编写线性逆元以及用其计算的组合数；release 0.6.0

Author: Mr-Python-in-China

library/mrpython/modint.hpp

@@ -74,6 +74,28 @@ template <unsigned P> class modint {
     return mrpython::fastPow(*this, n);
   }
   static constexpr unsigned modval() { return P; }
+
+  static modint linear_inv(unsigned int n) {
+    static std::vector<modint<P>> mem = {0, 1};
+    while (mem.size() <= n) {
+      unsigned int i = mem.size();
+      mem.push_back(modint<P>(P - (P / i)) * mem[P % i]);
+    }
+    return mem[n];
+  }
+  static modint frac_inv(unsigned int n) {
+    static std::vector<modint<P>> mem = {1};
+    while (mem.size() <= n) {
+      unsigned int i = mem.size();
+      mem.push_back(mem.back() * linear_inv(i));
+    }
+    return mem[n];
+  }
+  static modint comb(unsigned int n, unsigned int m) {
+    return n < m ? modint<P>(0)
+                 : frac<modint<P>>(n) * frac_inv(m) * frac_inv(n - m);
+  }
 };
+
 }  // namespace mrpython
 #endif  // MP_LIBRARY_MODINT_HPP

library/test/modint.cpp

@@ -262,6 +262,38 @@ TEST_F(ModIntTest, Power) {
   EXPECT_EQ(b.pow(MEDIUM_PRIME - 1).val(), 1);
 }
 
+TEST_F(ModIntTest, InverseHelpers) {
+  // linear_inv should behave like multiplicative inverse on [1, P)
+  for (unsigned int i = 1; i < SMALL_PRIME; ++i) {
+    auto inv = modint<SMALL_PRIME>::linear_inv(i);
+    EXPECT_EQ((inv * modint<SMALL_PRIME>(i)).val(), 1u);
+  }
+
+  // frac_inv is 1 / n!; verify by multiplying forward factorials
+  modint<SMALL_PRIME> fact = 1;
+  for (unsigned int i = 0; i <= 8; ++i) {
+    if (i > 0) fact *= modint<SMALL_PRIME>(i);
+    auto inv_fact = modint<SMALL_PRIME>::frac_inv(i);
+    EXPECT_EQ((fact * inv_fact).val(), 1u);
+  }
+}
+
+TEST_F(ModIntTest, Comb) {
+  // Small Pascal triangle slice to ensure comb matches expected values
+  const unsigned int n = 8;
+  for (unsigned int k = 0; k <= n; ++k) {
+    unsigned int expected = 1;
+    for (unsigned int i = 1; i <= k; ++i) {
+      expected = expected * (n - i + 1) / i;
+    }
+    EXPECT_EQ(modint<SMALL_PRIME>::comb(n, k).val(), expected % SMALL_PRIME);
+  }
+
+  // Zero and out-of-range cases
+  EXPECT_EQ(modint<SMALL_PRIME>::comb(0, 0).val(), 1u);
+  EXPECT_EQ(modint<SMALL_PRIME>::comb(5, 6).val(), 0u);
+}
+
 // Test edge cases and miscellaneous functionality
 TEST_F(ModIntTest, EdgeCases) {
   // Test modval() static method

package.json

@@ -2,7 +2,7 @@
   "name": "mp-oi-library",
   "displayName": "mp-oi-library",
   "description": "Some algorithms and data structures template for competitive programming.",
-  "version": "0.5.1",
+  "version": "0.6.0",
   "repository": "https://github.com/Mr-Python-in-China/mp-oi-library",
   "license": "LGPL-3.0-only",
   "author": {