; i < N; i++)
            cerr << (i ? "," : ""), print(arr[i]);
        cerr << "}";
        if (sizeof...(tail))
            cerr << " ||", printerArr(names + ind + 1, tail...);
        else
            cerr << "]\n";
    }
}
#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__)
#define debugArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...)
#define debugArr(...)
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
    if (a > b)
        return a;
    return b;
}
int min(int a, int b)
{
    if (a < b)
        return a;
    return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 1e6 + 10;

int n;
int p[N];
bool vis[N];
int res[N];
vector<int> vec;
map<int, vector<vector<int>>> siz;

void solve()
{
    cin >> n;
    rep(i, 1, n) cin >> p[i];
    rep(i, 1, n)
    {
        if (!vis[i])
        {
            vec.clear();
            vec.push_back(i);
            vis[i] = true;
            int x = p[i];
            while (x != i)
            {
                vec.push_back(x);
                vis[x] = true;
                x = p[x];
            }
            debug(vec.size());
            if (vec.size() & 1)
            {
                int len = vec.size();
                rep(i, 0, len / 2 - 1)
                {
                    res[vec[i]] = vec[len / 2 + i + 1];
                    res[vec[len / 2 + i + 1]] = vec[i + 1];
                }
                res[vec[len / 2]] = vec[0];
            }
            else
            {
                siz[vec.size()].push_back(vec);
            }
        }
    }
    for (auto [len, cur] : siz)
    {
        if (cur.size() % 2 == 1)
        {
            cout << "-1" << endl;
            return;
        }
        for (int i = 0; i < cur.size(); i += 2)
        {
            rep(j, 0, len - 1)
            {
                res[cur[i][j]] = cur[i + 1][j];
                res[cur[i + 1][j]] = (j == len - 1 ? cur[i][0] : cur[i][j + 1]);
            }
        }
    }
    rep(i, 1, n) cout << res[i] << ' ';
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
    // freopen(".in","r",stdin);
    // freopen(".out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int testcase = 1;
    // cin >> testcase;
    while (testcase--)
        solve();
#ifndef ONLINE_JUDGE
    cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
    cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
    return 0;
}

T5 P3825 [NOI2017] 游戏

如果不存在 \(x\) 的点，即每个点都只有 \(2\) 种可能，那么就可以转化为相互限制的条件，就是 2-SAT 板子了

枚举每个当前是 \(x\) 的位置改为 \(a\) 还是 \(b\)，做上面的算法即可

为什么不用枚举 \(x\rightarrow c\) 的情况，在考虑 \(x\rightarrow a,x\rightarrow b\) 的时候，已经考虑了当前这位在答案中为所有字母的情况，所以就不需要再考虑 \(x\rightarrow c\) 了

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
namespace __DEBUG_UTIL__
{
	using namespace std;
	/* Primitive Datatypes Print */
	void print(const char *x) { cerr << x; }
	void print(bool x) { cerr << (x ? "T" : "F"); }
	void print(char x) { cerr << '\'' << x << '\''; }
	void print(signed short int x) { cerr << x; }
	void print(unsigned short int x) { cerr << x; }
	void print(signed int x) { cerr << x; }
	void print(unsigned int x) { cerr << x; }
	void print(signed long int x) { cerr << x; }
	void print(unsigned long int x) { cerr << x; }
	void print(signed long long int x) { cerr << x; }
	void print(unsigned long long int x) { cerr << x; }
	void print(float x) { cerr << x; }
	void print(double x) { cerr << x; }
	void print(long double x) { cerr << x; }
	void print(string x) { cerr << '\"' << x << '\"'; }
	template <size_t N>
	void print(bitset<N> x) { cerr << x; }
	void print(vector<bool> v)
	{ /* Overloaded this because stl optimizes vector<bool> by using
		  _Bit_reference instead of bool to conserve space. */
		int f = 0;
		cerr << '{';
		for (auto &&i : v)
			cerr << (f++ ? "," : "") << (i ? "T" : "F");
		cerr << "}";
	}
	/* Templates Declarations to support nested datatypes */
	template <typename T>
	void print(T &&x);
	template <typename T>
	void print(vector<vector<T>> mat);
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M]);
	template <typename F, typename S>
	void print(pair<F, S> x);
	template <typename T, size_t N>
	struct Tuple;
	template <typename T>
	struct Tuple<T, 1>;
	template <typename... Args>
	void print(tuple<Args...> t);
	template <typename... T>
	void print(priority_queue<T...> pq);
	template <typename T>
	void print(stack<T> st);
	template <typename T>
	void print(queue<T> q);
	/* Template Datatypes Definitions */
	template <typename T>
	void print(T &&x)
	{
		/*  This works for every container that supports range-based loop
			i.e. vector, set, map, oset, omap, dequeue */
		int f = 0;
		cerr << '{';
		for (auto &&i : x)
			cerr << (f++ ? "," : ""), print(i);
		cerr << "}";
	}
	template <typename T>
	void print(vector<vector<T>> mat)
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M])
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename F, typename S>
	void print(pair<F, S> x)
	{
		cerr << '(';
		print(x.first);
		cerr << ',';
		print(x.second);
		cerr << ')';
	}
	template <typename T, size_t N>
	struct Tuple
	{
		static void printTuple(T t)
		{
			Tuple<T, N - 1>::printTuple(t);
			cerr << ",", print(get<N - 1>(t));
		}
	};
	template <typename T>
	struct Tuple<T, 1>
	{
		static void printTuple(T t) { print(get<0>(t)); }
	};
	template <typename... Args>
	void print(tuple<Args...> t)
	{
		cerr << "(";
		Tuple<decltype(t), sizeof...(Args)>::printTuple(t);
		cerr << ")";
	}
	template <typename... T>
	void print(priority_queue<T...> pq)
	{
		int f = 0;
		cerr << '{';
		while (!pq.empty())
			cerr << (f++ ? "," : ""), print(pq.top()), pq.pop();
		cerr << "}";
	}
	template <typename T>
	void print(stack<T> st)
	{
		int f = 0;
		cerr << '{';
		while (!st.empty())
			cerr << (f++ ? "," : ""), print(st.top()), st.pop();
		cerr << "}";
	}
	template <typename T>
	void print(queue<T> q)
	{
		int f = 0;
		cerr << '{';
		while (!q.empty())
			cerr << (f++ ? "," : ""), print(q.front()), q.pop();
		cerr << "}";
	}
	/* Printer functions */
	void printer(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printer(const char *names, T &&head, V &&...tail)
	{
		/* Using && to capture both lvalues and rvalues */
		int i = 0;
		for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
			if (names[i] == '(' or names[i] == '<' or names[i] == '{')
				bracket++;
			else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
				bracket--;
		cerr.write(names, i) << " = ";
		print(head);
		if (sizeof...(tail))
			cerr << " ||", printer(names + i + 1, tail...);
		else
			cerr << "]\n";
	}
	/* PrinterArr */
	void printerArr(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printerArr(const char *names, T arr[], size_t N, V... tail)
	{
		size_t ind = 0;
		for (; names[ind] and names[ind] != ','; ind++)
			cerr << names[ind];
		for (ind++; names[ind] and names[ind] != ','; ind++)
			;
		cerr << " = {";
		for (size_t i = 0; i < N; i++)
			cerr << (i ? "," : ""), print(arr[i]);
		cerr << "}";
		if (sizeof...(tail))
			cerr << " ||", printerArr(names + ind + 1, tail...);
		else
			cerr << "]\n";
	}
}
#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__)
#define debugArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...)
#define debugArr(...)
#endif
// #define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
	if (a > b)
		return a;
	return b;
}
int min(int a, int b)
{
	if (a < b)
		return a;
	return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 1e5 + 10;

struct lim
{
	int x, y;
	char a, b;
} lim[N];
int n, m, d;
char s[N];
vector<int> pos;
char c1[N], c2[N];

namespace twosat
{
#define maxn 1000010
	struct edge
	{
		int to, nxt;
	} e[maxn];
	int head[maxn], edge_cnt;
	void add(int from, int to)
	{
		e[++edge_cnt] = (edge){to, head[from]};
		head[from] = edge_cnt;
	}
	int dfn_cnt, co_cnt, top;
	int dfn[maxn], low[maxn], co[maxn], st[maxn];
	bool vis[maxn];
	void tarjan(int x)
	{
		dfn[x] = low[x] = ++dfn_cnt;
		st[++top] = x;
		vis[x] = true;
		for (int i = head[x]; i; i = e[i].nxt)
		{
			int y = e[i].to;
			if (!dfn[y])
			{
				tarjan(y);
				;
				low[x] = min(low[x], low[y]);
			}
			else if (vis[y])
				low[x] = min(low[x], dfn[y]);
		}
		if (low[x] == dfn[x])
		{
			co_cnt++;
			int now;
			do
			{
				now = st[top--];
				vis[now] = false;
				co[now] = co_cnt;
			} while (now != x);
		}
	}
	bool check()
	{
		for (int i = 1; i <= 2 * n; ++i)
			if (!dfn[i])
				tarjan(i);
		for (int i = 1; i <= n; ++i)
			if (co[i] == co[i + n])
				return false;
		return true;
	}
	void init()
	{
		edge_cnt = dfn_cnt = co_cnt = top = 0;
		memset(st, 0, sizeof(st));
		memset(co, 0, sizeof(co));
		memset(dfn, 0, sizeof(dfn));
		memset(low, 0, sizeof(low));
		memset(vis, 0, sizeof(vis));
		memset(head, 0, sizeof(head));
	}
}

void solve()
{
	cin >> n >> d;
	cin >> (s + 1);
	rep(i, 1, n)
	{
		if (s[i] == 'x')
			pos.push_back(i);
		if (s[i] == 'a')
		{
			c1[i] = 'b';
			c2[i] = 'c';
		}
		if (s[i] == 'b')
		{
			c1[i] = 'a';
			c2[i] = 'c';
		}
		if (s[i] == 'c')
		{
			c1[i] = 'a';
			c2[i] = 'b';
		}
	}
	cin >> m;
	rep(i, 1, m)
	{
		cin >> lim[i].x >> lim[i].a >> lim[i].y >> lim[i].b;
		lim[i].a -= 'A' - 'a';
		lim[i].b -= 'A' - 'a';
	}
	rep(msk, 0, (1 << d) - 1)
	{
		rep(i, 0, d - 1)
		{
			if (msk & (1 << i))
			{
				s[pos[i]] = 'a';
				c1[pos[i]] = 'b';
				c2[pos[i]] = 'c';
			}
			else
			{
				s[pos[i]] = 'b';
				c1[pos[i]] = 'a';
				c2[pos[i]] = 'c';
			}
		}
		twosat::init();
		rep(i, 1, m)
		{
			if (s[lim[i].x] == lim[i].a)
				continue;
			if (s[lim[i].y] == lim[i].b)
				twosat::add(lim[i].x + (c2[lim[i].x] == lim[i].a) * n, lim[i].x + (c1[lim[i].x] == lim[i].a) * n);
			else
			{
				twosat::add(lim[i].x + (c2[lim[i].x] == lim[i].a) * n, lim[i].y + (c2[lim[i].y] == lim[i].b) * n);
				twosat::add(lim[i].y + (c1[lim[i].y] == lim[i].b) * n, lim[i].x + (c1[lim[i].x] == lim[i].a) * n);
			}
		}
		if (twosat::check())
		{
			rep(i, 1, n)
			{
				if (twosat::co[i] > twosat::co[i + n])
					cout << (char)(c2[i] - 'a' + 'A');
				else
					cout << (char)(c1[i] - 'a' + 'A');
			}
			return;
		}
	}
	cout << "-1" << endl;
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int testcase = 1;
	// cin >> testcase;
	while (testcase--)
		solve();
#ifndef ONLINE_JUDGE
	cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
	cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
	return 0;
}

J P4006 小 Y 和二叉树

贪心的选择最小的 \(deg\leq 2\) 的点作为遍历序列的第一个点

然后分两种

  1. 下一个点为当前点的右子树
  2. 下一个点为当前点的祖先节点

考虑分类讨论这个东西

因为一开始的点是确定的，那么由一个点出发的子树的序列的第一个数可以 \(dp\) 求

如果 \(deg_x=2\)，将当前点出发，连向的 \(dp\) 值较小的挂到右子树，否则挂为父亲

否则根据 \(dp_v<v\) 分类

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
namespace __DEBUG_UTIL__
{
	using namespace std;
	/* Primitive Datatypes Print */
	void print(const char *x) { cerr << x; }
	void print(bool x) { cerr << (x ? "T" : "F"); }
	void print(char x) { cerr << '\'' << x << '\''; }
	void print(signed short int x) { cerr << x; }
	void print(unsigned short int x) { cerr << x; }
	void print(signed int x) { cerr << x; }
	void print(unsigned int x) { cerr << x; }
	void print(signed long int x) { cerr << x; }
	void print(unsigned long int x) { cerr << x; }
	void print(signed long long int x) { cerr << x; }
	void print(unsigned long long int x) { cerr << x; }
	void print(float x) { cerr << x; }
	void print(double x) { cerr << x; }
	void print(long double x) { cerr << x; }
	void print(string x) { cerr << '\"' << x << '\"'; }
	template <size_t N>
	void print(bitset<N> x) { cerr << x; }
	void print(vector<bool> v)
	{ /* Overloaded this because stl optimizes vector<bool> by using
		  _Bit_reference instead of bool to conserve space. */
		int f = 0;
		cerr << '{';
		for (auto &&i : v)
			cerr << (f++ ? "," : "") << (i ? "T" : "F");
		cerr << "}";
	}
	/* Templates Declarations to support nested datatypes */
	template <typename T>
	void print(T &&x);
	template <typename T>
	void print(vector<vector<T>> mat);
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M]);
	template <typename F, typename S>
	void print(pair<F, S> x);
	template <typename T, size_t N>
	struct Tuple;
	template <typename T>
	struct Tuple<T, 1>;
	template <typename... Args>
	void print(tuple<Args...> t);
	template <typename... T>
	void print(priority_queue<T...> pq);
	template <typename T>
	void print(stack<T> st);
	template <typename T>
	void print(queue<T> q);
	/* Template Datatypes Definitions */
	template <typename T>
	void print(T &&x)
	{
		/*  This works for every container that supports range-based loop
			i.e. vector, set, map, oset, omap, dequeue */
		int f = 0;
		cerr << '{';
		for (auto &&i : x)
			cerr << (f++ ? "," : ""), print(i);
		cerr << "}";
	}
	template <typename T>
	void print(vector<vector<T>> mat)
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M])
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename F, typename S>
	void print(pair<F, S> x)
	{
		cerr << '(';
		print(x.first);
		cerr << ',';
		print(x.second);
		cerr << ')';
	}
	template <typename T, size_t N>
	struct Tuple
	{
		static void printTuple(T t)
		{
			Tuple<T, N - 1>::printTuple(t);
			cerr << ",", print(get<N - 1>(t));
		}
	};
	template <typename T>
	struct Tuple<T, 1>
	{
		static void printTuple(T t) { print(get<0>(t)); }
	};
	template <typename... Args>
	void print(tuple<Args...> t)
	{
		cerr << "(";
		Tuple<decltype(t), sizeof...(Args)>::printTuple(t);
		cerr << ")";
	}
	template <typename... T>
	void print(priority_queue<T...> pq)
	{
		int f = 0;
		cerr << '{';
		while (!pq.empty())
			cerr << (f++ ? "," : ""), print(pq.top()), pq.pop();
		cerr << "}";
	}
	template <typename T>
	void print(stack<T> st)
	{
		int f = 0;
		cerr << '{';
		while (!st.empty())
			cerr << (f++ ? "," : ""), print(st.top()), st.pop();
		cerr << "}";
	}
	template <typename T>
	void print(queue<T> q)
	{
		int f = 0;
		cerr << '{';
		while (!q.empty())
			cerr << (f++ ? "," : ""), print(q.front()), q.pop();
		cerr << "}";
	}
	/* Printer functions */
	void printer(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printer(const char *names, T &&head, V &&...tail)
	{
		/* Using && to capture both lvalues and rvalues */
		int i = 0;
		for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
			if (names[i] == '(' or names[i] == '<' or names[i] == '{')
				bracket++;
			else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
				bracket--;
		cerr.write(names, i) << " = ";
		print(head);
		if (sizeof...(tail))
			cerr << " ||", printer(names + i + 1, tail...);
		else
			cerr << "]\n";
	}
	/* PrinterArr */
	void printerArr(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printerArr(const char *names, T arr[], size_t N, V... tail)
	{
		size_t ind = 0;
		for (; names[ind] and names[ind] != ','; ind++)
			cerr << names[ind];
		for (ind++; names[ind] and names[ind] != ','; ind++)
			;
		cerr << " = {";
		for (size_t i = 0; i < N; i++)
			cerr << (i ? "," : ""), print(arr[i]);
		cerr << "}";
		if (sizeof...(tail))
			cerr << " ||", printerArr(names + ind + 1, tail...);
		else
			cerr << "]\n";
	}
}
#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__)
#define debugArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...)
#define debugArr(...)
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
	if (a > b)
		return a;
	return b;
}
int min(int a, int b)
{
	if (a < b)
		return a;
	return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 1e6 + 10;

int n;
vector<int> g[N];
int rt = -1;
int dp[N];

void dfs(int x, int fa)
{
	if (g[x].size() <= 2)
		dp[x] = x;
	for (auto v : g[x])
	{
		if (v == fa)
			continue;
		dfs(v, x);
		dp[x] = min(dp[x], dp[v]);
	}
}

void calc(int x, int fa, bool flag)
{
	if (flag)
	{
		bool fl = false;
		if (g[x].size() < 3)
		{
			for (auto v : g[x])
			{
				if (v == fa)
					continue;
				if (dp[v] > x)
				{
					cout << x << ' ';
					fl = true;
				}
				calc(v, x, flag);
			}
		}
		else
		{
			bool fr = true;
			for (auto v : g[x])
			{
				if (v == fa)
					continue;
				calc(v, x, flag);
				if (fr)
				{
					cout << x << ' ';
					fr = false;
					fl = true;
				}
			}
		}
		if (!fl)
			cout << x << ' ';
		return;
	}
	cout << x << ' ';
	if (g[x].size() == 2)
	{
		for (auto v : g[x])
			if (v != fa)
				calc(v, x, dp[v] < v);
	}
	else if (g[x].size() == 3)
	{
		bool fr = true;
		for (auto v : g[x])
		{
			if (v != fa)
			{
				calc(v, x, fr);
				fr = false;
			}
		}
	}
}

bool cmp(int x, int y)
{
	return dp[x] < dp[y];
}

void solve()
{
	cin >> n;
	rep(i, 1, n)
	{
		int x;
		cin >> x;
		rep(j, 1, x)
		{
			int v;
			cin >> v;
			g[i].push_back(v);
		}
		if (g[i].size() <= 2 && rt == -1)
			rt = i;
	}
	memset(dp, 0x3f, sizeof(dp));
	g[rt].push_back(rt);
	dfs(rt, 0);
	rep(i, 1, n) sort(ALL(g[i]), cmp);
	calc(rt, rt, 0);
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
	// freopen("binary.in", "r", stdin);
	// freopen("binary.out", "w", stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int testcase = 1;
	// cin >> testcase;
	while (testcase--)
		solve();
#ifndef ONLINE_JUDGE
	cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
	cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
	return 0;
}

P7515 [省选联考 2021 A 卷] 矩阵游戏

先忽略上下界的条件，构造一个可行的方案，考虑怎么调整

发现可以进行这样的操作

\[\begin{bmatrix} r_1-c_1,-r_1+c_2,\cdots,-r_1+c_m\\ -r_2+c_1,r_2-c_2,\cdots,r_2-c_m\\ \cdots \\ r_{n-1}-c_1,-r_n+c_2,\cdots,-r_{n-1}+c_m\\ -r_n+c_1,r_n-c_2,\cdots,r_n-c_m\\ \end{bmatrix} \]

使得最后的数组合法

这样其实相当于每个格子都给出了一个不等式，然后差分约束即可

code 
// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#else
#define debug(x)
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
namespace __DEBUG_UTIL__
{
	using namespace std;
	/* Primitive Datatypes Print */
	void print(const char *x) { cerr << x; }
	void print(bool x) { cerr << (x ? "T" : "F"); }
	void print(char x) { cerr << '\'' << x << '\''; }
	void print(signed short int x) { cerr << x; }
	void print(unsigned short int x) { cerr << x; }
	void print(signed int x) { cerr << x; }
	void print(unsigned int x) { cerr << x; }
	void print(signed long int x) { cerr << x; }
	void print(unsigned long int x) { cerr << x; }
	void print(signed long long int x) { cerr << x; }
	void print(unsigned long long int x) { cerr << x; }
	void print(float x) { cerr << x; }
	void print(double x) { cerr << x; }
	void print(long double x) { cerr << x; }
	void print(string x) { cerr << '\"' << x << '\"'; }
	template <size_t N>
	void print(bitset<N> x) { cerr << x; }
	void print(vector<bool> v)
	{ /* Overloaded this because stl optimizes vector<bool> by using
		  _Bit_reference instead of bool to conserve space. */
		int f = 0;
		cerr << '{';
		for (auto &&i : v)
			cerr << (f++ ? "," : "") << (i ? "T" : "F");
		cerr << "}";
	}
	/* Templates Declarations to support nested datatypes */
	template <typename T>
	void print(T &&x);
	template <typename T>
	void print(vector<vector<T>> mat);
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M]);
	template <typename F, typename S>
	void print(pair<F, S> x);
	template <typename T, size_t N>
	struct Tuple;
	template <typename T>
	struct Tuple<T, 1>;
	template <typename... Args>
	void print(tuple<Args...> t);
	template <typename... T>
	void print(priority_queue<T...> pq);
	template <typename T>
	void print(stack<T> st);
	template <typename T>
	void print(queue<T> q);
	/* Template Datatypes Definitions */
	template <typename T>
	void print(T &&x)
	{
		/*  This works for every container that supports range-based loop
			i.e. vector, set, map, oset, omap, dequeue */
		int f = 0;
		cerr << '{';
		for (auto &&i : x)
			cerr << (f++ ? "," : ""), print(i);
		cerr << "}";
	}
	template <typename T>
	void print(vector<vector<T>> mat)
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename T, size_t N, size_t M>
	void print(T (&mat)[N][M])
	{
		int f = 0;
		cerr << "\n~~~~~\n";
		for (auto &&i : mat)
		{
			cerr << setw(2) << left << f++, print(i), cerr << "\n";
		}
		cerr << "~~~~~\n";
	}
	template <typename F, typename S>
	void print(pair<F, S> x)
	{
		cerr << '(';
		print(x.first);
		cerr << ',';
		print(x.second);
		cerr << ')';
	}
	template <typename T, size_t N>
	struct Tuple
	{
		static void printTuple(T t)
		{
			Tuple<T, N - 1>::printTuple(t);
			cerr << ",", print(get<N - 1>(t));
		}
	};
	template <typename T>
	struct Tuple<T, 1>
	{
		static void printTuple(T t) { print(get<0>(t)); }
	};
	template <typename... Args>
	void print(tuple<Args...> t)
	{
		cerr << "(";
		Tuple<decltype(t), sizeof...(Args)>::printTuple(t);
		cerr << ")";
	}
	template <typename... T>
	void print(priority_queue<T...> pq)
	{
		int f = 0;
		cerr << '{';
		while (!pq.empty())
			cerr << (f++ ? "," : ""), print(pq.top()), pq.pop();
		cerr << "}";
	}
	template <typename T>
	void print(stack<T> st)
	{
		int f = 0;
		cerr << '{';
		while (!st.empty())
			cerr << (f++ ? "," : ""), print(st.top()), st.pop();
		cerr << "}";
	}
	template <typename T>
	void print(queue<T> q)
	{
		int f = 0;
		cerr << '{';
		while (!q.empty())
			cerr << (f++ ? "," : ""), print(q.front()), q.pop();
		cerr << "}";
	}
	/* Printer functions */
	void printer(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printer(const char *names, T &&head, V &&...tail)
	{
		/* Using && to capture both lvalues and rvalues */
		int i = 0;
		for (size_t bracket = 0; names[i] != '\0' and (names[i] != ',' or bracket != 0); i++)
			if (names[i] == '(' or names[i] == '<' or names[i] == '{')
				bracket++;
			else if (names[i] == ')' or names[i] == '>' or names[i] == '}')
				bracket--;
		cerr.write(names, i) << " = ";
		print(head);
		if (sizeof...(tail))
			cerr << " ||", printer(names + i + 1, tail...);
		else
			cerr << "]\n";
	}
	/* PrinterArr */
	void printerArr(const char *) {} /* Base Recursive */
	template <typename T, typename... V>
	void printerArr(const char *names, T arr[], size_t N, V... tail)
	{
		size_t ind = 0;
		for (; names[ind] and names[ind] != ','; ind++)
			cerr << names[ind];
		for (ind++; names[ind] and names[ind] != ','; ind++)
			;
		cerr << " = {";
		for (size_t i = 0; i < N; i++)
			cerr << (i ? "," : ""), print(arr[i]);
		cerr << "}";
		if (sizeof...(tail))
			cerr << " ||", printerArr(names + ind + 1, tail...);
		else
			cerr << "]\n";
	}
}
#ifndef ONLINE_JUDGE
#define debug(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printer(#__VA_ARGS__, __VA_ARGS__)
#define debugArr(...) std::cerr << __LINE__ << ": [", __DEBUG_UTIL__::printerArr(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...)
#define debugArr(...)
#endif
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
	if (a > b)
		return a;
	return b;
}
int min(int a, int b)
{
	if (a < b)
		return a;
	return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 6e2 + 10;

int n, m;
int a[N][N], b[N][N];
vector<pii> g[N];
int dis[N];
bool vis[N];
int cnt[N];

void solve()
{
	cin >> n >> m;
	rep(i, 0, n + m) g[i].clear();
	mms(a, 0);
	rep(i, 1, n)
	{
		rep(j, 1, m)
		{
			if (i < n && j < m)
				cin >> b[i][j];
			if (i != 1 && j != 1)
				a[i][j] = b[i - 1][j - 1] - a[i - 1][j - 1] - a[i - 1][j] - a[i][j - 1];
		}
	}
	// debug(a);
	rep(i, 1, n)
	{
		rep(j, 1, m)
		{
			if ((i + j) & 1)
			{
				g[i].push_back({j + n, a[i][j]});
				g[j + n].push_back({i, 1e6 - a[i][j]});
			}
			else
			{
				g[i].push_back({j + n, 1e6 - a[i][j]});
				g[j + n].push_back({i, a[i][j]});
			}
		}
	}
	rep(i, 1, n + m)
	{
		g[0].push_back({i, 0});
	}
	queue<int> q;
	memset(dis, 0x3f, sizeof(dis));
	mms(vis, 0);
	q.push(0);
	dis[0] = 0;
	vis[0] = true;
	while (!q.empty())
	{
		int x = q.front();
		q.pop();
		vis[x] = false;
		for (auto [v, w] : g[x])
		{
			if (dis[v] > dis[x] + w)
			{
				dis[v] = dis[x] + w;
				cnt[v] = cnt[x] + 1;
				if (cnt[v] > n + m)
				{
					NO;
					return;
				}
				if (!vis[v])
				{
					q.push(v);
					vis[v] = true;
				}
			}
		}
	}
	YES;
	rep(i, 1, n)
	{
		rep(j, 1, m)
		{
			if ((i + j) & 1)
				cout << a[i][j] + dis[i] - dis[j + n] << ' ';
			else
				cout << a[i][j] - dis[i] + dis[j + n] << ' ';
		}
		cout << endl;
	}
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int testcase = 1;
	cin >> testcase;
	while (testcase--)
		solve();
#ifndef ONLINE_JUDGE
	cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
	cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
	return 0;
}

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