2018 IME Tryouts

比较简单的三星场，差一点AK

最近忙着面试，三个人都不在状态，我前期很C后期萎了，两个队友前期很萎后面很C，可能这就是队内文化8

题目链接：https://codeforces.com/gym/101858

---

A：

solver：zyh、lzh

#include <bits/stdc++.h>
using namespace std;
long long dp[2][8];
const long long M = 1e9 + 7;
int main() {
    int n;
    scanf("%d", &n);
    dp[1][0] = dp[1][6] = dp[1][3] = 1;
    for (int i = 2; i <= n; ++i) {
        int now = i & 1;
        int pre = (i - 1) & 1;
        dp[now][7] = (dp[pre][0] + dp[pre][6] + dp[pre][3]) % M;
        dp[now][6] = (dp[pre][1] + dp[pre][7]) % M;
        dp[now][5] = dp[pre][2];
        dp[now][4] = dp[pre][3];
        dp[now][3] = (dp[pre][4] + dp[pre][7]) % M;
        dp[now][2] = dp[pre][5];
        dp[now][1] = dp[pre][6];
        dp[now][0] = dp[pre][7];
        //cout<<dp[now][7]<<endl;
    }
    printf("%lld", dp[n & 1][7]);
}

B：

solver：czq

/* basic header */
#include <bits/stdc++.h>
/* define */
#define ll long long
#define pb emplace_back
#define mp make_pair
#define eps 1e-8
#define lson (curpos<<1)
#define rson (curpos<<1|1)
/* namespace */
using namespace std;
/* header end */

string s, ans = "";
int numC = 0, numS = 0;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> s;
    for (auto ch : s) {
        if (ch == 'C' && numC <= 1) {
            numC++, numS = 0;
            ans += 'B';
        } else if (ch == 'S' && numS <= 1) {
            numS++, numC = 0;
            ans += 'D';
        } else if (ch == 'C') {
            numC = 0, ans += 'P';
        } else if (ch == 'S') {
            numS = 0, ans += 'T';
        }
    }
    cout << ans << endl;
    return 0;
}

C：

solver：lzh

据说这个题随便剪一下枝就能过了，跑得飞起

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define ff first
#define ss second

int a[10][10], ok = 0;
int w[10][10], quyu[40], num[40];
int rvis[10][10], cvis[10][10], blockvis[10][10], quyuvis[40][10];
inline int getblock(int x, int y) {
    return (x + 1) / 2 * 2 - (y > 3 ? 0 : 1);
}
void dfs(int x, int y) {
    if (y == 7) {
        x++, y = 1;
        dfs(x, y);
        return;
    }
    if (ok)
        return;
    if (x == 7) {
        for (int i = 1; i <= 6; i++)
            for (int j = 1; j <= 6; j++)
                cout << a[i][j] << " \n"[j == 6];
        ok = 1;
        return;
    }

    if (num[w[x][y]] == 1) {
        int v = w[x][y], b = getblock(x, y), p = quyu[v];
        if (!rvis[x][p] && !cvis[y][p] && !blockvis[b][p] && !quyuvis[v][p]) {
            a[x][y] = p;
            quyu[v] = 0, num[v] = 0;
            rvis[x][p] = cvis[y][p] = blockvis[b][p] = quyuvis[v][p] = 1;
            dfs(x, y + 1);
            rvis[x][p] = cvis[y][p] = blockvis[b][p] = quyuvis[v][p] = 0;
            quyu[v] = p, num[v] = 1;
            a[x][y] = 0;
        }
        return;
    }
    for (int i = 1; i <= min(quyu[w[x][y]] - 1, 6); i++) {
        int v = w[x][y], b = getblock(x, y), p = i;
        if (!rvis[x][p] && !cvis[y][p] && !blockvis[b][p] && !quyuvis[v][p]) {
            a[x][y] = p;
            quyu[v] -= p, num[v]--;
            rvis[x][p] = cvis[y][p] = blockvis[b][p] = quyuvis[v][p] = 1;
            dfs(x, y + 1);
            rvis[x][p] = cvis[y][p] = blockvis[b][p] = quyuvis[v][p] = 0;
            quyu[v] += p, num[v]++;
            a[x][y] = 0;
        }
    }
}

int main() {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> quyu[i];
    for (int i = 1; i <= 6; i++)
        for (int j = 1, x; j <= 6; j++) {
            cin >> x;
            w[i][j] = x, num[x]++;
        }
    dfs(1, 1);
}

D：

solver：zyh、czq

#include <bits/stdc++.h>
using namespace std;
long long sum(long long x) {
    return x * (x + 1) / 2LL;
}
int main() {
    int T;
    scanf("%d", &T);
    while (T--) {
        long long n;
        scanf("%lld", &n);
        long long l = -1, r = (long long)sqrt(4 * (n + 1)) + 1;
        while (l + 1 < r) {
            long long mid = l + r >> 1;
            if (sum(mid) <= n) l = mid;
            else r = mid;
        }
        printf("%lld\n", l);
    }
    return 0;
}

E：

solver：lzh

最后绝杀AC，lzhnb

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define ff first
#define ss second

const int N = 1 << 18;
const double PI = acos(-1.0);

struct cpx {
    double x, y;
    cpx() {}
    cpx(double _x, double _y)
        : x(_x)
        , y(_y) {
    }
    cpx operator+(const cpx &b) const {
        return cpx(x + b.x, y + b.y);
    }
    cpx operator-(const cpx &b) const {
        return cpx(x - b.x, y - b.y);
    }
    cpx operator*(const cpx &b) const {
        return cpx(x * b.x - y * b.y, x * b.y + y * b.x);
    }
    cpx operator/(const int &b) const {
        return cpx(x / b, y / b);
    }
};

int rev[2 * N + 10];
void getrev(int len) {
    int bit = 0;
    while ((1 << bit) < len)
        bit++;
    for (int i = 0; i < len; i++)
        rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (bit - 1));
}

void fft(cpx x[], int len, int opt) {
    for (int i = 0; i < len; i++)
        if (i < rev[i])
            swap(x[i], x[rev[i]]);
    for (int mid = 1; mid < len; mid <<= 1) {
        cpx tmp(cos(PI / mid), opt * sin(PI / mid));
        for (int i = 0, add = mid << 1; i < len; i += add) {
            cpx base(1, 0);
            for (int j = i; j < i + mid; j++, base = base * tmp) {
                cpx a = x[j], b = base * x[j + mid];
                x[j] = a + b, x[j + mid] = a - b;
            }
        }
    }

    if (opt == -1)
        for (int i = 0; i < len; i++)
            x[i] = x[i] / len;
}

cpx ffta[2 * N + 10], fftb[2 * N + 10];
int solve(int a[], int b[], int lena, int lenb) {
    int len = 1;
    while (len < lena + lenb)
        len <<= 1;
    getrev(len);

    for (int i = 0; i < lena; i++)
        ffta[i] = cpx(a[i], 0);
    for (int i = lena; i < len; i++)
        ffta[i] = cpx(0, 0);
    for (int i = 0; i < lenb; i++)
        fftb[i] = cpx(b[i], 0);
    for (int i = lenb; i < len; i++)
        fftb[i] = cpx(0, 0);

    fft(ffta, len, 1), fft(fftb, len, 1);
    for (int i = 0; i < len; i++)
        ffta[i] = ffta[i] * fftb[i];
    fft(ffta, len, -1);
    return len;
}

char p[200010], t[200010];
ll dam[N * 2 + 10], ans[N];
const char s1[] = { "RNE" }, s2[] = { "ABC" };
int numa[200010], numb[200010], D[10];
int main() {
    int a, b, c, h;
    scanf("%d%d%d%d", &D[0], &D[1], &D[2], &h);
    scanf("%s%s", p + 1, t + 1);
    int n = strlen(p + 1), m = strlen(t + 1);
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j <= n; j++)
            numa[j] = numb[j] = 0;
        for (int j = 1; j <= n; j++)
            if (p[j] == s1[i])
                numa[j]++;
        for (int j = 1; j <= m; j++)
            if (t[j] == s2[i])
                numb[n - j + 1]++;
        int len = solve(numa, numb, n + 4, n + 4);
        for (int j = 0; j < len; j++)
            dam[j] += (ll)(ffta[j].x + 0.5) * D[i];
        //for (int j = 0; j < len; j++)
        //    printf("%d %d %lf\n", numa[j], numb[j], ffta[i].x);
    }
    int ansn = 0;
    for (int i = 0; i < 2 * N; i++) {
        ans[i % n] += dam[i];
    }
    for (int i = 0; i < n; i++) {
        if (ans[i] >= h)
            ansn++;
        //printf("%lld ", ans[i]);
    }
    int g = __gcd(ansn, n);
    printf("%d %d\n", ansn / g, n / g);
}

F：

solver：czq

很傻的并查集

/* basic header */
#include <bits/stdc++.h>
/* define */
#define ll long long
#define pb emplace_back
#define mp make_pair
#define eps 1e-8
#define lson (curpos<<1)
#define rson (curpos<<1|1)
/* namespace */
using namespace std;
/* header end */

const int MAXN = 1e5 + 10;
pair<int, int>edge[MAXN];
int n, m, cnt, fa[MAXN], p[MAXN], ans[MAXN];

int main() {
    scanf("%d%d", &n, &m); cnt = n;
    for (int i = 1; i <= n; i++) fa[i] = i;
    for (int i = 1, u, v; i <= m; i++) {
        scanf("%d%d", &u, &v);
        edge[i] = mp(u, v);
    }

    function<int(int)>findFa = [&](int cur)->int{
        return fa[cur] == cur ? cur : fa[cur] = findFa(fa[cur]);
    };

    for (int i = 1; i <= m; i++) scanf("%d", &p[i]);
    for (int i = m; i >= 1; i--) {
        ans[i] = cnt;
        int fa1 = findFa(edge[p[i]].first), fa2 = findFa(edge[p[i]].second);
        if (fa1 != fa2) {
            fa[fa1] = fa2;
            cnt--;
        }
    }
    for (int i = 1; i <= m; i++) printf("%d\n", ans[i]);
    return 0;
}

G：

补：zyh

思路完全正确，队友写挂了，比赛最后三分钟被我对拍拍出错误，但是没时间改

#include <bits/stdc++.h>
using namespace std;
int id[500001];
vector<int> factors[500001];
bool inSet[500001];
long long cnt[1000001];
void getFactors(int x, vector<int> &factor) {
    int len = sqrt(x);
    for (int i = 2; i <= len; ++i)
        if (x % i == 0) {
            factor.push_back(i);
            if (i * i != x) factor.push_back(x / i);
        }
    factor.push_back(x);
}
void updateCnt(vector<int> &factor, int d) {
    for (auto x : factor) {
        cnt[x] += d;
    }
}
void getPrime(int n, vector<int> &prime) {
    prime.clear();
    int len = sqrt(n);
    for (int i = 2; i <= len; ++i)
        if (n % i == 0) {
            prime.push_back(i);
            while (n % i == 0) n /= i;
        }
    if (n > 1) prime.push_back(n);
}
void dfs(int st, int sel, int product, long long &s, vector<int> &prime, int len) {
    if (sel > 0) {
        if (sel & 1) s += cnt[product];
        else s -= cnt[product];
    }
    for (int i = st; i < len; ++i) {
        dfs(i + 1, sel + 1, product * prime[i], s, prime, len);
    }
}
long long howMany(int x) {
    vector<int> prime;
    getPrime(x, prime);
    int len = prime.size();
    long long rnt = 0;
    dfs(0, 0, 1, rnt, prime, len);
    //cout<<"howMany: "<<rnt<<endl;
    return rnt;
}
int main() {
    int n, T;
    scanf("%d%d", &n, &T);
    for (int i = 0; i < n; ++i) {
        scanf("%d", &id[i]);
        getFactors(id[i], factors[i]);
        //cout<<"factor: ";
        //for (auto x:factors[i]) cout<<x<<' ';
        //cout<<endl;
    }
    long long ans = 0;
    long long sizeOfSet = 0;
    while (T--) {
        int t;
        scanf("%d", &t);
        --t;
        if (inSet[t]) {
            updateCnt(factors[t], -1);
            sizeOfSet--;
            ans -= sizeOfSet - howMany(id[t]);
        } else {
            ans += sizeOfSet - howMany(id[t]);
            updateCnt(factors[t], 1);
            sizeOfSet++;
        }
        inSet[t] = !inSet[t];
        printf("%lld\n", ans);
    }
}

H：

solver：czq

很傻的概率题

/* basic header */
#include <bits/stdc++.h>
/* define */
#define ll long long
#define pb emplace_back
#define mp make_pair
#define eps 1e-8
#define lson (curpos<<1)
#define rson (curpos<<1|1)
/* namespace */
using namespace std;
/* header end */

double n, a, p;

int main() {
    scanf("%lf%lf%lf", &n, &a, &p);
    printf("%.8f\n", (a * p - a * (100.0 - p)) / 100.0 + n);
    return 0;
}

I：

solver：lzh、zyh

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define ff first
#define ss second
const int mod = 1e9 + 7;

ll mul(pii a, pii b, pii c) {
    c.ff = c.ff - a.ff, c.ss = c.ss - a.ss;
    a.ff = b.ff - a.ff, a.ss = b.ss - a.ss;
    return 1ll * a.ff * c.ss - 1ll * a.ss * c.ff;
}

pii a[1010], b[1010], c[1010];
int main() {
    int s, r, m, n;
    cin >> s >> r >> m;
    for (int i = 1; i <= s; i++)
        cin >> a[i].ff >> a[i].ss;
    for (int i = 1; i <= r; i++)
        cin >> b[i].ff >> b[i].ss;
    for (int i = 1; i <= m; i++)
        cin >> c[i].ff >> c[i].ss;
    a[s + 1] = a[1], b[r + 1] = b[1], c[m + 1] = c[1];
    cin >> n;
    while (n--) {
        pii x;
        cin >> x.ff >> x.ss;
        int gg = 0;
        for (int i = 1; i <= s; i++)
            if (mul(a[i], a[i + 1], x) < 0) {
                gg++;
                break;
            }
        if (!gg) {
            cout << "Sheena\n";
            continue;
        }
        gg = 0;
        for (int i = 1; i <= r; i++)
            if (mul(b[i], b[i + 1], x) < 0) {
                gg++;
                break;
            }
        if (!gg) {
            cout << "Rose\n";
            continue;
        }
        gg = 0;
        for (int i = 1; i <= m; i++)
            if (mul(c[i], c[i + 1], x) < 0) {
                gg++;
                break;
            }
        if (!gg) {
            cout << "Maria\n";
            continue;
        }
        cout << "Outside\n";
    }
}

J：

solver：czq

树状数组

/* basic header */
#include <bits/stdc++.h>
/* define */
#define ll long long
#define pb emplace_back
#define mp make_pair
#define eps 1e-8
#define lson (curpos<<1)
#define rson (curpos<<1|1)
/* namespace */
using namespace std;
/* header end */

class FenwickTree {
private:
    // 存储的信息类型
    typedef int StoreType;
    int n;
    // num用于存储元素值，用于实现单点修改、区间查询
    // diff用于存储差分，用于实现区间修改
    vector<StoreType>num, diff;
public:
    FenwickTree(): n(0) {}
    FenwickTree(int _n) {
        n = _n;
        num.assign(n, 0);
    }
    // 单点修改
    void add(int pos, int val) {
        for (; pos < n; pos |= pos + 1) num[pos] += val;
    }
    // 查询区间[0..pos]的信息
    StoreType sum(int pos) {
        StoreType ret = 0;
        for (; pos >= 0; pos = (pos & (pos + 1)) - 1) ret += num[pos];
        return ret;
    }
    // 查询区间[l..r]的和
    StoreType querySum(int l, int r) {
        return sum(r) - sum(l - 1);
    }
    // 区间修改，给区间[l..r]里的元素都加上val
    void intervalFix(int l, int r, int val) {
        add(l, val); add(r + 1, -val);
    }
};

const int MAXN = 1e5 + 10;
int n, a[MAXN];
FenwickTree fwt(MAXN * 10);

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
        a[i]++;
        printf("%d\n", n - (i - fwt.sum(a[i] - 1)) + 1);
        fwt.add(a[i], 1);
    }
    return 0;
}

K：

solver：lzh

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define ff first
#define ss second

int dis[100010][3];
struct edge {
    int u, v, w;
    edge(int _u = 0, int _v = 0, int _w = 0) {
        u = _u, v = _v, w = _w;
    }
} e[200010];
int head[100010], num = 0, vis[200010];
void addedge() {
    int u, v, w;
    cin >> u >> v >> w;
    e[num] = edge(head[u], v, w);
    head[u] = num++;
    e[num] = edge(head[v], u, w);
    head[v] = num++;
}
struct node {
    int val, v, add;
    node(int _val = 0, int _v = 0, int _add = 0) {
        val = _val, v = _v;
        add = _add;
    }
    bool operator<(const node &b) const {
        return val > b.val;
    }
};
int main() {
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    memset(dis, 0x3f, sizeof dis);
    memset(head, -1, sizeof head);

    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= m; i++) {
        addedge();
    }
    priority_queue<node> q;
    q.push(node{ 0, 1, 0 });
    dis[1][0] = 0;
    while (!q.empty()) {
        node x = q.top();
        q.pop();
        for (int i = head[x.v]; i != -1; i = e[i].u) {
            if ((vis[i] & x.add) == 0 && (vis[i ^ 1] & x.add) == 0) {
                vis[i] |= x.add, vis[i ^ 1] |= x.add;
                for (int j = 0; j < 3; j++) {
                    int tmp = dis[e[i].v][j];
                    tmp = min(tmp, dis[x.v][(j + 2) % 3] + e[i].w);
                    if (e[i].v != n) {
                        tmp = min(tmp, dis[x.v][j] + e[i].w * 3);
                        tmp = min(tmp, dis[x.v][(j + 1) % 3] + e[i].w * 5);
                    }
                    if (e[i].v != n && dis[e[i].v][j] != tmp) {
                        if ((vis[i] & 1) == 0)
                            q.push(node{ dis[e[i].v][0], e[i].v, 1 });
                        if ((vis[i] & 2) == 0)
                            q.push(node{ dis[e[i].v][1], e[i].v, 2 });
                        if ((vis[i] & 4) == 0)
                            q.push(node{ dis[e[i].v][2], e[i].v, 4 });
                    }
                    dis[e[i].v][j] = tmp;
                }
            }
        }
    }
    pair<int, string> ans[10];
    ans[1] = { dis[n][0], "me" };
    ans[2] = { dis[n][1], "Gon" };
    ans[3] = { dis[n][2], "Killua" };
    sort(ans + 1, ans + 1 + 3);
    for (int i = 1; i <= 3; i++)
        cout << ans[i].ss << endl;
}

L：

solver：zyh、lzh、czq

读错题把队友坑了，锅++

#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> point;
vector<point> pts;
bool check(point a, point b) {
    return (a.first < b.first && abs(a.first - b.first) + abs(a.second - b.second) <= 5);
}
vector<int> edges[200001];
int dp[200001];
bool vis[200001];
bool reach0[200001];
map<int, map<int, int>> Map;
void dfs(int u) {
    vis[u] = true;
    dp[u] = 1;
    for (auto v : edges[u]) {
        if (!vis[v]) dfs(v);
        if (reach0[v]) dp[u] = max(dp[u], dp[v] + 1);
        reach0[u] |= reach0[v];
    }
}
int main() {
    int n, l;
    scanf("%d%d", &n, &l);
    pts.push_back(point(0, 0));
    Map[0][0] = 0;
    for (int i = 0; i < n; ++i) {
        int x, y;
        scanf("%d%d", &x, &y);
        pts.push_back(point(x, y));
        Map[x][y] = i + 1;
    }
    for (int i = 0; i <= n; ++i) {
        int x = pts[i].first;
        int y = pts[i].second;
        for (int j = 1; j <= 5; ++j) {
            if (Map.find(x + j) == Map.end()) continue;
            auto iter = Map[x + j].lower_bound(y - (5 - j));
            while (iter != Map[x + j].end() && iter->first <= y + 5 - j) {
                edges[iter->second].push_back(i);
                iter++;
            }
        }
    }
    reach0[0] = true;
    for (int i = 0; i <= n; ++i)
        if (!vis[i]) dfs(i);
    point end = {l, 0};
    int ans = 0;
    for (int i = 0; i <= n; ++i) {
        if (reach0[i] && check(pts[i], end)) ans = max(ans, dp[i] - 1);
    }
    printf("%d", ans);
}