$\|v\|^2 (v \in {\mathbb{Z}}^2)$ (normの2乗)
(src/geometry/Z2/operation/square-norm.hpp)

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• Last update: 2022-08-22 18:26:45+09:00
• Include: #include "src/geometry/Z2/operation/square-norm.hpp"

square_norm

Z square_norm(Vector<Z> v)

v の長さ(norm)の2乗を返す。

オーバーフローに注意。

Depends on

• ベクトル (整数幾何) (src/geometry/Z2/class/vector.hpp)
• $x^2 (x \in \mathbb{Z})$ (src/geometry/Z2/operation/square.hpp)

Required by

• 円と円の交差判定 (src/geometry/Z2/intersect/is-intersect-circle-circle.hpp)
• 点と円の交差判定 (src/geometry/Z2/intersect/is-intersect-point-circle.hpp)
• src/geometry/Z2/operation/ccw.hpp
• src/geometry/Z2/segment-function/counterbalance-segments.hpp

Verified with

• test/aoj/4011.test.cpp
• test/atcoder/abc259_d.test.cpp

Code

#pragma once

#include "src/geometry/Z2/class/vector.hpp"
#include "src/geometry/Z2/operation/square.hpp"

namespace luz::Z2 {

  template < typename Z >
  Z square_norm(Vector< Z > v) {
    return square(v.x()) + square(v.y());
  }

} // namespace luz::Z2

#line 2 "src/geometry/Z2/operation/square-norm.hpp"

#line 2 "src/geometry/Z2/class/vector.hpp"

#include <vector>

namespace luz::Z2 {

  template < typename Z >
  class Vector {

    Z x_, y_;

   public:
    Vector(): x_(0), y_(0) {}
    Vector(Z x, Z y): x_(x), y_(y) {}

    Z x() const {
      return x_;
    }

    Z y() const {
      return y_;
    }

    bool operator==(const Vector &v) const {
      return x_ == v.x_ and y_ == v.y_;
    }

    bool operator!=(const Vector &v) const {
      return x_ != v.x_ or y_ != v.y_;
    }

    Vector &operator+=(const Vector &v) {
      x_ += v.x_;
      y_ += v.y_;
      return *this;
    }
    Vector &operator-=(const Vector &v) {
      x_ -= v.x_;
      y_ -= v.y_;
      return *this;
    }

    Vector operator+(const Vector &v) const {
      return Vector(*this) += v;
    }
    Vector operator-(const Vector &v) const {
      return Vector(*this) -= v;
    }

    Vector operator+() const {
      return *this;
    }
    Vector operator-() const {
      return Vector() - *this;
    }
  };

  template < typename Z >
  using Vectors = std::vector< Vector< Z > >;

} // namespace luz::Z2
#line 2 "src/geometry/Z2/operation/square.hpp"

namespace luz::Z2 {

  template < typename Z >
  Z square(const Z x) {
    return x * x;
  }

} // namespace luz::Z2
#line 5 "src/geometry/Z2/operation/square-norm.hpp"

namespace luz::Z2 {

  template < typename Z >
  Z square_norm(Vector< Z > v) {
    return square(v.x()) + square(v.y());
  }

} // namespace luz::Z2

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