Closed interval
(Mylib/Math/closed_interval.cpp)

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

Operations

一つの閉区間を管理する。

• is_null()
  • 区間が空であるかを判定する。
• contains(a)
  • 区間に点aが含まれるかを判定する。
• intersect(a, b)
  • 区間aとbの共通部分を得る。
• left_expand(a, x)
  • 区間aの左端をxだけ伸縮したものを返す。
• right_expand(a, x)
  • 区間aの右端をxだけ伸縮したものを返す。

Requirements

Notes

Problems

References

Code

#pragma once
#include <algorithm>
#include <iostream>
#include <optional>
#include <utility>

namespace haar_lib {
  template <typename T>
  struct closed_interval {
    std::optional<std::pair<std::optional<T>, std::optional<T>>> value;

    closed_interval() {}
    closed_interval(std::optional<T> l, std::optional<T> r) : value(std::make_pair(l, r)) {}

    friend std::ostream &operator<<(std::ostream &s, const closed_interval<T> &a) {
      s << "[";
      if (a.value) {
        if ((a.value)->first)
          s << *((a.value)->first);
        else
          s << "-∞ ";
        s << ",";
        if ((a.value)->second)
          s << *((a.value)->second);
        else
          s << "∞ ";
      }
      s << "]";
      return s;
    }

    bool is_null() const {
      return not value;
    }

    bool contains(T v) const {
      if (not value) return false;
      if (value->first and v < *(value->first)) return false;
      if (value->second and v > *(value->second)) return false;

      return true;
    }
  };

  template <typename T>
  auto intersect(closed_interval<T> a, closed_interval<T> b) {
    if (not a.value or not b.value) return closed_interval<T>();
    std::optional<T> l, r;

    if ((a.value)->first) {
      l = *((a.value)->first);
    }

    if ((b.value)->first) {
      if (l)
        l = std::max(*l, *((b.value)->first));
      else
        l = *((b.value)->first);
    }

    if ((a.value)->second) {
      r = *((a.value)->second);
    }

    if ((b.value)->second) {
      if (r)
        r = std::min(*r, *((b.value)->second));
      else
        r = *((b.value)->second);
    }

    if (l and r) {
      if (*l > *r) {
        return closed_interval<T>();
      }
    }

    return closed_interval<T>(l, r);
  }

  template <typename T>
  auto left_expand(closed_interval<T> a, T x) {
    if (a.value and (a.value)->first) {
      *((a.value)->first) += x;
      if ((a.value)->second and *((a.value)->first) > *((a.value)->second)) {
        return closed_interval<T>();
      }
    }

    return a;
  }

  template <typename T>
  auto right_expand(closed_interval<T> a, T x) {
    if (a.value and (a.value)->second) {
      *((a.value)->second) += x;
      if ((a.value)->first and *((a.value)->first) > *((a.value)->second)) {
        return closed_interval<T>();
      }
    }

    return a;
  }

  template <typename T>
  auto operator+(closed_interval<T> a, T k) {
    if (a.value) {
      if (a.value->first) a.value->first.value() += k;
      if (a.value->second) a.value->second.value() += k;
    }
    return a;
  }

  template <typename T>
  auto operator-(closed_interval<T> a, T k) {
    if (a.value) {
      if (a.value->first) a.value->first.value() -= k;
      if (a.value->second) a.value->second.value() -= k;
    }
    return a;
  }

  template <typename T>
  auto operator*(closed_interval<T> a, T k) {
    if (a.value) {
      if (k < 0) std::swap(a.value->first, a.value->second);
      if (a.value->first) a.value->first.value() *= k;
      if (a.value->second) a.value->second.value() *= k;
    }
    return a;
  }
}  // namespace haar_lib

#line 2 "Mylib/Math/closed_interval.cpp"
#include <algorithm>
#include <iostream>
#include <optional>
#include <utility>

namespace haar_lib {
  template <typename T>
  struct closed_interval {
    std::optional<std::pair<std::optional<T>, std::optional<T>>> value;

    closed_interval() {}
    closed_interval(std::optional<T> l, std::optional<T> r) : value(std::make_pair(l, r)) {}

    friend std::ostream &operator<<(std::ostream &s, const closed_interval<T> &a) {
      s << "[";
      if (a.value) {
        if ((a.value)->first)
          s << *((a.value)->first);
        else
          s << "-∞ ";
        s << ",";
        if ((a.value)->second)
          s << *((a.value)->second);
        else
          s << "∞ ";
      }
      s << "]";
      return s;
    }

    bool is_null() const {
      return not value;
    }

    bool contains(T v) const {
      if (not value) return false;
      if (value->first and v < *(value->first)) return false;
      if (value->second and v > *(value->second)) return false;

      return true;
    }
  };

  template <typename T>
  auto intersect(closed_interval<T> a, closed_interval<T> b) {
    if (not a.value or not b.value) return closed_interval<T>();
    std::optional<T> l, r;

    if ((a.value)->first) {
      l = *((a.value)->first);
    }

    if ((b.value)->first) {
      if (l)
        l = std::max(*l, *((b.value)->first));
      else
        l = *((b.value)->first);
    }

    if ((a.value)->second) {
      r = *((a.value)->second);
    }

    if ((b.value)->second) {
      if (r)
        r = std::min(*r, *((b.value)->second));
      else
        r = *((b.value)->second);
    }

    if (l and r) {
      if (*l > *r) {
        return closed_interval<T>();
      }
    }

    return closed_interval<T>(l, r);
  }

  template <typename T>
  auto left_expand(closed_interval<T> a, T x) {
    if (a.value and (a.value)->first) {
      *((a.value)->first) += x;
      if ((a.value)->second and *((a.value)->first) > *((a.value)->second)) {
        return closed_interval<T>();
      }
    }

    return a;
  }

  template <typename T>
  auto right_expand(closed_interval<T> a, T x) {
    if (a.value and (a.value)->second) {
      *((a.value)->second) += x;
      if ((a.value)->first and *((a.value)->first) > *((a.value)->second)) {
        return closed_interval<T>();
      }
    }

    return a;
  }

  template <typename T>
  auto operator+(closed_interval<T> a, T k) {
    if (a.value) {
      if (a.value->first) a.value->first.value() += k;
      if (a.value->second) a.value->second.value() += k;
    }
    return a;
  }

  template <typename T>
  auto operator-(closed_interval<T> a, T k) {
    if (a.value) {
      if (a.value->first) a.value->first.value() -= k;
      if (a.value->second) a.value->second.value() -= k;
    }
    return a;
  }

  template <typename T>
  auto operator*(closed_interval<T> a, T k) {
    if (a.value) {
      if (k < 0) std::swap(a.value->first, a.value->second);
      if (a.value->first) a.value->first.value() *= k;
      if (a.value->second) a.value->second.value() *= k;
    }
    return a;
  }
}  // namespace haar_lib

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