{"id":288,"date":"2023-01-23T21:40:51","date_gmt":"2023-01-23T13:40:51","guid":{"rendered":"http:\/\/yuri3.cn\/?p=288"},"modified":"2023-02-12T03:32:24","modified_gmt":"2023-02-11T19:32:24","slug":"solution-for-atcoder-beginner-contest-286","status":"publish","type":"post","link":"http:\/\/yuri3.cn\/?p=288","title":{"rendered":"Solution for AtCoder Beginner Contest 286"},"content":{"rendered":"

\u4eca\u5e74\u7684\u5e74\u5473\u786e\u5b9e\u4e0d\u6d53\uff0c\u5f88\u65e0\u804a\uff0c\u4e8e\u662f\u6253\u6253AtCoder\u9632\u6b62\u667a\u529b\u4e0b\u964d\u3002<\/p>\n

\u9898\u76ee\u94fe\u63a5<\/a><\/p>\n

<\/p>\n

A – Range Swap<\/h2>\n

\u6709\u4e2a\u4e1c\u897f\u53ebstd::swap_ranges<\/code>\uff0c\u76f4\u63a5\u7528\u5c31\u884c\u4e86\u3002<\/p>\n

B – Cat<\/h2>\n

\u76f4\u63a5\u6a21\u62df\u5373\u53ef\u3002<\/p>\n

C – Rotate and Palindrome<\/h2>\n

\u679a\u4e3e\u4f4d\u79fb\u8ddd\u79bb\uff0c\u7136\u540e\u66b4\u529b\u7b97\u5c31\u884c\u4e86\u3002\\mathcal{O}(N^2)<\/span><\/p>\n

\nCode<\/summary>\n
i64 ans = std::numeric_limits<i64>::max() \/ 2.0;\nfor (int r = 0; r < N; r++) {\n  i64 cur = r * A;\n  for (int l = 0, r = N - 1; l < r; l++, r--) {\n    if (s[l] != s[r]) cur += B;\n  }\n  ans = std::min(ans, cur);\n  std::rotate(s.begin(), s.begin() + 1, s.end());\n}\n\nstd::cout << ans << std::endl;\n<\/code><\/pre>\n<\/details>\n
D – Money in Hand<\/h2>\n
\u4f3c\u4e4e\u662f\u4e2a\u88f8\u7684\u80cc\u5305\uff0c\\mathcal{O}(NXB)<\/span>\u8dd1\u4e00\u904d\u5c31\u884c\u3002<\/p>\n
\nCode<\/summary>\n
#include <bits\/stdc++.h>\n\nusing i64 = std::int64_t;\n\nint main() {\n    std::ios::sync_with_stdio(false);\n    std::cin.tie(nullptr);\n\n    int n, x;\n    std::cin >> n >> x;\n\n    std::vector<std::vector<int>> dp(n + 1, std::vector<int>(x + 1));\n\n    dp[0][0] = 1;\n    for (int i = 1; i <= n; i++) {\n        int a, b;\n\n        std::cin >> a >> b;\n\n        for (int j = 0; j <= x; j++) {\n            for (int t = 0; t <= b; t++) {\n                if (j + a * t > x) continue;\n                dp[i][j + a * t] |= dp[i - 1][j];\n            }\n        }\n    }\n\n    int ans = 0;\n\n    for (int i = 0; i <= n; i++) {\n        ans |= dp[i][x];\n    }\n\n    if (ans) {\n        std::cout << \"Yes\" << std::endl;\n    } else {\n        std::cout << \"No\" << std::endl;\n    }\n\n    return 0;\n}\n<\/code><\/pre>\n<\/details>\n
E – Souvenir<\/h2>\n
\u6570\u636e\u8303\u56f4\u6bd4\u8f83\u5c0f\uff0c\u53ef\u4ee5\u7528Floyd-Warshall algorithm<\/a>\uff0c\u70b9\u6743\u53ef\u4ee5\u53e0\u52a0\u5230\u8fb9\u6743\u4e0a\uff0c\u5408\u5e76\u65f6\u51cf\u53bb\u91cd\u590d\u8ba1\u7b97\u7684\u5c31\u884c\u3002\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\\mathcal{O}(N^3)<\/span>\u3002<\/p>\n
\nCode<\/summary>\n
#include <bits\/stdc++.h>\n\nusing i64 = std::int64_t;\nconstexpr i64 INF = std::numeric_limits<i64>::max() \/ 3.0;\n\nint main() {\n    std::ios::sync_with_stdio(false);\n    std::cin.tie(nullptr);\n\n    int n;\n\n    std::cin >> n;\n\n    std::vector<i64> val(n);\n\n    for (int i = 0; i < n; i++) std::cin >> val[i];\n\n    std::vector<std::vector<i64>> mp(n, std::vector<i64>(n, INF));\n    std::vector<std::vector<i64>> cost(n, std::vector<i64>(n, 0));\n\n    for (int i = 0; i < n; i++) {\n        std::string in;\n        std::cin >> in;\n        for (int j = 0; j < n; j++) {\n            if (in[j] == 'Y') mp[i][j] = 1;\n        }\n    }\n    for (int i = 0; i < n; i++) {\n        for (int j = 0; j < n; j++)\n            if (i != j) cost[i][j] = val[i] + val[j];\n    }\n\n    for (int k = 0; k < n; k++) {\n        for (int i = 0; i < n; i++) {\n            for (int j = 0; j < n; j++) {\n                if (mp[i][k] + mp[k][j] < mp[i][j]) {\n                    mp[i][j] = mp[i][k] + mp[k][j];\n                    cost[i][j] = cost[i][k] + cost[k][j] - val[k];\n                } else if (mp[i][k] + mp[k][j] == mp[i][j]) {\n                    cost[i][j] =\n                        std::max(cost[i][j], cost[i][k] + cost[k][j] - val[k]);\n                }\n            }\n        }\n    }\n\n    int q;\n    std::cin >> q;\n    while (q--) {\n        int u, v;\n        std::cin >> u >> v;\n        u--, v--;\n        if (mp[u][v] >= INF)\n            std::cout << \"Impossible\\n\";\n        else\n            std::cout << mp[u][v] << \" \" << cost[u][v] << '\\n';\n    }\n\n    return 0;\n}\n<\/code><\/pre>\n<\/details>\n
F – Guess The Number 2<\/h2>\n
\u662f\u4e2a\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\u9898\u3002<\/p>\n
\u8003\u8651\u5c06i\\rightarrow A_i<\/span>\u7684\u51fd\u6570\u5173\u7cfb\u5efa\u9020\u4e00\u4e2a\u6709\u5411\u56fe\uff0c\u6784\u9020\u82e5\u5e72\u4e2a\u73af\uff0c\u73af\u957f\u4e3am_1,m_2,…,m_t<\/span>\uff0c\u5219\\sum_{i=1}^t m_i =M<\/span>\u3002<\/p>\n
\u51fd\u6570\u590d\u5408\u76f8\u5f53\u4e8e\u7ed9\u5b9a\u8d77\u70b9\u5728\u73af\u5185\u5faa\u73af\uff0c\u5219N<\/span>\u6b21\u540e\u53ef\u4ee5\u5bf9\u6bcf\u4e2a\u73af\u7684\u6bcf\u4e2a\u4f4d\u7f6e\u7b97\u51fa\u76f8\u5bf9\u504f\u79fb\uff0c\u5373t<\/span>\u4e2a\u540c\u4f59\u65b9\u7a0bN \\equiv r_i\\mod m_i<\/span>\u3002\u76f4\u63a5CRT\u5373\u53ef\u3002<\/p>\n
\u4f46\u662f\u8981\u4fdd\u8bc1M<\/span>\u4e0d\u80fd\u8d85\u8fc7110<\/span>\uff0c\u4e14LCM({m_i})\\geq 10^9<\/span>\uff0c\u4e0d\u7136\u53ef\u80fd\u7b54\u6848\u4e0d\u552f\u4e00\u3002<\/p>\n
\u7b14\u8005\u9009\u62e9\u4e86\uff1a4, 5, 7, 9, 11, 13, 17, 19, 23<\/span>\u3002<\/p>\n
\nCode<\/summary>\n
#include <bits\/stdc++.h>\n\nusing i64 = std::int64_t;\n\ntemplate <typename T>\nconstexpr T safe_mod(T x, T m) {\n    x %= m;\n    if (x < 0) x += m;\n    return x;\n}\ntemplate <typename T>\nconstexpr std::pair<T, T> inv_gcd(T a, T b) {\n    a = safe_mod(a, b);\n    if (a == 0) return {b, 0};\n    T s = b, t = a;\n    T m0 = 0, m1 = 1;\n    while (t) {\n        T u = s \/ t;\n        s -= t * u;\n        m0 -= m1 * u;\n        auto tmp = s;\n        s = t;\n        t = tmp;\n        tmp = m0;\n        m0 = m1;\n        m1 = tmp;\n    }\n    if (m0 < 0) m0 += b \/ s;\n    return {s, m0};\n}\n\ntemplate <typename T>\nT inv_mod(T x, T m) {\n    assert(1 <= m);\n    auto z = inv_gcd(x, m);\n    assert(z.first == 1);\n    return z.second;\n}\n\ntemplate <typename T>\nstd::pair<T, T> crt(const std::vector<T>& r, const std::vector<T>& m) {\n    assert(r.size() == m.size());\n    int n = int(r.size());\n    \/\/ Contracts: 0 <= r0 < m0\n    T r0 = 0, m0 = 1;\n    for (int i = 0; i < n; i++) {\n        assert(1 <= m[i]);\n        T r1 = safe_mod(r[i], m[i]), m1 = m[i];\n        if (m0 < m1) {\n            std::swap(r0, r1);\n            std::swap(m0, m1);\n        }\n        if (m0 % m1 == 0) {\n            if (r0 % m1 != r1) return {0, 0};\n            continue;\n        }\n        auto [g, im] = inv_gcd(m0, m1);\n        T u1 = (m1 \/ g);\n        if ((r1 - r0) % g) return {0, 0};\n        T x = (r1 - r0) \/ g % u1 * im % u1;\n        r0 += x * m0;\n        m0 *= u1;\n        if (r0 < 0) r0 += m0;\n    }\n    return {r0, m0};\n}\n\nint main() {\n    std::ios::sync_with_stdio(false);\n    std::cin.tie(nullptr);\n\n    std::vector<int> p = {4, 5, 7, 9, 11, 13, 17, 19, 23};\n\n    int M = 108;\n\n    std::cout << M << std::endl;\n    std::cout.flush();\n\n    std::vector<int> to(M + 1);\n    int np = 1;\n    for (int i = 0; i < static_cast<int>(p.size()); i++) {\n        int cur = p[i];\n        int fn = np;\n        for (int j = 1; j <= cur; j++) {\n            if (j != cur)\n                to[np] = j + fn;\n            else\n                to[np] = fn;\n            np++;\n        }\n    }\n\n    for (int i = 1; i <= M; i++) {\n        std::cout << to[i] << \" \";\n    }\n    std::cout << std::endl;\n    std::cout.flush();\n\n    std::vector<int> ans(M + 1);\n    for (int i = 1; i <= M; i++) {\n        std::cin >> ans[i];\n    }\n\n    std::vector<int> res;\n\n    for (int i = 0, fs = 1; i < static_cast<int>(p.size()); i++) {\n        int diff = ((ans[fs] - fs) % p[i] + p[i]) % p[i];\n        res.push_back(diff);\n        fs += p[i];\n    }\n\n    auto [rem, mod] = crt<int>(res, p);\n\n    std::cout << rem << std::endl;\n\n    return 0;\n}\n<\/code><\/pre>\n<\/details>\n
G – Unique Walk<\/h2>\n
\u8fd9\u4e2a\u9898\u770b\u4e0a\u53bb\u5c31\u5f88\u6b27\u62c9\u56de\u8def\u3002<\/p>\n
\u8003\u8651\u5bf9\u4e0d\u5728S<\/span>\u96c6\u5408\u7684\u8fb9\u6784\u9020\u5b50\u56feG<\/span>\uff0c\u8be5\u5b50\u56fe\u80af\u5b9a\u662f\u82e5\u5e72\u4e2a\u8054\u901a\u5757\u3002\u8054\u901a\u5757\u5185\u7684\u5fc5\u7ecf\u4e00\u6b21\u7684\u8fb9\u53ef\u4ee5\u4e0d\u7528\u8003\u8651\uff0c\u56e0\u4e3a\u8054\u901a\u5757\u5185\u4efb\u610f\u4e24\u70b9\u90fd\u53ef\u4ee5\u7ecf\u8fc7\u975eS<\/span>\u5185\u7684\u8fb9\u5230\u8fbe\uff0c\u56e0\u6b64\u53ef\u4ee5\u8c03\u6574\u4f7f\u5f97\u8054\u901a\u5757\u5185\u7684S<\/span>\u5185\u7684\u8fb9\u4ec5\u7ecf\u8fc7\u4e00\u6b21\u3002<\/p>\n
\u7531\u4e8e\u8054\u901a\u5757\u5185\u90e8\u65e0\u5f71\u54cd\uff0c\u53ef\u4ee5\u7f29\u70b9\u5efa\u7acb\u65b0\u56fe\uff0c\u5e76\u4e14\u65b0\u56fe\u4e4b\u95f4\u7684\u8fb9\u90fd\u5728S<\/span>\u5185\u3002\u663e\u7136\u5145\u8981\u6761\u4ef6\u4e3a\u65b0\u56fe\u662f\u534a\u6b27\u62c9\u56fe\uff08\u5947\u6570\u5ea6\u6570\u7684\u70b9\u6709\u4e14\u4ec5\u67092\u4e2a\u62160\u4e2a\uff09\u3002<\/p>\n
\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\\mathcal{O}(N)<\/span><\/p>\n
\nCode<\/summary>\n
#include <bits\/stdc++.h>\n\nusing i64 = std::int64_t;\n\nint main() {\n    std::ios::sync_with_stdio(false);\n    std::cin.tie(nullptr);\n\n    int n, m;\n\n    std::cin >> n >> m;\n\n    std::vector<std::vector<int>> adj(n);\n\n    std::vector<std::pair<int, int>> E(m);\n\n    for (auto& [u, v] : E) {\n        std::cin >> u >> v;\n        u--, v--;\n    }\n\n    int k;\n    std::cin >> k;\n\n    std::vector<int> sig(m);\n    for (int i = 0; i < k; i++) {\n        int x;\n        std::cin >> x;\n        x--;\n        sig[x] = 1;\n    }\n\n    for (int i = 0; i < m; i++) {\n        if (!sig[i]) {\n            auto [u, v] = E[i];\n            adj[u].push_back(v);\n            adj[v].push_back(u);\n        }\n    }\n    std::vector<int> col(n, -1);\n\n    int p = 0;\n    for (int i = 0; i < n; i++) {\n        if (col[i] == -1) {\n            auto dfs = [&](auto&& self, int u) -> void {\n                col[u] = p;\n                for (const auto& v : adj[u]) {\n                    if (col[v] == -1) self(self, v);\n                }\n            };\n            dfs(dfs, i);\n            p++;\n        }\n    }\n\n    std::vector<int> deg(p);\n    for (int i = 0; i < m; i++) {\n        if (sig[i]) {\n            auto [u, v] = E[i];\n            deg[col[u]]++;\n            deg[col[v]]++;\n        }\n    }\n\n    int h = 0;\n    for (int i = 0; i < p; i++) {\n        h += (deg[i] % 2);\n    }\n\n    if (h == 2 || h == 0)\n        std::cout << \"Yes\" << std::endl;\n    else\n        std::cout << \"No\" << std::endl;\n\n    return 0;\n}\n<\/code><\/pre>\n<\/details>\n
Ex – Don’t Swim<\/h2>\n
\u795e\u79d8\u8ba1\u7b97\u51e0\u4f55\u3002<\/p>\n
\u4f3c\u4e4e\u5c31\u662f\u4e2a\u8ba1\u7b97\u51e0\u4f55\u6a21\u7248+\u6700\u77ed\u8def\u3002<\/p>\n
\u8003\u8651\u5efa\u56fe\uff0c\u51f8\u5305\u4e0a\u7684\u70b9\u548cS\uff0cT\u8fde\u8fb9\uff0c\u9700\u8981\u5199\u4e00\u4e2a\u7ebf\u6bb5\u548c\u51f8\u5305\u5224\u4ea4\u6765\u5254\u9664\u4e0d\u5408\u6cd5\u7684\u8fb9\u3002\u7136\u540e\u76f4\u63a5\u8dd1Dijkstra\u7b97\u6cd5\u5373\u53ef\u3002<\/p>\n
\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\\mathcal{O}(N\\log N)<\/span>\u3002<\/p>\n
\u5f53\u7136\u6709\u4e00\u4e9b\u7ebf\u6027\u505a\u6cd5\uff0c\u4e0d\u8fc7\u7b14\u8005\u9009\u62e9\u62d2\u7edd\u601d\u8003\uff0c\u6284\u4e86KACTL\u8ba1\u7b97\u51e0\u4f55\u6a21\u7248\u3002<\/p>\n
\nCode<\/summary>\n
#include <bits\/stdc++.h>\n\nusing i64 = std::int64_t;\nconstexpr double INF = std::numeric_limits<double>::max() \/ 3.0;\ntemplate <class T>\nint sgn(T x) {\n    return (x > 0) - (x < 0);\n}\ntemplate <class T = double>\nstruct Point {\n    typedef Point P;\n    T x, y;\n    explicit Point(T x = 0, T y = 0) : x(x), y(y) {}\n    bool operator<(P p) const { return std::tie(x, y) < std::tie(p.x, p.y); }\n    bool operator==(P p) const { return std::tie(x, y) == std::tie(p.x, p.y); }\n    P operator+(P p) const { return P(x + p.x, y + p.y); }\n    P operator-(P p) const { return P(x - p.x, y - p.y); }\n    P operator*(T d) const { return P(x * d, y * d); }\n    P operator\/(T d) const { return P(x \/ d, y \/ d); }\n    T dot(P p) const { return x * p.x + y * p.y; }\n    T cross(P p) const { return x * p.y - y * p.x; }\n    T cross(P a, P b) const { return (a - *this).cross(b - *this); }\n    T dist2() const { return x * x + y * y; }\n    double dist() const { return sqrt((double)dist2()); }\n    \/\/ angle to x-axis in interval [-pi, pi]\n    double angle() const { return atan2(y, x); }\n    P unit() const { return *this \/ dist(); }  \/\/ makes dist()=1\n    P perp() const { return P(-y, x); }        \/\/ rotates +90 degrees\n    P normal() const { return perp().unit(); }\n    \/\/ returns point rotated 'a' radians ccw around the origin\n    P rotate(double a) const {\n        return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));\n    }\n};\n#define cmp(i, j) sgn(dir.perp().cross(poly[(i) % n] - poly[(j) % n]))\n#define extr(i) cmp(i + 1, i) >= 0 && cmp(i, i - 1 + n) < 0\ntemplate <class P>\nint extrVertex(std::vector<P>& poly, P dir) {\n    int n = size(poly), lo = 0, hi = n;\n    if (extr(0)) return 0;\n    while (lo + 1 < hi) {\n        int m = (lo + hi) \/ 2;\n        if (extr(m)) return m;\n        int ls = cmp(lo + 1, lo), ms = cmp(m + 1, m);\n        (ls < ms || (ls == ms && ls == cmp(lo, m)) ? hi : lo) = m;\n    }\n    return lo;\n}\ntemplate <class P>\nbool onSegment(P s, P e, P p) {\n    return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0;\n}\ntemplate <class P>\nstd::vector<P> segInter(P a, P b, P c, P d) {\n    auto oa = c.cross(d, a), ob = c.cross(d, b), oc = a.cross(b, c),\n         od = a.cross(b, d);\n    \/\/ Checks if intersection is single non-endpoint point.\n    if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0)\n        return {(a * ob - b * oa) \/ (ob - oa)};\n    std::set<P> s;\n    if (onSegment(c, d, a)) s.insert(a);\n    if (onSegment(c, d, b)) s.insert(b);\n    if (onSegment(a, b, c)) s.insert(c);\n    if (onSegment(a, b, d)) s.insert(d);\n    return {s.begin(), s.end()};\n}\n#define cmpL(i) sgn(a.cross(poly[i], b))\ntemplate <class P>\nbool lineHull(P a, P b, std::vector<P>& poly) {\n    int endA = extrVertex(poly, (a - b).perp());\n    int endB = extrVertex(poly, (b - a).perp());\n    if (cmpL(endA) < 0 || cmpL(endB) > 0) return true;\n    std::array<int, 2> res;\n    for (int i = 0; i < 2; i++) {\n        int lo = endB, hi = endA, n = size(poly);\n        while ((lo + 1) % n != hi) {\n            int m = ((lo + hi + (lo < hi ? 0 : n)) \/ 2) % n;\n            (cmpL(m) == cmpL(endB) ? lo : hi) = m;\n        }\n        res[i] = (lo + !cmpL(hi)) % n;\n        std::swap(endA, endB);\n    }\n    std::array<int, 2> ans = res;\n    if (res[0] == res[1]) return true;\n    if (!cmpL(res[0]) && !cmpL(res[1]))\n        switch ((res[0] - res[1] + size(poly) + 1) % size(poly)) {\n            case 0:\n                ans = std::array<int, 2>{res[0], res[0]};\n            case 2:\n                ans = std::array<int, 2>{res[1], res[1]};\n        }\n    auto [f1, f2] = res;\n    if (f1 == -1 || f2 == -1) return true;\n    int sz1 = segInter(a, b, poly[f1], poly[(f1 + 1) % poly.size()]).size();\n    int sz2 = segInter(a, b, poly[f2], poly[(f2 + 1) % poly.size()]).size();\n    if (sz1 == 1 && sz2 == 1) return false;\n    return true;\n}\n\nint main() {\n    std::ios::sync_with_stdio(false);\n    std::cin.tie(nullptr);\n\n    int n;\n\n    std::cin >> n;\n\n    std::vector<Point<double>> hull(n);\n\n    for (auto& [x, y] : hull) std::cin >> x >> y;\n\n    Point s, t;\n    std::cin >> s.x >> s.y >> t.x >> t.y;\n\n    int cnt = n + 2;\n\n    std::vector<std::vector<std::pair<int, double>>> adj(cnt);\n\n    auto Dist = [](const Point<double>& a, const Point<double>& b) -> double {\n        double rx = a.x - b.x;\n        double ry = a.y - b.y;\n        return std::sqrt(rx * rx + ry * ry);\n    };\n\n    for (int i = 0; i < n; i++) {\n        double curDist = Dist(hull[i], hull[(i + 1) % n]);\n        adj[i].emplace_back((i + 1) % n, curDist);\n        adj[(i + 1) % n].emplace_back(i, curDist);\n    }\n\n    for (int i = 0; i < n; i++) {\n        if (!lineHull(s, hull[i], hull)) continue;\n        double curDist = Dist(s, hull[i]);\n        adj[n].emplace_back(i, curDist);\n        adj[i].emplace_back(n, curDist);\n    }\n\n    for (int i = 0; i < n; i++) {\n        if (!lineHull(t, hull[i], hull)) continue;\n        double curDist = Dist(t, hull[i]);\n        adj[n + 1].emplace_back(i, curDist);\n        adj[i].emplace_back(n + 1, curDist);\n    }\n\n    if (lineHull(s, t, hull)) {\n        double curDist = Dist(s, t);\n        adj[n + 1].emplace_back(n, curDist);\n        adj[n].emplace_back(n + 1, curDist);\n    }\n\n    std::vector<double> dis(cnt, INF);\n    std::vector<int> vis(cnt);\n    dis[n] = 0;\n    std::priority_queue<std::pair<double, int>,\n                        std::vector<std::pair<double, int>>,\n                        std::greater<std::pair<double, int>>>\n        Q;\n    Q.push({0, n});\n    while (!Q.empty()) {\n        auto [uw, u] = Q.top();\n        Q.pop();\n        if (vis[u]) continue;\n        vis[u] = 1;\n        for (auto [v, w] : adj[u]) {\n            if (dis[v] > dis[u] + w) {\n                dis[v] = dis[u] + w;\n                Q.push({dis[v], v});\n            }\n        }\n    }\n\n    std::cout << std::fixed << std::setprecision(10) << dis[n + 1];\n    return 0;\n}\n<\/code><\/pre>\n<\/details>\n","protected":false},"excerpt":{"rendered":"
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