From 92870f31523fecf32e4b982accfdfbc57fc7614c Mon Sep 17 00:00:00 2001
From: Nachia Vivias <piyopiyograph@gol.com>
Date: Sat, 13 Jul 2024 21:31:37 +0900
Subject: [PATCH 1/2] [graph/counting_c4] add problem

---
 graph/counting_c4/checker.cpp                 |  62 ++++++++
 graph/counting_c4/gen/dense.cpp               |  20 +++
 graph/counting_c4/gen/erdos_renyi.h           |  41 ++++++
 graph/counting_c4/gen/example_00.in           |   6 +
 graph/counting_c4/gen/example_01.in           |   8 +
 graph/counting_c4/gen/large_random_simple.cpp |  15 ++
 graph/counting_c4/gen/max_complete.cpp        |  16 ++
 graph/counting_c4/gen/max_near_k_simple.cpp   |  58 ++++++++
 graph/counting_c4/gen/max_random_simple.cpp   |  13 ++
 graph/counting_c4/gen/minimum_00.in           |   2 +
 graph/counting_c4/gen/multiplied_c4.cpp       |  42 ++++++
 graph/counting_c4/gen/small_dense_simple.cpp  |  18 +++
 graph/counting_c4/gen/small_sparse_simple.cpp |  20 +++
 graph/counting_c4/gen/star.cpp                |  35 +++++
 graph/counting_c4/hash.json                   |  60 ++++++++
 graph/counting_c4/info.toml                   |  47 ++++++
 graph/counting_c4/sol/correct.cpp             | 139 ++++++++++++++++++
 graph/counting_c4/sol/naive.cpp               |  47 ++++++
 graph/counting_c4/task.md                     |  45 ++++++
 graph/counting_c4/verifier.cpp                |  24 +++
 20 files changed, 718 insertions(+)
 create mode 100644 graph/counting_c4/checker.cpp
 create mode 100644 graph/counting_c4/gen/dense.cpp
 create mode 100644 graph/counting_c4/gen/erdos_renyi.h
 create mode 100644 graph/counting_c4/gen/example_00.in
 create mode 100644 graph/counting_c4/gen/example_01.in
 create mode 100644 graph/counting_c4/gen/large_random_simple.cpp
 create mode 100644 graph/counting_c4/gen/max_complete.cpp
 create mode 100644 graph/counting_c4/gen/max_near_k_simple.cpp
 create mode 100644 graph/counting_c4/gen/max_random_simple.cpp
 create mode 100644 graph/counting_c4/gen/minimum_00.in
 create mode 100644 graph/counting_c4/gen/multiplied_c4.cpp
 create mode 100644 graph/counting_c4/gen/small_dense_simple.cpp
 create mode 100644 graph/counting_c4/gen/small_sparse_simple.cpp
 create mode 100644 graph/counting_c4/gen/star.cpp
 create mode 100644 graph/counting_c4/hash.json
 create mode 100644 graph/counting_c4/info.toml
 create mode 100644 graph/counting_c4/sol/correct.cpp
 create mode 100644 graph/counting_c4/sol/naive.cpp
 create mode 100644 graph/counting_c4/task.md
 create mode 100644 graph/counting_c4/verifier.cpp

diff --git a/graph/counting_c4/checker.cpp b/graph/counting_c4/checker.cpp
new file mode 100644
index 000000000..6a66d5330
--- /dev/null
+++ b/graph/counting_c4/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");
+    }
+}
diff --git a/graph/counting_c4/gen/dense.cpp b/graph/counting_c4/gen/dense.cpp
new file mode 100644
index 000000000..13bf0c741
--- /dev/null
+++ b/graph/counting_c4/gen/dense.cpp
@@ -0,0 +1,20 @@
+#include "../params.h"
+#include "random.h"
+#include <cstdio>
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = 10;
+  int m = M_MAX;
+
+  std::printf("%d %d\n", n, m);
+
+  for(int i=0; i<m; i++){
+    int u = gen.uniform(0, n-1);
+    int v = gen.uniform(0, n-2);
+    if(u <= v) v += 1;
+    std::printf("%d %d\n", u, v);
+  }
+}
diff --git a/graph/counting_c4/gen/erdos_renyi.h b/graph/counting_c4/gen/erdos_renyi.h
new file mode 100644
index 000000000..4a0549178
--- /dev/null
+++ b/graph/counting_c4/gen/erdos_renyi.h
@@ -0,0 +1,41 @@
+#include "random.h"
+#include <algorithm>
+#include <cassert>
+#include <cstdio>
+#include <set>
+#include <utility>
+#include <vector>
+
+void erdos_renyi(int n, int m, Random &gen) {
+  assert(static_cast<long long>(n) * (n - 1) / 2 >= m);
+
+  std::vector<std::pair<int, int>> edges(m);
+  if (static_cast<long long>(n) * (n - 1) / 2 > m * 2) {
+    // sparse
+    std::set<std::pair<int, int>> eset;
+    for (auto &e : edges) {
+      do {
+        e = gen.uniform_pair(0, n - 1);
+      } while (!eset.insert(std::minmax(e.first, e.second)).second);
+    }
+  } else {
+    // dense
+    std::vector<std::pair<int, int>> all;
+    for (int u = 0; u < n; ++u) {
+      for (int v = 0; v < u; ++v) {
+        if (gen.uniform_bool()) {
+          all.emplace_back(u, v);
+        } else {
+          all.emplace_back(v, u);
+        }
+      }
+    }
+    gen.shuffle(all.begin(), all.end());
+    std::copy(all.begin(), all.begin() + m, edges.begin());
+  }
+
+  std::printf("%d %d\n", n, m);
+  for (const auto &e : edges) {
+    std::printf("%d %d\n", e.first, e.second);
+  }
+}
diff --git a/graph/counting_c4/gen/example_00.in b/graph/counting_c4/gen/example_00.in
new file mode 100644
index 000000000..3aeeedf28
--- /dev/null
+++ b/graph/counting_c4/gen/example_00.in
@@ -0,0 +1,6 @@
+4 5
+0 3
+2 0
+2 1
+2 3
+1 3
diff --git a/graph/counting_c4/gen/example_01.in b/graph/counting_c4/gen/example_01.in
new file mode 100644
index 000000000..3b39aba22
--- /dev/null
+++ b/graph/counting_c4/gen/example_01.in
@@ -0,0 +1,8 @@
+4 7
+0 1
+0 1
+0 1
+0 3
+0 3
+1 2
+2 3
diff --git a/graph/counting_c4/gen/large_random_simple.cpp b/graph/counting_c4/gen/large_random_simple.cpp
new file mode 100644
index 000000000..b4d9f77dd
--- /dev/null
+++ b/graph/counting_c4/gen/large_random_simple.cpp
@@ -0,0 +1,15 @@
+#include "../params.h"
+#include "./erdos_renyi.h"
+#include "random.h"
+#include <algorithm>
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(N_MIN, N_MAX);
+  int m = gen.uniform<int>(
+      M_MIN, std::min(M_MAX, static_cast<long long>(n) * (n - 1) / 2));
+
+  erdos_renyi(n, m, gen);
+}
diff --git a/graph/counting_c4/gen/max_complete.cpp b/graph/counting_c4/gen/max_complete.cpp
new file mode 100644
index 000000000..ce1a544a6
--- /dev/null
+++ b/graph/counting_c4/gen/max_complete.cpp
@@ -0,0 +1,16 @@
+#include "../params.h"
+#include "./erdos_renyi.h"
+#include "random.h"
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MIN;
+  while (n < N_MAX && n * (n + 1) / 2 <= M_MAX) {
+    n += 1;
+  }
+  int m = n * (n - 1) / 2;
+
+  erdos_renyi(n, m, gen);
+}
diff --git a/graph/counting_c4/gen/max_near_k_simple.cpp b/graph/counting_c4/gen/max_near_k_simple.cpp
new file mode 100644
index 000000000..3461c169c
--- /dev/null
+++ b/graph/counting_c4/gen/max_near_k_simple.cpp
@@ -0,0 +1,58 @@
+#include "../params.h"
+#include "random.h"
+#include <algorithm>
+#include <cstdio>
+#include <utility>
+#include <vector>
+
+std::vector<int> generate_phase(int n, int k){
+  std::vector<int> nph;
+  for(int t=0; t<k; t++) nph.push_back((n+t)/k);
+  return nph;
+}
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int m = int(M_MAX);
+  int k = seed + 2;
+
+  int n = 1;
+  while(true){
+    n++;
+    auto nph = generate_phase(n, k);
+    int nxm = 0;
+    for(int t=0; t<k; t++) for(int s=0; s<t; s++){
+      nxm += nph[t] * nph[s];
+    }
+    if(nxm >= m) break;
+  }
+
+  auto nph = generate_phase(n, k);
+  std::vector<int> beg_phase(k+1);
+  for(int t=0; t<k; t++) beg_phase[t+1] = beg_phase[t] + nph[t];
+
+  std::vector<std::pair<int, int>> edges;
+  for(int t=0; t<k; t++) for(int s=0; s<t; s++){
+    for(int p=0; p<nph[t]; p++) for(int q=0; q<nph[s]; q++){
+      int a = beg_phase[t] + p;
+      int b = beg_phase[s] + q;
+      edges.push_back({ a, b });
+    }
+  }
+
+  gen.shuffle(edges.begin(), edges.end());
+  edges.resize(m);
+
+  for (auto &e : edges) {
+    if (gen.uniform_bool()) {
+      std::swap(e.first, e.second);
+    }
+  }
+
+  std::printf("%d %d\n", n, m);
+  for (const auto &e : edges) {
+    std::printf("%d %d\n", e.first, e.second);
+  }
+}
diff --git a/graph/counting_c4/gen/max_random_simple.cpp b/graph/counting_c4/gen/max_random_simple.cpp
new file mode 100644
index 000000000..1a187b9d4
--- /dev/null
+++ b/graph/counting_c4/gen/max_random_simple.cpp
@@ -0,0 +1,13 @@
+#include "../params.h"
+#include "./erdos_renyi.h"
+#include "random.h"
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = M_MAX;
+
+  erdos_renyi(n, m, gen);
+}
diff --git a/graph/counting_c4/gen/minimum_00.in b/graph/counting_c4/gen/minimum_00.in
new file mode 100644
index 000000000..5d0dfc619
--- /dev/null
+++ b/graph/counting_c4/gen/minimum_00.in
@@ -0,0 +1,2 @@
+2 1
+0 1
diff --git a/graph/counting_c4/gen/multiplied_c4.cpp b/graph/counting_c4/gen/multiplied_c4.cpp
new file mode 100644
index 000000000..d7ce6f496
--- /dev/null
+++ b/graph/counting_c4/gen/multiplied_c4.cpp
@@ -0,0 +1,42 @@
+#include "../params.h"
+#include "random.h"
+#include <algorithm>
+#include <cstdio>
+#include <utility>
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = M_MAX;
+
+  // seed 0 : divide equally
+  // seed 1 : divide randomly
+
+  auto sp = gen.choice(3, 1, m-1);
+  if(seed == 0){
+    sp[0] = m / 4;
+    sp[1] = m * 2 / 4;
+    sp[2] = m * 3 / 4;
+  }
+  auto nodes = gen.choice(4, 0, n-1);
+
+  std::vector<std::pair<int, int>> edges;
+  for(int i=0;     i<sp[0]; i++) edges.push_back({ nodes[0], nodes[1] });
+  for(int i=sp[0]; i<sp[1]; i++) edges.push_back({ nodes[1], nodes[2] });
+  for(int i=sp[1]; i<sp[2]; i++) edges.push_back({ nodes[2], nodes[3] });
+  for(int i=sp[2]; i<m;     i++) edges.push_back({ nodes[3], nodes[0] });
+
+  for (auto &e : edges) {
+    if (gen.uniform_bool()) {
+      std::swap(e.first, e.second);
+    }
+  }
+  gen.shuffle(edges.begin(), edges.end());
+
+  std::printf("%d %d\n", n, m);
+  for (const auto &e : edges) {
+    std::printf("%d %d\n", e.first, e.second);
+  }
+}
diff --git a/graph/counting_c4/gen/small_dense_simple.cpp b/graph/counting_c4/gen/small_dense_simple.cpp
new file mode 100644
index 000000000..5870d522b
--- /dev/null
+++ b/graph/counting_c4/gen/small_dense_simple.cpp
@@ -0,0 +1,18 @@
+#include "../params.h"
+#include "./erdos_renyi.h"
+#include "random.h"
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int N_MAX_2 = 1;
+  while (N_MAX_2 < N_MAX && N_MAX_2 * (N_MAX_2 + 1) / 2 <= M_MAX) {
+    N_MAX_2 += 1;
+  }
+
+  int n = gen.uniform<int>(N_MIN, N_MAX_2);
+  int m = gen.uniform<int>(M_MIN, n * (n - 1) / 2);
+
+  erdos_renyi(n, m, gen);
+}
diff --git a/graph/counting_c4/gen/small_sparse_simple.cpp b/graph/counting_c4/gen/small_sparse_simple.cpp
new file mode 100644
index 000000000..b3a9c55c8
--- /dev/null
+++ b/graph/counting_c4/gen/small_sparse_simple.cpp
@@ -0,0 +1,20 @@
+#include "../params.h"
+#include "./erdos_renyi.h"
+#include "random.h"
+#include <algorithm>
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int N_MAX_2 = 1;
+  while (N_MAX_2 < N_MAX && N_MAX_2 * (N_MAX_2 + 1) / 2 <= M_MAX) {
+    N_MAX_2 += 1;
+  }
+
+  int n = gen.uniform<int>(N_MIN, N_MAX_2);
+  int m =
+      gen.uniform<int>(M_MIN, std::min<int>({M_MAX, n * 2, n * (n - 1) / 2}));
+
+  erdos_renyi(n, m, gen);
+}
diff --git a/graph/counting_c4/gen/star.cpp b/graph/counting_c4/gen/star.cpp
new file mode 100644
index 000000000..944de7885
--- /dev/null
+++ b/graph/counting_c4/gen/star.cpp
@@ -0,0 +1,35 @@
+#include "../params.h"
+#include "random.h"
+#include <algorithm>
+#include <cstdio>
+#include <utility>
+
+int main(int, char **argv) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = std::min(N_MAX, M_MAX + 1);
+  int m = n - 1;
+
+  int center = gen.uniform(0, n - 1);
+
+  std::vector<std::pair<int, int>> edges;
+  for (int i = 0; i < n; ++i) {
+    if (i != center) {
+      edges.emplace_back(center, i);
+    }
+  }
+
+  for (auto &e : edges) {
+    if (gen.uniform_bool()) {
+      std::swap(e.first, e.second);
+    }
+  }
+
+  gen.shuffle(edges.begin(), edges.end());
+
+  std::printf("%d %d\n", n, m);
+  for (const auto &e : edges) {
+    std::printf("%d %d\n", e.first, e.second);
+  }
+}
diff --git a/graph/counting_c4/hash.json b/graph/counting_c4/hash.json
new file mode 100644
index 000000000..72c852ac8
--- /dev/null
+++ b/graph/counting_c4/hash.json
@@ -0,0 +1,60 @@
+{
+  "dense_00.in": "e094020e96b98962eb929388c46421334b09c734cea8995af39b5f87b245977e",
+  "dense_00.out": "7d97f03351ee77d5301238323b9a328b03f0c8f6c384a7323660daccf6d96142",
+  "dense_01.in": "9988c9cef78e20ceec57aa49319381b6053660dbc9fc462c170fb0b90f8506b2",
+  "dense_01.out": "a993386deda82be497fa2ccfe1d4ff1afca8856bd52a2c13f02e5ef3792c8397",
+  "dense_02.in": "087cb8df79855a4fae2d7f60f3126b8ff42d5a975c3e01a669b6c6b833c0439c",
+  "dense_02.out": "98b75020089d1d03b652a892124842dd0aa40f82a50203a854c24325c69ba770",
+  "dense_03.in": "ae3be9059e3bbf481671496fb3fc37e897ca438de46d14591099a3abed715083",
+  "dense_03.out": "59696fcce2ddcf9bb625c22bcd26af748d0e214236027c1d7bdff3481a8cdb68",
+  "dense_04.in": "03672372e216fadee5b088d757428c4006875d8806e4569e8b84eabf93eda86f",
+  "dense_04.out": "c3e749357d8b72cb2984b71e37a9a7a17db5a79bb15dfa6e4a4113198f2fc0c0",
+  "example_00.in": "cc57432262a7d38b259e2fb989aedfda116c5d57dd0ca80b2d5efc3bcceb3784",
+  "example_00.out": "4d63f406a3bcef559f00b5f813653f1af9df3aa68b74a7ffeb807a6aac50e4b5",
+  "example_01.in": "bfa92308133a7d4e3243715928f76308b2558be73b2b04003c48b55984e843e8",
+  "example_01.out": "dba632e9f3ed534062fc9cb1baa9359e6793be03ee7763ec77144b3f829f6d50",
+  "large_random_simple_00.in": "44cb27620d64b62f047ba8f8a423dbed80acfa23cd59e93cf54224cbf9b61723",
+  "large_random_simple_00.out": "d36652df2526a4c7138dfee0c223cf920ef62ca7e15ada504c47f55f6d7b2ad1",
+  "large_random_simple_01.in": "9e64f63c2dbfb9f690672c05526a430ef84f916176e9a623c5abf1449078487a",
+  "large_random_simple_01.out": "548a36dea177236cf83a5f64891953e0a2e3ff1e9d86c3accab157d5a2fcc1f3",
+  "large_random_simple_02.in": "d26fa7116f774d95d2e7d99369cc7b3f0a5cfacee7199b305e186233846fc191",
+  "large_random_simple_02.out": "238d4004061ef66946c03f90ad41b4843df66341ed8d7db5b45863a1954865a4",
+  "max_complete_00.in": "faa8f55ece1e03c5bbf84c0dd3ffb666311da65bff1fabe845efdf87c41f8f67",
+  "max_complete_00.out": "7d7afb1647bbf969f458cffc99ef56ce01371df76c18427a655ccfbb925d35d9",
+  "max_near_k_simple_00.in": "5a30f2b4749da5b232f4935c48da94313fda3eb98d14c0bfc1ca5eba50bb6c30",
+  "max_near_k_simple_00.out": "032f8bd34e76f3d2fd5015501b7be8a6899b834aae2cfc34b47c29868047407c",
+  "max_near_k_simple_01.in": "ecff5afd66e8cd61c99e00ad271fcb0840c1aa4707408643efa590d00c10e961",
+  "max_near_k_simple_01.out": "868fdfba76941e275f75854f19e55cd026c359084f4d20204b69f72f8b183c4a",
+  "max_near_k_simple_02.in": "64a2231ec062d81879e3bb324f95c46f6f288988fb56ce7f9915e3a594f096e0",
+  "max_near_k_simple_02.out": "84c7fadb836a1991e18a952a493f81490afe2865fcc458d50f9606f43274ba32",
+  "max_near_k_simple_03.in": "d0c92cf80129a01bd54e4d0e2ca70b6379395c2b5c350355ca526e0358414865",
+  "max_near_k_simple_03.out": "f90d691355122301132562a2a6f880cb5fcb82c8d6a09916c7d85772da3b8a0b",
+  "max_random_simple_00.in": "6d62e0a770f55545c6cbc2a72a79daf29594dac81bec7f5d7a8ce91f3bf59a4c",
+  "max_random_simple_00.out": "199cd45e48fed339ae19915bc06dac09c089d05422c4d446561194310e97cc89",
+  "max_random_simple_01.in": "1698c470864ad106b0966c9783c889dcaed99e7988036d20436b40786124ee1e",
+  "max_random_simple_01.out": "9751a557d208ce9093dbffb930c98b4a51bec37659b8765ccc0ac71a1695d695",
+  "max_random_simple_02.in": "1542361e07db5072604b0e4deea51869b38bc4181b3846db52953d884ea792ae",
+  "max_random_simple_02.out": "9751a557d208ce9093dbffb930c98b4a51bec37659b8765ccc0ac71a1695d695",
+  "minimum_00.in": "4a6ae7226283a4b6277ce3e77a91585c0cad93929046f3c7bd9105d7ed101834",
+  "minimum_00.out": "9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa",
+  "multiplied_c4_00.in": "ac20ac463708fff6b2ae74ab072ddd801d807b0e99444b41ddd20f8ac17ae4f0",
+  "multiplied_c4_00.out": "fb609cbf127b3b57d5a37db729a4c06fb739fd38314aada9930fd4837ae11205",
+  "multiplied_c4_01.in": "d89740ef8722439394989088d2eb56153cb27878fef7b5bf0baa57b33b63e3f1",
+  "multiplied_c4_01.out": "76c1472c0ebe10d2692d74ec0eb829026c630f33f7a610ab5c886e55c34a1a87",
+  "small_dense_simple_00.in": "4026e5c3c70e13a13fcb6822fa1ea5740a522036b6330f530823fcebed6a785b",
+  "small_dense_simple_00.out": "bf5de309d2f5082675cb5cc72cca04dc11ec0b64dc59e7cff4749ffd49acec23",
+  "small_dense_simple_01.in": "e2c872ad4f3be89102459c3a723591906c20e61e90b2717df2342cd6899b7b34",
+  "small_dense_simple_01.out": "f4fa3e67247b138fb01ef342d0ba569c5a8933845f08934380e7e1d1ba2cc4eb",
+  "small_dense_simple_02.in": "7327e34632e7fc581c6b8cbe102c2e3f9724ea8e538587707122df6f53a22f62",
+  "small_dense_simple_02.out": "f4f5b0750d196dc875594cd91cd2f1fc21f2acf2487ce8aac024f8631bc7037c",
+  "small_sparse_simple_00.in": "2ac3dae959ad57452a968dd7cc52b15c27e61e74c74b9de77c09dab157e14006",
+  "small_sparse_simple_00.out": "3c9752241fd367167acb485d31e21ae10c16f45ea5afda3a139761aac6456fbd",
+  "small_sparse_simple_01.in": "b9bf6eaf04589a863ddeb01bad2476201d2f65d24a97119124d6f3cb2334601d",
+  "small_sparse_simple_01.out": "72bfe168435d32a0ecc4a907c1eb5aaf92eba8ad63f5087c0fb5a40dab0467ba",
+  "small_sparse_simple_02.in": "5a01175d6c3f45d92f67acf75619e19d779251229b85dda1981f74d6f9b33935",
+  "small_sparse_simple_02.out": "afde75fab8c06d89460032f59a7d28d8684d93d8006d2e120727c1e7c075c9ad",
+  "star_00.in": "789d728a7dc148dcac46e927ead606f1d3aeb1f5930bca3cbf428f1adf56742f",
+  "star_00.out": "3f213530dc3b6d43b2cee656c9e8f61037a3872c4c6b93781b91f30837f15cb1",
+  "star_01.in": "14ab39e690b81115380a89f1e93e1d15275b3dd850b196cdc86a173c6175f9da",
+  "star_01.out": "3f213530dc3b6d43b2cee656c9e8f61037a3872c4c6b93781b91f30837f15cb1"
+}
\ No newline at end of file
diff --git a/graph/counting_c4/info.toml b/graph/counting_c4/info.toml
new file mode 100644
index 000000000..f967c0ace
--- /dev/null
+++ b/graph/counting_c4/info.toml
@@ -0,0 +1,47 @@
+title = "Counting $C _ 4$'s"
+timelimit = 10.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/973"
+
+[[tests]]
+	name = "example.in"
+	number = 2
+[[tests]]
+	name = "minimum.in"
+	number = 1
+[[tests]]
+	name = "small_sparse_simple.cpp"
+	number = 3
+[[tests]]
+	name = "small_dense_simple.cpp"
+	number = 3
+[[tests]]
+	name = "large_random_simple.cpp"
+	number = 3
+[[tests]]
+	name = "max_random_simple.cpp"
+	number = 3
+[[tests]]
+	name = "star.cpp"
+	number = 2
+[[tests]]
+	name = "max_near_k_simple.cpp"
+	number = 4
+[[tests]]
+	name = "max_complete.cpp"
+	number = 1
+[[tests]]
+	name = "multiplied_c4.cpp"
+	number = 2
+[[tests]]
+	name = "dense.cpp"
+	number = 5
+
+[[solutions]]
+	name = "naive.cpp"
+    expect = "TLE"
+
+[params]
+	N_MIN = 1
+	N_MAX = 300000
+	M_MIN = 1
+	M_MAX = 300000
diff --git a/graph/counting_c4/sol/correct.cpp b/graph/counting_c4/sol/correct.cpp
new file mode 100644
index 000000000..e53c4057b
--- /dev/null
+++ b/graph/counting_c4/sol/correct.cpp
@@ -0,0 +1,139 @@
+#include <cstdio>
+#include <vector>
+#include <algorithm>
+#include <utility>
+#include <cassert>
+
+// simple graph
+// for each edge
+// O( n + m sqrt(m) ) time
+std::vector<long long> CountC4Simple(
+    int n,
+    std::vector<int> U,
+    std::vector<int> V,
+    std::vector<long long> W
+){
+    int m = int(W.size());
+    
+    // less incident edges, smaller index
+    std::vector<int> deg(n);
+    for(int e=0; e<m; e++){ deg[U[e]]++; deg[V[e]]++; }
+    std::vector<int> I(n); for(int i=0; i<n; i++) I[i] = i;
+    std::stable_sort(I.begin(), I.end(), [&](int l, int r){ return deg[l] < deg[r]; });
+    {
+        std::vector<int> O(n);
+        for(int i=0; i<n; i++) O[I[i]] = i;
+        for(int& u : U) u = O[u];
+        for(int& u : V) u = O[u];
+    }
+
+    for(int e=0; e<m; e++) if(U[e] < V[e]) std::swap(U[e], V[e]);
+    
+    // adjacency list
+
+    std::vector<int> estart(n);
+    for(int i=0; i<n-1; i++) estart[i+1] = estart[i] + deg[I[i]];
+    std::vector<int> eend = estart;
+    std::vector<int> eid(m*2);
+    std::vector<int> eto(m*2);
+
+    for(int e=0; e<m; e++){
+        int v = U[e];
+        int w = V[e];
+        eid[eend[v]] = e;
+        eto[eend[v]] = w;
+        eend[v]++;
+    }
+    std::vector<int> eendx = eend;
+    for(int v=0; v<n; v++){
+        for(int i=estart[v]; i<eendx[v]; i++){
+            int e = eid[i];
+            int w = eto[i];
+            eid[eend[w]] = e;
+            eto[eend[w]] = v;
+            eend[w]++;
+        }
+    }
+    
+    std::vector<long long> c(n); // c[x] : number of paths(v --> w --> x)
+    std::vector<long long> ans(m);
+    for(int v=n-1; v>=0; v--){
+        for(int i=estart[v]; i<eend[v]; i++){
+            int evw = eid[i];
+            int w = eto[i];
+            eend[w] -= 1; // remove w -> v
+            for(int j=estart[w]; j<eend[w]; j++){
+                int ewx = eid[j];
+                int x = eto[j];
+                c[x] += W[evw] * W[ewx];
+            }
+        }
+        for(int i=estart[v]; i<eend[v]; i++){
+            int evw = eid[i];
+            int w = eto[i];
+            for(int j=estart[w]; j<eend[w]; j++){
+                int ewx = eid[j];
+                int x = eto[j];
+                long long val = c[x] - W[evw] * W[ewx];
+                ans[evw] += val * W[ewx];
+                ans[ewx] += val * W[evw];
+            }
+        }
+        for(int i=estart[v]; i<eend[v]; i++){
+            int w = eto[i];
+            for(int j=estart[w]; j<eend[w]; j++) c[eto[j]] = 0;
+        }
+    }
+    return ans;
+}
+
+// for each edge
+// O( n + m sqrt(m) ) time
+std::vector<long long> CountC4(
+    int n,
+    std::vector<int> U,
+    std::vector<int> V,
+    std::vector<long long> W
+){
+    int m = int(W.size());
+    for(int i=0; i<m; i++) if(U[i] > V[i]) std::swap(U[i], V[i]);
+    std::vector<int> I(m);
+    for(int i=0; i<m; i++) I[i] = i;
+    std::stable_sort(I.begin(), I.end(), [&](int l, int r){ return V[l] < V[r]; });
+    std::stable_sort(I.begin(), I.end(), [&](int l, int r){ return U[l] < U[r]; });
+
+    std::vector<int> Q(m);
+    std::vector<int> U2;
+    std::vector<int> V2;
+    std::vector<long long> W2;
+    for(int i=0; i<m; i++){
+        int e = I[i];
+        if(i == 0 || U2.back() != U[e] || V2.back() != V[e]){
+            U2.push_back(U[e]);
+            V2.push_back(V[e]);
+            W2.push_back(0);
+        }
+        W2.back() += W[e];
+        Q[e] = int(U2.size()) - 1;
+    }
+
+    auto simple_res = CountC4Simple(n, std::move(U2), std::move(V2), std::move(W2));
+    std::vector<long long> ans(m);
+    for(int e=0; e<m; e++) ans[e] = simple_res[Q[e]];
+    return ans;
+}
+
+using namespace std;
+
+int main(){
+    int N, M; scanf("%d%d", &N, &M);
+    std::vector<int> U(M), V(M);
+    for(int i=0; i<M; i++) scanf("%d%d", &U[i], &V[i]);
+    auto ans = CountC4(N, U, V, std::vector<long long>(M, 1));
+    for(int i=0; i<M; i++){
+        if(i) printf(" ");
+        printf("%lld", ans[i]);
+    }
+    printf("\n");
+    return 0;
+}
diff --git a/graph/counting_c4/sol/naive.cpp b/graph/counting_c4/sol/naive.cpp
new file mode 100644
index 000000000..8c98f0730
--- /dev/null
+++ b/graph/counting_c4/sol/naive.cpp
@@ -0,0 +1,47 @@
+#include <cstdio>
+#include <vector>
+#include <algorithm>
+#include <utility>
+#include <cassert>
+using namespace std;
+
+int main(){
+    int N, M; scanf("%d%d", &N, &M);
+    std::vector<int> U(M), V(M);
+    for(int i=0; i<M; i++) scanf("%d%d", &U[i], &V[i]);
+    for(int i=0; i<M; i++) if(U[i] > V[i]) std::swap(U[i], V[i]);
+    std::vector<long long> ans(M);
+    int D[8] = {};
+    for(int i=0; i<M; i++){
+        for(int j=i+1; j<M; j++){
+            if(U[i] == U[j] && V[i] == V[j]) continue;
+            for(int k=j+1; k<M; k++){
+                if(U[i] == U[k] && V[i] == V[k]) continue;
+                if(U[j] == U[k] && V[j] == V[k]) continue;
+                for(int f=k+1; f<M; f++){
+                    D[0] = U[i];
+                    D[1] = V[i];
+                    D[2] = U[j];
+                    D[3] = V[j];
+                    D[4] = U[k];
+                    D[5] = V[k];
+                    D[6] = U[f];
+                    D[7] = V[f];
+                    std::sort(D, D+8);
+                    if(D[0] == D[1] && D[1] != D[2] && D[2] == D[3] && D[3] != D[4] && D[4] == D[5] && D[5] != D[6] && D[6] == D[7]){
+                        ans[i] += 1;
+                        ans[j] += 1;
+                        ans[k] += 1;
+                        ans[f] += 1;
+                    }
+                }
+            }
+        }
+    }
+    for(int i=0; i<M; i++){
+        if(i) printf(" ");
+        printf("%lld", ans[i]);
+    }
+    printf("\n");
+    return 0;
+}
diff --git a/graph/counting_c4/task.md b/graph/counting_c4/task.md
new file mode 100644
index 000000000..e8a40eabd
--- /dev/null
+++ b/graph/counting_c4/task.md
@@ -0,0 +1,45 @@
+## @{keyword.statement}
+
+@{lang.en}
+You are given an undirected graph, consisting of $N$ vertices and $M$ edges. This graph may not be simple.
+The $i$-th edge is $\lbrace u _ i, v _ i \rbrace$.
+
+For each edge $i$, find $A _ i$ , as the number of unordered combinations of $3$ edges $x$ , $y$ , $z$
+that those $4$ edges ( $i,x,y,z$ ) forms a subgraph isomorphic to $C _ 4$ ( A cycle with $4$ edges ).
+
+@{lang.ja}
+$N$ 頂点 $M$ 辺の無向グラフが与えられます。 $i$ 番目の辺は $\lbrace u _ i, v _ i \rbrace$ です。このグラフは単純とは限りません。
+
+各辺 $i$ について、 $3$ つの辺 $x$ , $y$ , $z$ の非順序組であって、 $4$ 辺 $i,x,y,z$ が $C _ 4$ ( $4$ 辺かならなるサイクル )に同型な部分グラフをなすものの個数 $A _ i$ を求めてください。
+
+@{lang.end}
+
+## @{keyword.constraints}
+
+- $@{param.N_MIN} \le N \le @{param.N_MAX}$
+- $@{param.M_MIN} \le M \le @{param.M_MAX}$
+- $0 \le u _ i \lt N$
+- $0 \le v _ i \lt N$
+- $u _ i \neq v _ i$
+
+## @{keyword.input}
+
+```
+$N$ $M$
+$u _ 0$ $v _ 0$
+$u _ 1$ $v _ 1$
+$\vdots$
+$u _ {M-1}$ $v _ {M-1}$
+```
+
+## @{keyword.output}
+
+```
+$A _ 0$ $A _ 1$ $\cdots$ $A _ {N-1}$
+```
+
+## @{keyword.sample}
+
+@{example.example_00}
+
+@{example.example_01}
diff --git a/graph/counting_c4/verifier.cpp b/graph/counting_c4/verifier.cpp
new file mode 100644
index 000000000..4041cb016
--- /dev/null
+++ b/graph/counting_c4/verifier.cpp
@@ -0,0 +1,24 @@
+#include "params.h"
+#include "testlib.h"
+#include <algorithm>
+#include <set>
+#include <utility>
+
+int main() {
+  registerValidation();
+
+  int n = inf.readInt(N_MIN, N_MAX);
+  inf.readSpace();
+  int m = inf.readInt(M_MIN, M_MAX);
+  inf.readChar('\n');
+
+  for (int i = 0; i < m; ++i) {
+    int u = inf.readInt(0, n - 1);
+    inf.readSpace();
+    int v = inf.readInt(0, n - 1);
+    inf.readChar('\n');
+    ensure(u != v);
+  }
+
+  inf.readEof();
+}

From 5be08b42faca27c0a40825a6f28ede4b0ed807f4 Mon Sep 17 00:00:00 2001
From: NachiaVivias <nachiavivias@gmail.com>
Date: Mon, 4 Nov 2024 22:16:59 +0900
Subject: [PATCH 2/2] [graph/counting_c4] apply review comment

---
 graph/counting_c4/hash.json | 36 ++++++++++++++++++------------------
 graph/counting_c4/info.toml |  2 +-
 graph/counting_c4/task.md   |  2 +-
 3 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/graph/counting_c4/hash.json b/graph/counting_c4/hash.json
index 72c852ac8..12b9c13a5 100644
--- a/graph/counting_c4/hash.json
+++ b/graph/counting_c4/hash.json
@@ -13,12 +13,12 @@
   "example_00.out": "4d63f406a3bcef559f00b5f813653f1af9df3aa68b74a7ffeb807a6aac50e4b5",
   "example_01.in": "bfa92308133a7d4e3243715928f76308b2558be73b2b04003c48b55984e843e8",
   "example_01.out": "dba632e9f3ed534062fc9cb1baa9359e6793be03ee7763ec77144b3f829f6d50",
-  "large_random_simple_00.in": "44cb27620d64b62f047ba8f8a423dbed80acfa23cd59e93cf54224cbf9b61723",
-  "large_random_simple_00.out": "d36652df2526a4c7138dfee0c223cf920ef62ca7e15ada504c47f55f6d7b2ad1",
-  "large_random_simple_01.in": "9e64f63c2dbfb9f690672c05526a430ef84f916176e9a623c5abf1449078487a",
-  "large_random_simple_01.out": "548a36dea177236cf83a5f64891953e0a2e3ff1e9d86c3accab157d5a2fcc1f3",
-  "large_random_simple_02.in": "d26fa7116f774d95d2e7d99369cc7b3f0a5cfacee7199b305e186233846fc191",
-  "large_random_simple_02.out": "238d4004061ef66946c03f90ad41b4843df66341ed8d7db5b45863a1954865a4",
+  "large_random_simple_00.in": "14b5d1a028977df03661e2520c683cc2037ce61fd6268fad52400fce2cc14da0",
+  "large_random_simple_00.out": "70136d4393178036e3758ed994292ba81c24954f731ec06545645e5adcdf0063",
+  "large_random_simple_01.in": "faced67b3643dd0254c6b4556b2098f18d0eeec145a9f3dc6b645ff8ccf5cd93",
+  "large_random_simple_01.out": "51f88c18bae2d1c7c2c0aa9dee11d4d8deb31aac6dd64aa7c1bbb5ab14c13900",
+  "large_random_simple_02.in": "86e4fd47363100ef342e583f8a7e61a199cf804223e175e95802b44ddcf57aee",
+  "large_random_simple_02.out": "3e2062a317a352cc85454945b084a8d5932c1880815a8eb64f712cab519a62b8",
   "max_complete_00.in": "faa8f55ece1e03c5bbf84c0dd3ffb666311da65bff1fabe845efdf87c41f8f67",
   "max_complete_00.out": "7d7afb1647bbf969f458cffc99ef56ce01371df76c18427a655ccfbb925d35d9",
   "max_near_k_simple_00.in": "5a30f2b4749da5b232f4935c48da94313fda3eb98d14c0bfc1ca5eba50bb6c30",
@@ -41,18 +41,18 @@
   "multiplied_c4_00.out": "fb609cbf127b3b57d5a37db729a4c06fb739fd38314aada9930fd4837ae11205",
   "multiplied_c4_01.in": "d89740ef8722439394989088d2eb56153cb27878fef7b5bf0baa57b33b63e3f1",
   "multiplied_c4_01.out": "76c1472c0ebe10d2692d74ec0eb829026c630f33f7a610ab5c886e55c34a1a87",
-  "small_dense_simple_00.in": "4026e5c3c70e13a13fcb6822fa1ea5740a522036b6330f530823fcebed6a785b",
-  "small_dense_simple_00.out": "bf5de309d2f5082675cb5cc72cca04dc11ec0b64dc59e7cff4749ffd49acec23",
-  "small_dense_simple_01.in": "e2c872ad4f3be89102459c3a723591906c20e61e90b2717df2342cd6899b7b34",
-  "small_dense_simple_01.out": "f4fa3e67247b138fb01ef342d0ba569c5a8933845f08934380e7e1d1ba2cc4eb",
-  "small_dense_simple_02.in": "7327e34632e7fc581c6b8cbe102c2e3f9724ea8e538587707122df6f53a22f62",
-  "small_dense_simple_02.out": "f4f5b0750d196dc875594cd91cd2f1fc21f2acf2487ce8aac024f8631bc7037c",
-  "small_sparse_simple_00.in": "2ac3dae959ad57452a968dd7cc52b15c27e61e74c74b9de77c09dab157e14006",
-  "small_sparse_simple_00.out": "3c9752241fd367167acb485d31e21ae10c16f45ea5afda3a139761aac6456fbd",
-  "small_sparse_simple_01.in": "b9bf6eaf04589a863ddeb01bad2476201d2f65d24a97119124d6f3cb2334601d",
-  "small_sparse_simple_01.out": "72bfe168435d32a0ecc4a907c1eb5aaf92eba8ad63f5087c0fb5a40dab0467ba",
-  "small_sparse_simple_02.in": "5a01175d6c3f45d92f67acf75619e19d779251229b85dda1981f74d6f9b33935",
-  "small_sparse_simple_02.out": "afde75fab8c06d89460032f59a7d28d8684d93d8006d2e120727c1e7c075c9ad",
+  "small_dense_simple_00.in": "e049cbd4560b5794bed7ed257b7c570e37fc936e8c9d90553d2792b5063ca8ad",
+  "small_dense_simple_00.out": "65c33e5a8e23ad3ae3e9eedcad670361503601de3a43b846b1811e0e24e52ced",
+  "small_dense_simple_01.in": "234a9d7a84baa31ed908778a29b3ead196bd52881ccccd588565b7e680ea12b3",
+  "small_dense_simple_01.out": "b668cc0d1b8251a9d772668a939a446d56f4b1d94a7035d774d87eec42f9d38f",
+  "small_dense_simple_02.in": "ed9240ab3d7d86404e7204e5ff9cc2588cf37a9d88956f7f95957cb67745651c",
+  "small_dense_simple_02.out": "a99bffd672da98017ed2415b821da94aba4f22dc0252780cd55c0d4fce7aece4",
+  "small_sparse_simple_00.in": "bc90cd416ca69b7f3357b0b2180ddb546eb42f1ed32afd85c6fb6ba0fafbac22",
+  "small_sparse_simple_00.out": "b5589774c732a33c2415ba1c9020f43e7acb9696c5dd40846bb204a97895a553",
+  "small_sparse_simple_01.in": "a7d64c2ed5f3ee6b7572b2a7d68f30335ef493950fc97adae2f18913d95172b5",
+  "small_sparse_simple_01.out": "0017d9f8d3bdf9e95de189cfffe3e1040b8207ef8264632eaa25c68a83da0192",
+  "small_sparse_simple_02.in": "4ebc3a3c2af8505fa07beab03f0ae081ad9df9bfcc715f171422fbda60a2ea80",
+  "small_sparse_simple_02.out": "fd9c3768851f7f1c300836f563d41cafc56909cd8d7fbe65e04e7f85c457a1cc",
   "star_00.in": "789d728a7dc148dcac46e927ead606f1d3aeb1f5930bca3cbf428f1adf56742f",
   "star_00.out": "3f213530dc3b6d43b2cee656c9e8f61037a3872c4c6b93781b91f30837f15cb1",
   "star_01.in": "14ab39e690b81115380a89f1e93e1d15275b3dd850b196cdc86a173c6175f9da",
diff --git a/graph/counting_c4/info.toml b/graph/counting_c4/info.toml
index f967c0ace..8fef6ffa7 100644
--- a/graph/counting_c4/info.toml
+++ b/graph/counting_c4/info.toml
@@ -41,7 +41,7 @@ forum = "https://github.com/yosupo06/library-checker-problems/issues/973"
     expect = "TLE"
 
 [params]
-	N_MIN = 1
+	N_MIN = 2
 	N_MAX = 300000
 	M_MIN = 1
 	M_MAX = 300000
diff --git a/graph/counting_c4/task.md b/graph/counting_c4/task.md
index e8a40eabd..cd3005f6a 100644
--- a/graph/counting_c4/task.md
+++ b/graph/counting_c4/task.md
@@ -35,7 +35,7 @@ $u _ {M-1}$ $v _ {M-1}$
 ## @{keyword.output}
 
 ```
-$A _ 0$ $A _ 1$ $\cdots$ $A _ {N-1}$
+$A _ 0$ $A _ 1$ $\cdots$ $A _ {M-1}$
 ```
 
 ## @{keyword.sample}