feat: algo/mapping/cycle_finder.hpp

src/armkn/algo/mapping/cycle_finder.hpp

@@ -0,0 +1,66 @@
+#pragma once
+#include <cstddef>
+#include <type_traits>
+#include <utility>
+#include <vector>
+
+/// Floyd's Tortoise and Hare Algorithm
+template <class T>
+class CycleFinder {
+  uint32_t _until_cycle_start;
+  uint32_t _cycle_len;
+  std::vector<T> nf;  // nf[i] := `start` から `f` を `i` 回適用した結果
+
+ public:
+  CycleFinder() = default;
+
+  template <class Fn, std::enable_if_t<std::is_invocable_r_v<T, Fn, T>, std::nullptr_t> = nullptr>
+  CycleFinder(T start, Fn&& f, std::size_t capacity = 512) : _until_cycle_start(0), _cycle_len(0) {
+    T tortoise = start, hare = start;
+    do {
+      tortoise = f(tortoise);
+      hare = f(f(hare));
+    } while (tortoise != hare);
+
+    nf.reserve(capacity);
+    nf.push_back(start);
+    tortoise = start;
+    while (tortoise != hare) {
+      hare = f(hare);
+      tortoise = f(tortoise);
+      nf.push_back(tortoise);
+      ++_until_cycle_start;
+    }
+
+    do {
+      tortoise = f(tortoise);
+      nf.push_back(tortoise);
+      ++_cycle_len;
+    } while (tortoise != hare);
+  }
+
+  /// mapping[x] を写像 f(x) とみなす
+  template <
+      class IndexAccessible,
+      class = std::void_t<decltype(std::declval<IndexAccessible>()[0])>>
+  CycleFinder(T start, IndexAccessible const& mapping)
+      : CycleFinder(
+            start,
+            [&](T x) { return (T)mapping[x]; },
+            mapping.size() + 1
+        ) {}
+
+  inline uint32_t until_cycle_start() const {
+    return _until_cycle_start;
+  }
+
+  inline uint32_t cycle_len() const {
+    return _cycle_len;
+  }
+
+  /// start に f を n 回適用した結果を O(1) で求める。
+  inline const T apply_repeat(uint64_t n) const {
+    if (n <= _until_cycle_start + _cycle_len) return nf[n];
+    return nf[_until_cycle_start + (n - _until_cycle_start) % _cycle_len];
+  }
+};

tests/CMakeLists.txt

@@ -12,6 +12,7 @@ set(CMAKE_CXX_EXTENSIONS OFF)
 add_subdirectory(lib/Catch2)
 
 add_executable(tests
+  armkn/algo/mapping/cycle_finder.cpp
   armkn/dp/k_choose_prod_sum.cpp
   armkn/dsu/union_find.cpp
   armkn/fmt/printer.cpp

tests/armkn/algo/mapping/cycle_finder.cpp

@@ -0,0 +1,76 @@
+#include <armkn/algo/mapping/cycle_finder.hpp>
+#include <catch2/catch_test_macros.hpp>
+
+#include <vector>
+
+TEST_CASE("CycleFinder") {
+  std::vector<int> f(7);
+  f[0] = 1;
+  f[1] = 2;
+  f[2] = 3;
+  f[3] = 4;
+  f[4] = 5;
+  f[5] = 3;
+  f[6] = 6;
+
+  SECTION("start=1") {
+    auto cf = CycleFinder(1, f);
+    CHECK(cf.until_cycle_start() == 2);
+    CHECK(cf.cycle_len() == 3);
+    CHECK(cf.apply_repeat(0) == 1);
+    CHECK(cf.apply_repeat(1) == 2);
+    CHECK(cf.apply_repeat(2) == 3);
+    CHECK(cf.apply_repeat(3) == 4);
+    CHECK(cf.apply_repeat(4) == 5);
+    CHECK(cf.apply_repeat(5) == 3);
+    CHECK(cf.apply_repeat(6) == 4);
+    CHECK(cf.apply_repeat(7) == 5);
+    CHECK(cf.apply_repeat(8) == 3);
+    CHECK(cf.apply_repeat(9) == 4);
+    CHECK(cf.apply_repeat(10) == 5);
+    CHECK(cf.apply_repeat(11) == 3);
+  }
+  SECTION("start=3") {
+    auto cf = CycleFinder(3, f);
+    CHECK(cf.until_cycle_start() == 0);
+    CHECK(cf.cycle_len() == 3);
+    CHECK(cf.apply_repeat(0) == 3);
+    CHECK(cf.apply_repeat(1) == 4);
+    CHECK(cf.apply_repeat(2) == 5);
+    CHECK(cf.apply_repeat(3) == 3);
+    CHECK(cf.apply_repeat(4) == 4);
+    CHECK(cf.apply_repeat(5) == 5);
+    CHECK(cf.apply_repeat(6) == 3);
+    CHECK(cf.apply_repeat(7) == 4);
+    CHECK(cf.apply_repeat(8) == 5);
+    CHECK(cf.apply_repeat(9) == 3);
+    CHECK(cf.apply_repeat(10) == 4);
+    CHECK(cf.apply_repeat(11) == 5);
+  }
+  SECTION("start=4") {
+    auto cf = CycleFinder(4, f);
+    CHECK(cf.until_cycle_start() == 0);
+    CHECK(cf.cycle_len() == 3);
+    CHECK(cf.apply_repeat(0) == 4);
+    CHECK(cf.apply_repeat(1) == 5);
+    CHECK(cf.apply_repeat(2) == 3);
+    CHECK(cf.apply_repeat(3) == 4);
+    CHECK(cf.apply_repeat(4) == 5);
+    CHECK(cf.apply_repeat(5) == 3);
+    CHECK(cf.apply_repeat(6) == 4);
+    CHECK(cf.apply_repeat(7) == 5);
+    CHECK(cf.apply_repeat(8) == 3);
+    CHECK(cf.apply_repeat(9) == 4);
+    CHECK(cf.apply_repeat(10) == 5);
+    CHECK(cf.apply_repeat(11) == 3);
+  }
+  SECTION("start=6") {
+    auto cf = CycleFinder(6, f);
+    CHECK(cf.until_cycle_start() == 0);
+    CHECK(cf.cycle_len() == 1);
+    CHECK(cf.apply_repeat(0) == 6);
+    CHECK(cf.apply_repeat(1) == 6);
+    CHECK(cf.apply_repeat(2) == 6);
+    CHECK(cf.apply_repeat(3) == 6);
+  }
+}