Extended Euclidean algorithm
(Mylib/Number/extended_gcd.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Required by

• Binomial coefficient (Mylib/Combinatorics/binomial_coefficient.cpp)
• Bézout's identity (Mylib/Number/bezout_identity.cpp)
• Chinese remainder theorem (Mylib/Number/chinese_remainder_algorithm.cpp)

Verified with

• test/aoj/NTL_1_E/main.test.cpp
• test/yosupo-judge/binomial_coefficient/main.test.cpp
• test/yukicoder/186/main.test.cpp

Code

#pragma once
#include <tuple>

namespace haar_lib {
  auto ext_gcd(int64_t a, int64_t b) -> std::tuple<
      int64_t,  // gcd
      int64_t,  // p
      int64_t   // q
      > {
    if (b == 0) return std::make_tuple(a, 1, 0);
    const auto [d, q, p] = ext_gcd(b, (a + b) % b);
    return std::make_tuple(d, p, q - a / b * p);
  }
}  // namespace haar_lib

#line 2 "Mylib/Number/extended_gcd.cpp"
#include <tuple>

namespace haar_lib {
  auto ext_gcd(int64_t a, int64_t b) -> std::tuple<
      int64_t,  // gcd
      int64_t,  // p
      int64_t   // q
      > {
    if (b == 0) return std::make_tuple(a, 1, 0);
    const auto [d, q, p] = ext_gcd(b, (a + b) % b);
    return std::make_tuple(d, p, q - a / b * p);
  }
}  // namespace haar_lib

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