Merge branch 'yosupo06:master' into master

graph/assignment/task.md

@@ -25,7 +25,7 @@ $N$
 $a_{00}$ $a_{01}$ ... $a_{0,{N-1}}$
 $a_{10}$ $a_{11}$ ... $a_{1,{N-1}}$
 :
-$a_{{N-1},0}$ $a_{{N-1},1}$ ... $a_{{N-1},{N-1}}$
+$a_{ {N-1}, 0 }$ $a_{ {N-1}, 1 }$ ... $a_{ {N-1}, {N-1} }$
 ~~~
 
 ## @{keyword.output}

math/exp_of_set_power_series/gen/overflow.cpp

@@ -0,0 +1,186 @@
+// Reference : https://codeforces.com/blog/entry/92183
+
+#include <algorithm>
+#include <cassert>
+#include <vector>
+
+#include "../params.h"
+#include "random.h"
+
+namespace noshi91 {
+
+namespace composition_egf_sps_internal {
+
+template <class T, class F> void bitwise_transform(std::vector<T> &a, F f) {
+  const int n = a.size();
+  for (int w = 1; w < n; w *= 2) {
+    for (int i = 0; i < n; i += w * 2) {
+      for (int j = 0; j < w; j++) {
+        f(a[i + j], a[i + w + j]);
+      }
+    }
+  }
+}
+
+// f: sequence of length n + 1
+// s: n variable set power series, constant term is 0
+// output: \sum_{k=0}^{n} f_k s^k / k!
+template <class T>
+std::vector<T> composition_egf_sps(const std::vector<T> &f,
+                                   const std::vector<T> &s) {
+  const int n = int(f.size()) - 1;
+  assert(0 <= n && n <= 30);
+  assert(int(s.size()) == 1 << n);
+
+  std::vector<std::vector<std::vector<T>>> a(n + 1);
+  for (int i = 0; i <= n; i++) {
+    a[i].assign(i + 1, std::vector<T>(1 << i));
+    a[i][0][0] = f[n - i];
+  }
+
+  for (int v = 0; v < n; v++) {
+    std::vector h(v + 1, std::vector<T>(1 << v));
+    for (int i = 0; i < 1 << v; i++)
+      h[__builtin_popcount(i)][i] = s[(1 << v) + i];
+    for (int i = 0; i <= v; i++)
+      bitwise_transform(h[i], [](T &l, T &r) { r += l; });
+    for (int i = v + 1; i <= n; i++) {
+      for (int j = 0; j <= i; j++) {
+        std::copy_n(a[i][j].begin(), 1 << v, a[i][j].begin() + (1 << v));
+      }
+    }
+    for (int i = v; i < n; i++) {
+      for (int j = 0; j <= v; j++) {
+        for (int k = 0; j + k <= i; k++) {
+          for (int p = 0; p < 1 << v; p++) {
+            a[i + 1][j + k + 1][(1 << v) + p] += h[j][p] * a[i][k][p];
+          }
+        }
+      }
+    }
+  }
+
+  for (int i = 0; i <= n; i++)
+    bitwise_transform(a[n][i], [](T &l, T &r) { r -= l; });
+  std::vector<T> t(1 << n);
+  for (int i = 0; i < 1 << n; i++)
+    t[i] = a[n][__builtin_popcount(i)][i];
+  return t;
+}
+
+// f: polynomial
+// s: set power series
+// output: f(s)
+template <class T>
+std::vector<T> composition_poly_sps(std::vector<T> f, const std::vector<T> &s) {
+  assert(!s.empty());
+  const int n = __builtin_ctz(s.size());
+  assert(int(s.size()) == 1 << n);
+  std::vector<T> eval(n + 1, T(0));
+  const T c = s[0];
+  for (int i = 0; i <= n && !f.empty(); i++) {
+    T t = 0;
+    for (int j = f.size(); j-- > 0;)
+      t = t * c + f[j];
+    eval[i] = t;
+    for (int j = 1; j < int(f.size()); j++)
+      f[j - 1] = f[j] * j;
+    f.pop_back();
+  }
+  return composition_egf_sps(eval, s);
+}
+
+} // namespace composition_egf_sps_internal
+
+using composition_egf_sps_internal::composition_egf_sps;
+using composition_egf_sps_internal::composition_poly_sps;
+
+} // namespace noshi91
+
+#include <cstdio>
+
+constexpr int mod = 998244353;
+using ll = long long;
+struct mm {
+  int x;
+  mm() : x(0) {}
+  mm(ll x_) : x(x_ % mod) {
+    if (x < 0)
+      x += mod;
+  }
+  mm &operator+=(mm b) {
+    if ((x += b.x) >= mod)
+      x -= mod;
+    return *this;
+  }
+  mm &operator-=(mm b) {
+    if ((x -= b.x) < 0)
+      x += mod;
+    return *this;
+  }
+  mm &operator*=(mm b) {
+    x = ll(x) * b.x % mod;
+    return *this;
+  }
+  mm &operator/=(mm b) { return *this *= b.pow(mod - 2); }
+  friend mm operator+(mm a, mm b) { return a += b; }
+  friend mm operator-(mm a, mm b) { return a -= b; }
+  friend mm operator*(mm a, mm b) { return a *= b; }
+  friend mm operator/(mm a, mm b) { return a /= b; }
+  mm pow(ll e) const {
+    mm r = 1, b = *this;
+    while (e) {
+      if (e & 1)
+        r *= b;
+      b *= b;
+      e >>= 1;
+    }
+    return r;
+  }
+};
+
+using mint = mm;
+
+int popcnt(int x) { return __builtin_popcount(x); }
+
+int main(int, char **argv) {
+
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    const int n = N_MAX;
+    std::vector<int> binom(n + 1);
+    binom[0] = 1;
+    binom[n] = 1;
+    for (int i = 1; i <= n - 1; ++i) {
+        binom[i] = binom[i - 1] * (n - i) / i;
+    }
+
+    std::vector<mint> a(1 << n);
+    for (int i = 0; i < (1 << n); ++i) {
+        int cnt = popcnt(i & ~(1 << (n - 1)));
+        int q = (MOD - 1) / binom[cnt];
+        a[i] = gen.uniform<int>(q / 100 * 99, q);
+    }
+
+    std::vector<mint> s{a.begin(), a.begin() + (1 << (n - 1))}, ln(n);
+    mint sign = 1;
+    for (int i = 1; i < n; ++i) {
+        ln[i] = sign / i;
+        sign = 0 - sign;
+    }
+
+    auto pre = noshi91::composition_egf_sps(ln, s);
+
+    for (int i = 0; i < (1 << (n - 1)); ++i) {
+        a[i] = pre[i];
+    }
+
+    printf("%d\n", n);
+    for (int i = 0; i < (1 << n); i++) {
+        printf("%d%c", a[i].x, " \n"[i + 1 == 1 << n]);
+    }
+
+    return 0;
+}
+

math/exp_of_set_power_series/hash.json

@@ -11,6 +11,8 @@
   "n_01_00.out": "4355a46b19d348dc2f57c046f8ef63d4538ebb936000f3c9ee954a27460dd865",
   "n_01_01.in": "eda407e4be0e446975a488667646ef3cbbf6a5b6fbec459a2a6142b6c232635c",
   "n_01_01.out": "32ede1ac358dd8ee38d2157a560c4ca4f23a19ef3e431b8ccc479b2e24aea6c5",
+  "overflow_00.in": "ed7934e717aa489a7520ba89877a7861960f4c91f1658a9f5bc0af316dc006b6",
+  "overflow_00.out": "9b2bd77e9180b846f6b608e1440e3bfef1cf9b74bc6192263ee0aea99452e9f4",
   "random_00.in": "fd363d616f80af7402396a912f3faad2f8b38c9cc8ff6d69ff0a643ac9339b73",
   "random_00.out": "cff16ebca6bb37e81e5da7f3f8a9f8bfe0c0f2c5f032f59a6674675d1ef830b3",
   "random_01.in": "b2d31191b8cb4657ea85b230f353f814e78001d893a06090a954ccf0fe5fca7a",

math/exp_of_set_power_series/info.toml

@@ -17,6 +17,9 @@ forum = "https://github.com/yosupo06/library-checker-problems/issues/974"
 [[tests]]
     name = "n_01.cpp"
     number = 2
+[[tests]]
+    name = "overflow.cpp"
+    number = 1
 
 [[solutions]]
     name = "naive.cpp"

math/sharp_p_subset_sum/hash.json

@@ -1,50 +1,50 @@
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   "big_03.in": "48ac9f3d78df0c537243e178939e5f442ab66e5e8b2264e7faf24edd31b63770",
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   "many_sets_04.in": "9eacb929bb249c7eefffbb3d10271db3e41e33e70503cc21d3ada94bf670744e",
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   "random_02.in": "f565cc402290128ef7a79f2c3b10dfe3b67896765a7b18c2bf672bc8c60b2166",
-  "random_02.out": "9ac2e5118a21cdd7b9ce858954c9f3a64062949020b5107607fbcd25e0d3e1da",
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   "random_04.in": "2f354dc76a61715b6299006f1ba15758a63efe9dad11c5f04386a830d32b8083",
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   "small_00.in": "48421ad16ad0aec745f376b378ed07c13631f32e6606dbec76e332fa1314d352",
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   "small_01.in": "6342d55b126c4c4a570c08491f7794e541261442782dc22cca72dbdde733fa77",
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   "small_02.in": "b9f86b86337c450cb48d3c5019cba9c92308915c8d48ef4dd011355abee97426",
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   "small_03.in": "14932b02f5bf32318f44fddb93c0c9e3f9d48dda7c65a10331f3665d01346455",
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   "small_04.in": "f0744b7e10d21be515fbbc1353dc6dd15a7a3c16eb7fcf7fba9094da5c51c5fd",
-  "small_04.out": "29cf24941cd2ac99095799d31b8ef6e026cc4df6345b3f5d3829daea9df2e798",
+  "small_04.out": "7f7340989ed15271dd1cc548b78d1f379e4f1e5229d24b1426554485d8492c1e",
   "small_N_large_T_00.in": "4d74d2e31476556c78c7839eb929f6a5f20287c5f99aca0aa6d75940c3bca59a",
-  "small_N_large_T_00.out": "6815be512ceb5568f609eeae2fcefb79c5defcb77cce2d92bedeaa3736ddfb51",
+  "small_N_large_T_00.out": "8aba7f57111639b97055915af4458753b795a88973824014aaad88d8878a9378",
   "small_N_large_T_01.in": "d8187ef720a6336a96c0f4da2a48c8abfe25ee88c045c38ba5ed93366ba0eb34",
-  "small_N_large_T_01.out": "2ff9af9e0f155c87e2eabbf1cb47065a63bdfd996a74491feba142cbb86bb4b0",
+  "small_N_large_T_01.out": "6c742016c4e0530becf5d9c068965a49963e23d1aca9a1ff0d82c0bfc7019ccb",
   "small_N_large_T_02.in": "8c5fe1489ff55d15158a696418e5adc088b4d284922b92b0140bef989ab878cb",
-  "small_N_large_T_02.out": "62ad6a9ce70c31ecdfb27207dd506b521a60fe4ecbebf1605f0aae6f8dfaf721"
+  "small_N_large_T_02.out": "3e5507adce2796e4b106ae680e558ebee8d36b77934ed707cb5d827edaa721b1"
 }

math/sharp_p_subset_sum/sol/correct.cpp

@@ -201,6 +201,10 @@ int main(){
       Mint add=fact.inv(j)*cnt[k];
       if(j&1)f[k*j]+=add; else f[k*j]-=add;
    } f=f.exp();
-   for(int i=1;i<=t;i++)printf("%d ",f[i].val);
+   for(int i=1;i<=t;i++) {
+      printf("%d",f[i].val);
+      if(i<t)printf(" ");
+   }
+   printf("\n");
    return 0;
 }