[auto-verifier] docs commit d10caf9

hitonanode · Dec 26, 2023 · b4ab88d · b4ab88d
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diff --git a/index.md b/index.md
@@ -1349,6 +1349,9 @@ data:
     - icon: ':heavy_check_mark:'
       path: number/test/gen_primes.test.cpp
       title: number/test/gen_primes.test.cpp
+    - icon: ':heavy_check_mark:'
+      path: number/test/is_prime.test.cpp
+      title: number/test/is_prime.test.cpp
     - icon: ':heavy_check_mark:'
       path: number/test/lcm_convolution.test.cpp
       title: number/test/lcm_convolution.test.cpp
@@ -1524,6 +1527,9 @@ data:
     - icon: ':heavy_check_mark:'
       path: string/test/lcp.test.cpp
       title: string/test/lcp.test.cpp
+    - icon: ':heavy_check_mark:'
+      path: string/test/lyndon.test.cpp
+      title: string/test/lyndon.test.cpp
     - icon: ':heavy_check_mark:'
       path: string/test/manacher.test.cpp
       title: string/test/manacher.test.cpp

diff --git a/number/factorize.hpp.md b/number/factorize.hpp.md
@@ -18,6 +18,9 @@ data:
   - icon: ':heavy_check_mark:'
     path: number/test/factorize_longlong.test.cpp
     title: number/test/factorize_longlong.test.cpp
+  - icon: ':heavy_check_mark:'
+    path: number/test/is_prime.test.cpp
+    title: number/test/is_prime.test.cpp
   - icon: ':heavy_check_mark:'
     path: number/test/miller-rabin-5e7.test.cpp
     title: number/test/miller-rabin-5e7.test.cpp
@@ -148,6 +151,7 @@ data:
   - number/test/factorize_longlong.test.cpp
   - number/test/miller-rabin.test.cpp
   - number/test/miller-rabin-5e7.test.cpp
+  - number/test/is_prime.test.cpp
   - number/test/factorize_aoj.test.cpp
   - graph/test/chromatic_number.test.cpp
 documentation_of: number/factorize.hpp

diff --git a/number/test/is_prime.test.cpp.md b/number/test/is_prime.test.cpp.md
@@ -0,0 +1,97 @@
+---
+data:
+  _extendedDependsOn:
+  - icon: ':heavy_check_mark:'
+    path: number/factorize.hpp
+    title: "Integer factorization \uFF08\u7D20\u56E0\u6570\u5206\u89E3\uFF09"
+  - icon: ':heavy_check_mark:'
+    path: random/xorshift.hpp
+    title: random/xorshift.hpp
+  _extendedRequiredBy: []
+  _extendedVerifiedWith: []
+  _isVerificationFailed: false
+  _pathExtension: cpp
+  _verificationStatusIcon: ':heavy_check_mark:'
+  attributes:
+    '*NOT_SPECIAL_COMMENTS*': ''
+    PROBLEM: https://judge.yosupo.jp/problem/primality_test
+    links:
+    - https://judge.yosupo.jp/problem/primality_test
+  bundledCode: "#line 1 \"number/test/is_prime.test.cpp\"\n#define PROBLEM \"https://judge.yosupo.jp/problem/primality_test\"\
+    \n#line 2 \"random/xorshift.hpp\"\n#include <cstdint>\n\n// CUT begin\nuint32_t\
+    \ rand_int() // XorShift random integer generator\n{\n    static uint32_t x =\
+    \ 123456789, y = 362436069, z = 521288629, w = 88675123;\n    uint32_t t = x ^\
+    \ (x << 11);\n    x = y;\n    y = z;\n    z = w;\n    return w = (w ^ (w >> 19))\
+    \ ^ (t ^ (t >> 8));\n}\ndouble rand_double() { return (double)rand_int() / UINT32_MAX;\
+    \ }\n#line 3 \"number/factorize.hpp\"\n#include <algorithm>\n#include <array>\n\
+    #include <cassert>\n#include <numeric>\n#include <vector>\n\nnamespace SPRP {\n\
+    // http://miller-rabin.appspot.com/\nconst std::vector<std::vector<__int128>>\
+    \ bases{\n    {126401071349994536},                              // < 291831\n\
+    \    {336781006125, 9639812373923155},                  // < 1050535501 (1e9)\n\
+    \    {2, 2570940, 211991001, 3749873356},               // < 47636622961201 (4e13)\n\
+    \    {2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 2^64\n};\ninline\
+    \ int get_id(long long n) {\n    if (n < 291831) {\n        return 0;\n    } else\
+    \ if (n < 1050535501) {\n        return 1;\n    } else if (n < 47636622961201)\n\
+    \        return 2;\n    else { return 3; }\n}\n} // namespace SPRP\n\n// Miller-Rabin\
+    \ primality test\n// https://ja.wikipedia.org/wiki/%E3%83%9F%E3%83%A9%E3%83%BC%E2%80%93%E3%83%A9%E3%83%93%E3%83%B3%E7%B4%A0%E6%95%B0%E5%88%A4%E5%AE%9A%E6%B3%95\n\
+    // Complexity: O(lg n) per query\nstruct {\n    long long modpow(__int128 x, __int128\
+    \ n, long long mod) noexcept {\n        __int128 ret = 1;\n        for (x %= mod;\
+    \ n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret;\n        return\
+    \ ret;\n    }\n    bool operator()(long long n) noexcept {\n        if (n < 2)\
+    \ return false;\n        if (n % 2 == 0) return n == 2;\n        int s = __builtin_ctzll(n\
+    \ - 1);\n\n        for (__int128 a : SPRP::bases[SPRP::get_id(n)]) {\n       \
+    \     if (a % n == 0) continue;\n            a = modpow(a, (n - 1) >> s, n);\n\
+    \            bool may_composite = true;\n            if (a == 1) continue;\n \
+    \           for (int r = s; r--; a = a * a % n) {\n                if (a == n\
+    \ - 1) may_composite = false;\n            }\n            if (may_composite) return\
+    \ false;\n        }\n        return true;\n    }\n} is_prime;\n\nstruct {\n  \
+    \  // Pollard's rho algorithm: find factor greater than 1\n    long long find_factor(long\
+    \ long n) {\n        assert(n > 1);\n        if (n % 2 == 0) return 2;\n     \
+    \   if (is_prime(n)) return n;\n        long long c = 1;\n        auto f = [&](__int128\
+    \ x) -> long long { return (x * x + c) % n; };\n\n        for (int t = 1;; t++)\
+    \ {\n            for (c = 0; c == 0 or c + 2 == n;) c = rand_int() % n;\n    \
+    \        long long x0 = t, m = std::max(n >> 3, 1LL), x, ys, y = x0, r = 1, g,\
+    \ q = 1;\n            do {\n                x = y;\n                for (int i\
+    \ = r; i--;) y = f(y);\n                long long k = 0;\n                do {\n\
+    \                    ys = y;\n                    for (int i = std::min(m, r -\
+    \ k); i--;)\n                        y = f(y), q = __int128(q) * std::abs(x -\
+    \ y) % n;\n                    g = std::__gcd<long long>(q, n);\n            \
+    \        k += m;\n                } while (k < r and g <= 1);\n              \
+    \  r <<= 1;\n            } while (g <= 1);\n            if (g == n) {\n      \
+    \          do {\n                    ys = f(ys);\n                    g = std::__gcd(std::abs(x\
+    \ - ys), n);\n                } while (g <= 1);\n            }\n            if\
+    \ (g != n) return g;\n        }\n    }\n\n    std::vector<long long> operator()(long\
+    \ long n) {\n        std::vector<long long> ret;\n        while (n > 1) {\n  \
+    \          long long f = find_factor(n);\n            if (f < n) {\n         \
+    \       auto tmp = operator()(f);\n                ret.insert(ret.end(), tmp.begin(),\
+    \ tmp.end());\n            } else\n                ret.push_back(n);\n       \
+    \     n /= f;\n        }\n        std::sort(ret.begin(), ret.end());\n       \
+    \ return ret;\n    }\n    long long euler_phi(long long n) {\n        long long\
+    \ ret = 1, last = -1;\n        for (auto p : this->operator()(n)) ret *= p - (last\
+    \ != p), last = p;\n        return ret;\n    }\n} FactorizeLonglong;\n#line 3\
+    \ \"number/test/is_prime.test.cpp\"\n\n#include <iostream>\nusing namespace std;\n\
+    \nint main() {\n    cin.tie(nullptr);\n    ios_base::sync_with_stdio(false);\n\
+    \n    int Q;\n    cin >> Q;\n    while (Q--) {\n        unsigned long long N;\n\
+    \        cin >> N;\n        cout << (is_prime(N) ? \"Yes\" : \"No\") << '\\n';\n\
+    \    }\n}\n"
+  code: "#define PROBLEM \"https://judge.yosupo.jp/problem/primality_test\"\n#include\
+    \ \"../factorize.hpp\"\n\n#include <iostream>\nusing namespace std;\n\nint main()\
+    \ {\n    cin.tie(nullptr);\n    ios_base::sync_with_stdio(false);\n\n    int Q;\n\
+    \    cin >> Q;\n    while (Q--) {\n        unsigned long long N;\n        cin\
+    \ >> N;\n        cout << (is_prime(N) ? \"Yes\" : \"No\") << '\\n';\n    }\n}\n"
+  dependsOn:
+  - number/factorize.hpp
+  - random/xorshift.hpp
+  isVerificationFile: true
+  path: number/test/is_prime.test.cpp
+  requiredBy: []
+  timestamp: '2023-12-26 22:37:19+09:00'
+  verificationStatus: TEST_ACCEPTED
+  verifiedWith: []
+documentation_of: number/test/is_prime.test.cpp
+layout: document
+redirect_from:
+- /verify/number/test/is_prime.test.cpp
+- /verify/number/test/is_prime.test.cpp.html
+title: number/test/is_prime.test.cpp
+---
diff --git a/random/xorshift.hpp.md b/random/xorshift.hpp.md
@@ -36,6 +36,9 @@ data:
   - icon: ':heavy_check_mark:'
     path: number/test/factorize_longlong.test.cpp
     title: number/test/factorize_longlong.test.cpp
+  - icon: ':heavy_check_mark:'
+    path: number/test/is_prime.test.cpp
+    title: number/test/is_prime.test.cpp
   - icon: ':heavy_check_mark:'
     path: number/test/miller-rabin-5e7.test.cpp
     title: number/test/miller-rabin-5e7.test.cpp
@@ -95,6 +98,7 @@ data:
   - number/test/factorize_longlong.test.cpp
   - number/test/miller-rabin.test.cpp
   - number/test/miller-rabin-5e7.test.cpp
+  - number/test/is_prime.test.cpp
   - number/test/factorize_aoj.test.cpp
   - tree/test/frequency_table_of_tree_distance.stress.test.cpp
   - graph/test/chromatic_number.test.cpp

diff --git a/string/lyndon.hpp.md b/string/lyndon.hpp.md
@@ -3,6 +3,9 @@ data:
   _extendedDependsOn: []
   _extendedRequiredBy: []
   _extendedVerifiedWith:
+  - icon: ':heavy_check_mark:'
+    path: string/test/lyndon.test.cpp
+    title: string/test/lyndon.test.cpp
   - icon: ':heavy_check_mark:'
     path: string/test/run_enumerate_lyndon_hash.test.cpp
     title: string/test/run_enumerate_lyndon_hash.test.cpp
@@ -148,6 +151,7 @@ data:
   verificationStatus: LIBRARY_ALL_AC
   verifiedWith:
   - string/test/run_enumerate_lyndon_hash.test.cpp
+  - string/test/lyndon.test.cpp
   - string/test/run_enumerate_lyndon_mersenne61.test.cpp
   - string/test/run_enumerate_lyndon_rmq.test.cpp
 documentation_of: string/lyndon.hpp

diff --git a/string/test/lyndon.test.cpp.md b/string/test/lyndon.test.cpp.md
@@ -0,0 +1,101 @@
+---
+data:
+  _extendedDependsOn:
+  - icon: ':heavy_check_mark:'
+    path: string/lyndon.hpp
+    title: "Lyndon words \uFF08Lyndon \u6587\u5B57\u5217\u306B\u95A2\u3059\u308B\u5404\
+      \u7A2E\u95A2\u6570\uFF09"
+  _extendedRequiredBy: []
+  _extendedVerifiedWith: []
+  _isVerificationFailed: false
+  _pathExtension: cpp
+  _verificationStatusIcon: ':heavy_check_mark:'
+  attributes:
+    '*NOT_SPECIAL_COMMENTS*': ''
+    PROBLEM: https://judge.yosupo.jp/problem/lyndon_factorization
+    links:
+    - https://judge.yosupo.jp/problem/lyndon_factorization
+  bundledCode: "#line 1 \"string/test/lyndon.test.cpp\"\n#define PROBLEM \"https://judge.yosupo.jp/problem/lyndon_factorization\"\
+    \n#line 2 \"string/lyndon.hpp\"\n#include <algorithm>\n#include <cassert>\n#include\
+    \ <functional>\n#include <string>\n#include <tuple>\n#include <utility>\n#include\
+    \ <vector>\n\n// CUT begin\n// Lyndon factorization based on Duval's algorithm\n\
+    // **NOT VERIFIED YET**\n// Reference:\n// [1] K. T. Chen, R. H. Fox, R. C. Lyndon,\n\
+    //     \"Free Differential Calculus, IV. The Quotient Groups of the Lower Central\
+    \ Series,\"\n//     Annals of Mathematics, 68(1), 81-95, 1958.\n// [2] J. P. Duval,\
+    \ \"Factorizing words over an ordered alphabet,\"\n//     Journal of Algorithms,\
+    \ 4(4), 363-381, 1983.\n// - https://cp-algorithms.com/string/lyndon_factorization.html\n\
+    // - https://qiita.com/nakashi18/items/66882bd6e0127174267a\ntemplate <typename\
+    \ T>\nstd::vector<std::pair<int, int>> lyndon_factorization(const std::vector<T>\
+    \ &S) {\n    const int N = S.size();\n    std::vector<std::pair<int, int>> ret;\n\
+    \    for (int l = 0; l < N;) {\n        int i = l, j = i + 1;\n        while (j\
+    \ < N and S[i] <= S[j]) i = (S[i] == S[j] ? i + 1 : l), j++;\n        int n =\
+    \ (j - l) / (j - i);\n        for (int t = 0; t < n; t++) ret.emplace_back(l,\
+    \ j - i), l += j - i;\n    }\n    return ret;\n}\n\nstd::vector<std::pair<int,\
+    \ int>> lyndon_factorization(const std::string &s) {\n    const int N = int(s.size());\n\
+    \    std::vector<int> v(N);\n    for (int i = 0; i < N; i++) v[i] = s[i];\n  \
+    \  return lyndon_factorization<int>(v);\n}\n\n// Compute the longest Lyndon prefix\
+    \ for each suffix s[i:N]\n// (Our implementation is $O(N \\cdot (complexity of\
+    \ lcplen()))$)\n// Example:\n// - `teletelepathy` -> [1,4,1,2,1,4,1,2,1,4,1,2,1]\n\
+    // Reference:\n// [1] H. Bannai et al., \"The \"Runs\" Theorem,\"\n//     SIAM\
+    \ Journal on Computing, 46(5), 1501-1514, 2017.\ntemplate <typename String, typename\
+    \ LCPLENCallable>\nstd::vector<int> longest_lyndon_prefixes(const String &s, const\
+    \ LCPLENCallable &lcp) {\n    const int N = s.size();\n    std::vector<std::pair<int,\
+    \ int>> st{{N, N}};\n    std::vector<int> ret(N);\n    for (int i = N - 1, j =\
+    \ i; i >= 0; i--, j = i) {\n        while (st.size() > 1) {\n            int iv\
+    \ = st.back().first, jv = st.back().second;\n            int l = lcp.lcplen(i,\
+    \ iv);\n            if (!(iv + l < N and s[i + l] < s[iv + l])) break;\n     \
+    \       j = jv;\n            st.pop_back();\n        }\n        st.emplace_back(i,\
+    \ j);\n        ret[i] = j - i + 1;\n    }\n    return ret;\n}\n\n// Compute all\
+    \ runs in given string\n// Complexity: $O(N \\cdot (complexity of lcplen()))$\
+    \ in this implementation\n// (Theoretically $O(N)$ achievable)\n// N = 2e5 ->\
+    \ ~120 ms\n// Reference:\n// [1] H. Bannai et al., \"The \"Runs\" Theorem,\"\n\
+    //     SIAM Journal on Computing, 46(5), 1501-1514, 2017.\ntemplate <typename\
+    \ LCPLENCallable, typename String>\nstd::vector<std::tuple<int, int, int>> run_enumerate(String\
+    \ s) {\n    if (s.empty()) return {};\n    LCPLENCallable lcp(s);\n    std::reverse(s.begin(),\
+    \ s.end());\n    LCPLENCallable revlcp(s);\n    std::reverse(s.begin(), s.end());\n\
+    \    auto t = s;\n    auto lo = *std::min_element(s.begin(), s.end()), hi = *std::max_element(s.begin(),\
+    \ s.end());\n    for (auto &c : t) c = hi - (c - lo);\n    auto l1 = longest_lyndon_prefixes(s,\
+    \ lcp), l2 = longest_lyndon_prefixes(t, lcp);\n    int N = s.size();\n    std::vector<std::tuple<int,\
+    \ int, int>> ret;\n    for (int i = 0; i < N; i++) {\n        int j = i + l1[i],\
+    \ L = i - revlcp.lcplen(N - i, N - j), R = j + lcp.lcplen(i, j);\n        if (R\
+    \ - L >= (j - i) * 2) ret.emplace_back(j - i, L, R);\n\n        if (l1[i] != l2[i])\
+    \ {\n            j = i + l2[i], L = i - revlcp.lcplen(N - i, N - j), R = j + lcp.lcplen(i,\
+    \ j);\n            if (R - L >= (j - i) * 2) ret.emplace_back(j - i, L, R);\n\
+    \        }\n    }\n    std::sort(ret.begin(), ret.end());\n    ret.erase(std::unique(ret.begin(),\
+    \ ret.end()), ret.end());\n    return ret;\n}\n\n// Enumerate Lyndon words up\
+    \ to length n in lexical order\n// https://github.com/bqi343/USACO/blob/master/Implementations/content/combinatorial%20(11.2)/DeBruijnSeq.h\n\
+    // Example: k=2, n=4 => [[0,],[0,0,0,1,],[0,0,1,],[0,0,1,1,],[0,1,],[0,1,1,],[0,1,1,1,],[1,],]\n\
+    // Verified: https://codeforces.com/gym/102001/problem/C / https://codeforces.com/gym/100162/problem/G\n\
+    std::vector<std::vector<int>> enumerate_lyndon_words(int k, int n) {\n    assert(k\
+    \ > 0);\n    assert(n > 0);\n    std::vector<std::vector<int>> ret;\n    std::vector<int>\
+    \ aux(n + 1);\n\n    std::function<void(int, int)> gen = [&](int t, int p) {\n\
+    \        // t: current length\n        // p: current min cycle length\n      \
+    \  if (t == n) {\n            std::vector<int> tmp(aux.begin() + 1, aux.begin()\
+    \ + p + 1);\n            ret.push_back(std::move(tmp));\n        } else {\n  \
+    \          ++t;\n            aux[t] = aux[t - p];\n            gen(t, p);\n  \
+    \          while (++aux[t] < k) gen(t, t);\n        }\n    };\n    gen(0, 1);\n\
+    \    return ret;\n}\n#line 3 \"string/test/lyndon.test.cpp\"\n\n#include <iostream>\n\
+    #line 6 \"string/test/lyndon.test.cpp\"\nusing namespace std;\n\nint main() {\n\
+    \    cin.tie(nullptr);\n    ios_base::sync_with_stdio(false);\n\n    string S;\n\
+    \    cin >> S;\n    auto ret = lyndon_factorization(S);\n    for (auto [l, len]\
+    \ : ret) cout << l << ' ';\n    cout << S.size() << '\\n';\n}\n"
+  code: "#define PROBLEM \"https://judge.yosupo.jp/problem/lyndon_factorization\"\n\
+    #include \"../lyndon.hpp\"\n\n#include <iostream>\n#include <string>\nusing namespace\
+    \ std;\n\nint main() {\n    cin.tie(nullptr);\n    ios_base::sync_with_stdio(false);\n\
+    \n    string S;\n    cin >> S;\n    auto ret = lyndon_factorization(S);\n    for\
+    \ (auto [l, len] : ret) cout << l << ' ';\n    cout << S.size() << '\\n';\n}\n"
+  dependsOn:
+  - string/lyndon.hpp
+  isVerificationFile: true
+  path: string/test/lyndon.test.cpp
+  requiredBy: []
+  timestamp: '2023-12-26 22:37:19+09:00'
+  verificationStatus: TEST_ACCEPTED
+  verifiedWith: []
+documentation_of: string/test/lyndon.test.cpp
+layout: document
+redirect_from:
+- /verify/string/test/lyndon.test.cpp
+- /verify/string/test/lyndon.test.cpp.html
+title: string/test/lyndon.test.cpp
+---