Merge pull request #826 from maspypy/stirling

Stirling Number (small p)

math/stirling_number_of_the_first_kind_small_p_large_n/checker.cpp

@@ -0,0 +1,62 @@
+// https://github.com/MikeMirzayanov/testlib/blob/master/checkers/wcmp.cpp
+
+// The MIT License (MIT)
+
+// Copyright (c) 2015 Mike Mirzayanov
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "testlib.h"
+
+using namespace std;
+
+int main(int argc, char * argv[])
+{
+    setName("compare sequences of tokens");
+    registerTestlibCmd(argc, argv);
+
+    int n = 0;
+    string j, p;
+
+    while (!ans.seekEof() && !ouf.seekEof()) 
+    {
+        n++;
+
+        ans.readWordTo(j);
+        ouf.readWordTo(p);
+
+        if (j != p)
+            quitf(_wa, "%d%s words differ - expected: '%s', found: '%s'", n, englishEnding(n).c_str(), compress(j).c_str(), compress(p).c_str());
+    }
+
+    if (ans.seekEof() && ouf.seekEof())
+    {
+        if (n == 1)
+            quitf(_ok, "\"%s\"", compress(j).c_str());
+        else
+            quitf(_ok, "%d tokens", n);
+    }
+    else
+    {
+        if (ans.seekEof())
+            quitf(_wa, "Participant output contains extra tokens");
+        else
+            quitf(_wa, "Unexpected EOF in the participants output");
+    }
+}

math/stirling_number_of_the_first_kind_small_p_large_n/gen/example_00.in

@@ -0,0 +1,10 @@
+9 7
+0 0
+1 0
+1 1
+5 0
+5 1
+5 2
+5 3
+5 4
+5 5

math/stirling_number_of_the_first_kind_small_p_large_n/gen/example_01.in

@@ -0,0 +1,8 @@
+7 7
+40 0
+40 10
+40 20
+40 30
+40 40
+1000000007 998244353
+1000000000000000000 1000000000000000000

math/stirling_number_of_the_first_kind_small_p_large_n/gen/random.cpp

@@ -0,0 +1,31 @@
+#include <iostream>
+
+#include "../params.h"
+#include "random.h"
+
+bool is_prime(int p) {
+  if (p <= 1) return false;
+  for (int i = 2; i < p; ++i)
+    if (p % i == 0) return false;
+  return true;
+}
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  int p;
+  while (1) {
+    p = gen.uniform<int>(P_MIN, P_MAX);
+    if (is_prime(p)) break;
+  }
+  printf("%d %d\n", T, p);
+
+  for (int t = 0; t < T; ++t) {
+    long long n = gen.uniform<long long>(0, N_MAX);
+    long long k = gen.uniform<long long>(0, n);
+    printf("%lld %lld\n", n, k);
+  }
+  return 0;
+}

math/stirling_number_of_the_first_kind_small_p_large_n/gen/small_n.cpp

@@ -0,0 +1,23 @@
+#include <iostream>
+
+#include "../params.h"
+#include "random.h"
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int primes[] = {2, 3, 5, 7, 101, 4999};
+
+  int T = T_MAX;
+  int p = primes[seed % 6];
+  printf("%d %d\n", T, p);
+
+  int n_max = 5000;
+  for (int t = 0; t < T; ++t) {
+    long long n = gen.uniform<int>(0, n_max);
+    long long k = gen.uniform<int>(0, n);
+    printf("%lld %lld\n", n, k);
+  }
+  return 0;
+}

math/stirling_number_of_the_first_kind_small_p_large_n/gen/small_p.cpp

@@ -0,0 +1,54 @@
+#include <iostream>
+
+#include "../params.h"
+#include "random.h"
+
+using namespace std;
+using ll = long long;
+bool is_prime(int p) {
+  if (p <= 1) return false;
+  for (int i = 2; i < p; ++i)
+    if (p % i == 0) return false;
+  return true;
+}
+
+// p が小さいケースは、答が 0 ばかりにならないように注意して作る
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int primes[] = {2, 3, 5, 7, 11, 13};
+
+  int T = T_MAX;
+  int p = primes[seed % 6];
+  printf("%d %d\n", T, p);
+
+  auto nonzero_binom = [&]() -> pair<ll, ll> {
+    ll a = gen.uniform<ll>(0, N_MAX / p);
+    auto dfs = [&](auto& dfs, ll a) -> ll {
+      if (a <= p) return gen.uniform<ll>(0, a);
+      ll r = a % p;
+      a /= p;
+      ll b = dfs(dfs, a);
+      return p * b + (gen.uniform<ll>(0, r));
+    };
+    ll b = dfs(dfs, a);
+    return {a, b};
+  };
+
+  auto gen_nk = [&]() -> pair<ll, ll> {
+    while (1) {
+      auto [a, b] = nonzero_binom();
+      ll m = gen.uniform<ll>(0, p);
+      ll n = a * p + m;
+      ll k = p * b + (a - b) + gen.uniform<ll>(0, m);
+      if (0 <= k && k <= n && n <= N_MAX) return {n, k};
+    }
+  };
+
+  for (int t = 0; t < T; ++t) {
+    auto [n, k] = gen_nk();
+    printf("%lld %lld\n", n, k);
+  }
+  return 0;
+}

math/stirling_number_of_the_first_kind_small_p_large_n/hash.json

@@ -0,0 +1,42 @@
+{
+  "example_00.in": "c16f54d7f1281fb5f618a684053b512cf2cba71689396b4e1fb5a56cf11667ce",
+  "example_00.out": "21f95cb1af14205f145524442956ae96eabe6bfd2082388002d1247174d7b86e",
+  "example_01.in": "f0a91f062c908735a6c24a5ef90fd16bf45324e11aec4d283052f7e4ff0cbe42",
+  "example_01.out": "eed1a4b4a1d0b04c8ff891c2cb3aa69168063d3e0e46515241826ef040927a61",
+  "random_00.in": "1249d44ad552ed2ccab609641a194e7fd07b8e544222e8fa124ffe9fec8209b0",
+  "random_00.out": "51489d3975cf9f695e48f374334c80c498e62dfaaae2c8329b8ad73e293194f9",
+  "random_01.in": "1dc43972adae22056f0731f678b56ff3835630f01e5196a34bd844fd346edc3e",
+  "random_01.out": "aac767c4d9e2b94c536ac192396ebdc53b4230bc185faaf6cb8874097731e755",
+  "random_02.in": "f1d80f1bcab3b9a18fe95b57caa181bb20f65c8ea05a806559ac2249f370eaec",
+  "random_02.out": "4d298e3e75e3b746ca92195255b60834f79ed722503a551e333cc7648060cc8b",
+  "random_03.in": "7e369e909ede8bc8e09e2354a11d793cd3a394957d0b2fb9d68b7194a14ecae1",
+  "random_03.out": "112ff12de4e7e58fbac0e45ffb488473e2b8339e28e6cd0f6f9a2cec0c86eee4",
+  "random_04.in": "240fc7f8d572e270fc5a6a7dc97a132f67029f2a45892ed4ee071672f5d02560",
+  "random_04.out": "41ec82937b9155ed81c626a0ce08fdcd739cb3213cb429b77133a0ded5aa53b9",
+  "random_05.in": "1fc63785c8f706efd2527959ba233ba63e1b2bf6761ab2180e66b07d0319c519",
+  "random_05.out": "ec84aa3cc92b3c996d2230f55464f574a572c2e5ccce0fa6ddeb61a04ceb33af",
+  "small_n_00.in": "558d85596cbccb5ab52d78d1cef3ff802b414084c4a80594516da44c7d2bd70a",
+  "small_n_00.out": "002363e799a2a584fa2c94b3aa0d771ba13366edc016bb1b6ed667622cdeb5ec",
+  "small_n_01.in": "38c07365f1cd6720e3c6248e96eaadb24433116d1812ce83ac03e2d301b13efe",
+  "small_n_01.out": "70b9fac1ce6d3bb6fde73c11bf1656e3b5830360e20392b6ea7494c1fc818461",
+  "small_n_02.in": "d4714164c0d4e8508d103fbb8bdcd6ad8b82c140b102f8786cc5d1e609d888bb",
+  "small_n_02.out": "49c86d0dbd6c436e9c2702efaf7d32fc430cc6749601970949e6fb38eedfb028",
+  "small_n_03.in": "cb17551e532c85adceed45fdb28b58d453a31b339f5a195e8c06138e8cecebdd",
+  "small_n_03.out": "447a2eeaa0b106ba8c59f45f631209d61efa2156b779a00aff8704a9cf60227f",
+  "small_n_04.in": "7b779b58ff77e31cc74dd392c3fc55433c5750f96a373704cfa1df804efde947",
+  "small_n_04.out": "e1d6794c6575c6870ed2db1315b76661a9a365e3255b29d5fdabd676cfd6fe05",
+  "small_n_05.in": "8a9b0832a9f14d3eb3f42dfe85a1f3f655e4daca91a0826486e51076c051632f",
+  "small_n_05.out": "9c1a2b4a3ed6ba4469df5ce67d01c5baba7f4b2c528e62e3bf26df97b81bcd74",
+  "small_p_00.in": "ab99ea648c4580e59e630ee1a6334fda467bf0c57b2e3dbab8aea534a84eb5ef",
+  "small_p_00.out": "a7e6f4bf5a8f215badc2778583448218a72c388a339f726b7c72e507015288d9",
+  "small_p_01.in": "048439738fe7542dc7ac23383dd9e07b7972ed60f2c092632830048556efbea9",
+  "small_p_01.out": "e1d3dd7ba36411c0ac234dfcefe90d394db44a64448402d05dfc73fa6c5717cf",
+  "small_p_02.in": "09668c9bb5f5bf3ac56dfbaf6bb45a1456228166ef3989208b13e434f32bcdbd",
+  "small_p_02.out": "ea11acc2723773b8b4e045125039a14876994be6fa202d7862b1182eb6db2ffc",
+  "small_p_03.in": "e3d16b21a96874c33e33089da94888aa7f6472b10e8013a53a8032cd32b0767d",
+  "small_p_03.out": "1c59b8f5b1afc076784ea1656c17575731f0b9af14afe98412b772fa5cf3bf25",
+  "small_p_04.in": "4f3ef959eeec6e1990244de1ebacfbbb75fa05f47a2e5d131ed19a1aaabbcff4",
+  "small_p_04.out": "6358f7f1e653bb57b0e2f5da859baa58dddbc2e375db99ea93507a19f053740b",
+  "small_p_05.in": "547bce4b9c3d933c60c7767a34af4f97bd7b77f4a3db815e11215dd844be3c85",
+  "small_p_05.out": "7b71601410cb890439f38c1b246f473f59166ed66ebea84db98a57c062d4abe4"
+}

math/stirling_number_of_the_first_kind_small_p_large_n/info.toml

@@ -0,0 +1,29 @@
+title = 'Stirling Number of the First Kind (small p, large n)'
+timelimit = 10.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/817"
+
+[[tests]]
+    name = "example.in"
+    number = 2
+[[tests]]
+    name = "small_n.cpp"
+    number = 6
+[[tests]]
+    name = "random.cpp"
+    number = 6
+[[tests]]
+    name = "small_p.cpp"
+    number = 6
+
+
+[[solutions]]
+    name = "naive.cpp"
+    wrong = false
+    allow_tle = true
+
+[params]
+    T_MAX = 200_000
+    P_MIN = 2
+    P_MAX = 5000
+    N_MIN = 0
+    N_MAX = 1_000_000_000_000_000_000

math/stirling_number_of_the_first_kind_small_p_large_n/sol/correct.cpp

@@ -0,0 +1,22 @@
+#include <cstdio>
+#include <iostream>
+#include <vector>
+using namespace std;
+using ll = long long;
+
+#include "stirling_number_query.hpp"
+
+int main() {
+  int T, p;
+  scanf("%d %d\n", &T, &p);
+
+  Stirling_Number_Query X(p, 1, 0);
+
+  for (int t = 0; t < T; ++t) {
+    long long n, k;
+    scanf("%lld %lld\n", &n, &k);
+    int ans = X.S1(n, k);
+    printf("%d\n", ans);
+  }
+  return 0;
+}

math/stirling_number_of_the_first_kind_small_p_large_n/sol/naive.cpp

@@ -0,0 +1,40 @@
+#include <stdio.h>
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+const int LIM = 5010;
+
+int S[LIM][LIM];
+
+void gen_S(int p) {
+  S[0][0] = 1;
+  for (int i = 1; i < LIM; ++i) {
+    for (int j = 0; j < i + 1; ++j) {
+      int &x = S[i][j];
+      if (j) x += S[i - 1][j - 1];
+      x -= S[i - 1][j] * (i - 1);
+      x %= p;
+      if (x < 0) x += p;
+    }
+  }
+}
+
+void TLE() {
+  while (1) {}
+}
+
+int main() {
+  int T, p;
+  scanf("%d %d", &T, &p);
+
+  gen_S(p);
+
+  for (int t = 0; t < T; ++t) {
+    long long n, k;
+    scanf("%lld %lld", &n, &k);
+    if (n >= LIM) { TLE(); }
+    printf("%d\n", S[n][k]);
+  }
+  return 0;
+}