#799334 (C++17) No.1087 転倒数の転倒数

• 問題: No.1087 転倒数の転倒数
• ユーザー: tokusakurai
• 提出日時: 2022-09-20 20:46:38
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 57 ms / 2,000 ms
• コード長: 7,586 bytes
• コンパイル時間: 2,093 ms
• コンパイル使用メモリ: 206,200 KB
• 最終ジャッジ日時: 2025-02-07 13:07:55
• ジャッジサーバーID （参考情報）: judge2 / judge1

ファイルパターン	結果
sample	AC * 6
other	AC * 31

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <typename T>
struct Binary_Indexed_Tree {
    vector<T> bit;
    const int n;

    Binary_Indexed_Tree(const vector<T> &v) : n((int)v.size()) {
        bit.resize(n + 1);
        copy(begin(v), end(v), begin(bit) + 1);
        for (int a = 2; a <= n; a <<= 1) {
            for (int b = a; b <= n; b += a) bit[b] += bit[b - a / 2];
        }
    }

    Binary_Indexed_Tree(int n, const T &x) : Binary_Indexed_Tree(vector<T>(n, x)) {}

    void add(int i, const T &x) {
        for (i++; i <= n; i += (i & -i)) bit[i] += x;
    }

    void change(int i, const T &x) { add(i, x - query(i, i + 1)); }

    T sum(int i) const {
        i = min(i, n);
        T ret = 0;
        for (; i > 0; i -= (i & -i)) ret += bit[i];
        return ret;
    }

    T query(int l, int r) const {
        if (l >= r) return 0;
        return sum(r) - sum(l);
    }

    T operator[](int i) const { return query(i, i + 1); }

    // v[0]+...+v[r] >= x を満たす最小の r (なければ n)
    int lower_bound(T x) const {
        int ret = 0;
        for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
            if (ret + (1 << k) <= n && bit[ret + (1 << k)] < x) x -= bit[ret += (1 << k)];
        }
        return ret;
    }

    // v[0]+...+v[r] > x を満たす最小の r (なければ n)
    int upper_bound(T x) const {
        int ret = 0;
        for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
            if (ret + (1 << k) <= n && bit[ret + (1 << k)] <= x) x -= bit[ret += (1 << k)];
        }
        return ret;
    }
};

template <typename T>
long long inversion_number(const vector<T> &a) {
    int n = a.size();
    vector<int> v(n);
    iota(begin(v), end(v), 0);
    sort(begin(v), end(v), [&](int i, int j) {
        if (a[i] != a[j]) return a[i] < a[j];
        return i < j;
    });
    Binary_Indexed_Tree<int> bit(n, 0);
    long long ret = 0;
    for (int i = 0; i < n; i++) {
        ret += bit.query(v[i] + 1, n);
        bit.add(v[i], 1);
    }
    return ret;
}

// a を b に変換するのに必要な最小バブルソート回数
template <typename T>
long long inversion_number(const vector<T> &a, const vector<T> &b) {
    int n = a.size();
    assert(b.size() == n);
    vector<int> u(n), v(n);
    iota(begin(u), end(u), 0);
    sort(begin(u), end(u), [&](int i, int j) {
        if (a[i] != a[j]) return a[i] < a[j];
        return i < j;
    });
    iota(begin(v), end(v), 0);
    sort(begin(v), end(v), [&](int i, int j) {
        if (b[i] != b[j]) return b[i] < b[j];
        return i < j;
    });
    vector<int> w(n);
    for (int i = 0; i < n; i++) {
        if (a[u[i]] != b[v[i]]) return -1;
        w[v[i]] = u[i];
    }
    Binary_Indexed_Tree<int> bit(n, 0);
    long long ret = 0;
    for (int i = 0; i < n; i++) {
        ret += bit.query(w[i] + 1, n);
        bit.add(w[i], 1);
    }
    return ret;
}

int judge(const vector<vector<int>> &a) {
    int N = sz(a);
    vector<int> x(N), y(N);
    rep(i, N) x[i] = inversion_number(a[i]);
    rep(j, N) {
        vector<int> v(N);
        rep(i, N) v[i] = a[i][j];
        y[j] = inversion_number(v);
    }
    return inversion_number(x) + inversion_number(y);
}

int main() {
    int N, K;
    cin >> N >> K;

    if (K > N * (N - 1)) {
        cout << "No\n";
        return 0;
    }

    cout << "Yes\n";

    if (K == 1) {
        vector<vector<int>> a(N, vector<int>(N, 0));
        a[N - 2][N - 2] = 1;
        rep(i, N) a[N - 1][i] = 1;
        rep(i, N) print(a[i]);
        // if (judge(a) != K) cout << "-1\n";
        return 0;
    }
    if (K == 3) {
        vector<vector<int>> a(N, vector<int>(N, 0));
        rep(i, N) a[N - 2][i] = 1;
        rep(i, N) a[N - 1][i] = 2;
        a[N - 3][N - 3] = 1;
        a[N - 2][N - 2] = 2;
        rep(i, N) print(a[i]);
        // if (judge(a) != K) cout << "-1\n";
        return 0;
    }

    int L = K / 2;

    vector<int> P(N);
    iota(all(P), 0);

    rep(i, N) {
        per2(j, i, N - 1) {
            if (L > 0) {
                swap(P[j], P[j + 1]);
                L--;
            }
        }
    }
    // print(P);

    if (K & 1) {
        per(i, N - 1) {
            if (P[i] < P[i + 1]) {
                swap(P[i], P[i + 1]);
                break;
            }
        }
    }

    if (K == N * (N - 1) - 3) {
        rep(i, N) P[i] = N - 1 - i;
        swap(P[0], P[1]);
    }
    // print(P);

    vector<vector<int>> a(N, vector<int>(N, 1));
    rep(i, N) a[i][P[i]] = 0;

    if (K & 1) {
        int x = -1;
        rep(i, N) {
            if (P[i] == N - 1) x = i;
        }
        int y = P[N - 2];
        a[x][y] = 2;
    }

    rep(i, N) print(a[i]);

    // if (judge(a) != K) cout << "-1\n";
}