Hello 2022 A-E

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视频版讲解

A. Stable Arrangement of Rooks

贪心

#include <bits/stdc++.h>
using namespace std;
#define inc(x, l, r) for (int x = l; x <= r; x++)

void solve() {
    int n, x;
    cin >> n >> x;
    if ((n + 1) / 2 < x) {
        cout << "-1\n";
    } else {
        inc(i, 1, n) {
            inc(j, 1, n) {
                if ((i & 1) && (i + 1) / 2 <= x && i == j)
                    cout << 'R';
                else
                    cout << '.';
            }
            cout << '\n';
        }
    }
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        solve();
    }
}

B. Integers Shop

分类, 模拟

#include <bits/stdc++.h>
using namespace std;
#define inc(x, l, r) for (int x = l; x <= r; x++)

const int inf = INT_MAX;

void solve() {
    int n, l, r, c1, c2;
    cin >> n >> l >> r >> c1;
    c2 = c1;
    int Cost = c1;
    cout << Cost << "\n";
    inc(i, 2, n) {
        int x, y, c;
        cin >> x >> y >> c;
        int f = 0;
        if (x < l) {
            c1 = c;
            l = x;
            f = 1;
        } else if (x == l) {
            c1 = min(c1, c);
        }
        if (y > r) {
            c2 = c;
            r = y;
            f = 1;
        } else if (y == r) {
            c2 = min(c2, c);
        }
        if (f) {
            if (l == x && r == y) {
                Cost = c;
            } else {
                Cost = inf;
            }
        } else {
            if (l == x && r == y) {
                Cost = min(Cost, c);
            }
        }
        cout << min(Cost, c1 + c2) << "\n";
    }
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        solve();
    }
}

C. Hidden Permutations

置换, 环

#include <bits/stdc++.h>
using namespace std;
#define inc(x, l, r) for (int x = l; x <= r; x++)

const int maxn = 1e6 + 5;

int r[maxn];

void solve() {
    int n;
    cin >> n;
    inc(i, 1, n) r[i] = 0;
    int x;
    inc(i, 1, n) {
        if (!r[i]) {
            vector<int> v;
            while (1) {
                cout << "? " << i << "\n";
                cout.flush();
                cin >> x;
                if (x == i)
                    break;
            }
            while (1) {
                cout << "? " << i << "\n";
                cout.flush();
                cin >> x;
                v.push_back(x);
                if (x == i)
                    break;
            }
            v.push_back(v[0]);
            int p = i;
            inc(i, 0, (int)v.size() - 2) {
                r[p] = v[i];
                p = v[i];
            }
        }
    }
    cout << "!";
    inc(i, 1, n) cout << " " << r[i];
    cout << "\n";
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        solve();
    }
}

D. The Winter Hike

镜像, 思维

#include <bits/stdc++.h>
using namespace std;
#define inc(x, l, r) for (int x = l; x <= r; x++)
#define ll long long

const int maxn = 1e3 + 5;

int a[maxn][maxn];

void solve() {
    int n;
    cin >> n;
    inc(i, 1, 2 * n) inc(j, 1, 2 * n) cin >> a[i][j];
    ll res = 0;
    inc(i, 1, n) inc(j, 1, n) res += a[i + n][j + n];
    cout << res + min({a[n][2 * n], a[n + 1][1], a[n][n + 1], a[n + 1][n],
                       a[1][2 * n], a[2 * n][1], a[1][n + 1], a[2 * n][n]})
         << "\n";
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        solve();
    }
}

E. New School

二分, 前缀和/线段树

#include <bits/stdc++.h>
using namespace std;
#define inc(x, l, r) for (int x = l; x <= r; x++)
#define dec(x, l, r) for (int x = l; x >= r; x--)
#define ll long long
#define pii pair<int, int>
#define fi first
#define se second

const int maxn = 1e6 + 5;

int a[maxn], val[maxn], suf[maxn];
vector<int> b[maxn];
pii st[maxn];
ll pre[maxn], T[maxn];

ll sum(int l, int r) {
    if (l > r)
        return 0;
    return pre[r] - pre[l - 1];
}

void solve() {
    int n, m;
    cin >> n >> m;
    inc(i, 1, n) cin >> a[i];
    inc(i, 1, m) {
        int k;
        cin >> k;
        b[i].resize(k);
        inc(j, 0, k - 1) cin >> b[i][j];
        T[i] = 0;
        inc(j, 0, k - 1) T[i] += b[i][j];
        val[i] = (T[i] + k - 1) / k;
    }
    inc(i, 1, m) st[i] = {val[i], 1};
    inc(i, 1, n) st[m + i] = {a[i], 2};
    sort(st + 1, st + n + m + 1);
    suf[n + m + 1] = 0;
    int r = 1;
    dec(i, n + m, 1) {
        if (st[i].se == 2)
            suf[i] = suf[i + 1] + 1;
        else
            suf[i] = suf[i + 1] - 1;
        if (suf[i] == -1)
            r = min(r, 0);
        if (suf[i] < -1)
            r = min(r, -1);
    }
    if (r == -1) {
        inc(i, 1, m) for (auto e : b[i]) cout << '0';
        cout << "\n";
        inc(i, 1, m) b[i].clear();
        return;
    }

    pre[0] = 0;
    if (r) {
        inc(i, 1, n + m + 1) pre[i] = pre[i - 1] + (int)(suf[i] == 0);
    } else {
        inc(i, 1, n + m + 1) pre[i] = pre[i - 1] + (int)(suf[i] == -1);
    }
    inc(i, 1, m) for (auto e : b[i]) {
        if (r) {
            int rf = (T[i] - e + b[i].size() - 2) / (b[i].size() - 1);
            if (rf <= val[i]) {
                cout << 1;
                continue;
            }
            int r = lower_bound(st + 1, st + n + m + 1, pii(rf, 0)) - st;
            int l = lower_bound(st + 1, st + n + m + 1, pii(val[i], 0)) - st;
            if (sum(l + 1, r))
                cout << 0;
            else
                cout << 1;
        } else {
            int rf = (T[i] - e + b[i].size() - 2) / (b[i].size() - 1);
            if (rf >= val[i]) {
                cout << 0;
                continue;
            }
            int l = lower_bound(st + 1, st + n + m + 1, pii(rf, 0)) - st;
            int r = lower_bound(st + 1, st + n + m + 1, pii(val[i], 0)) - st;
            if (sum(l + 1, r) == sum(1, n + m + 1))
                cout << 1;
            else
                cout << 0;
        }
    }
    cout << "\n";
    inc(i, 1, m) b[i].clear();
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        solve();
    }
}