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# Untitled

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1. #include <iostream>
2. #include <vector>
3. #include <cmath>
4. #include <algorithm>
5. #include <string>
6. #include <limits>
7.
8. namespace pr {
9.     struct Point {
10.         double x,
11.                y;
12.
13.         Point(double x, double y) noexcept : x(x), y(y) {}
14.     };
15.
16.     std::ostream& operator<<(std::ostream& o, const Point p) {
17.         o << "(" << p.x << ", " << p.y << ")";
18.
19.         return o;
20.     }
21.
22.     inline
23.     auto dist(Point a, Point b) noexcept {
24.         return std::sqrt(
25.             (a.x - b.x) * (a.x - b.x) +
26.             (a.y - b.y) * (a.y - b.y)
27.         );
28.     }
29.
30.     inline
31.     auto perimeter(const std::vector<Point>& points) noexcept {
32.         double sum = 0.;
33.
34.         for (auto it = points.begin(); it != points.end() - 1; ++it)
35.             sum += dist(*it, *(it + 1));
36.
37.         return sum;
38.     }
39.
40.     inline
41.     auto is_prime(double num) {
42.         if (num > (double) std::numeric_limits<unsigned long long>::max())
43.             return false;
44.
45.         unsigned long long n = num;
46.
47.         if (n == 2)
48.             return true;
49.         else if (n < 2 || n % 2 == 0)
50.             return false;
51.         else
52.             for (unsigned long long i = 3; i < n / 2; ++i)
53.                 if (n % i == 0)
54.                     return false;
55.
56.         return true;
57.     }
58.
59.     inline
60.     auto ccw(Point a, Point b, Point c) noexcept {
61.         return a.x * (b.y - c.y) +
62.                b.x * (c.y - a.y) +
63.                c.x * (a.y - b.y);
64.     }
65.
66.     inline
67.     auto ch(std::vector<Point>& points) noexcept {
68.         std::vector<Point> upper, lower;
69.         std::size_t size;
70.
71.         std::sort(points.begin(), points.end(),
72.             [](const auto& l, const auto& r) -> bool {
73.                 return l.x < r.x || (l.x == r.x && l.y < r.y);
74.             }
75.         );
76.
77.         for (auto&& point : points) {
78.             while ((size = upper.size()) >= 2 && ccw(upper[size - 2], upper[size - 1], point) >= 0)
79.                 upper.pop_back();
80.
81.             upper.emplace_back(point);
82.         }
83.
84.         upper.pop_back();
85.
86.         for (auto r_it = points.rbegin(); r_it != points.rend(); ++r_it) {
87.             while ((size = lower.size()) >= 2 && ccw(lower[size - 2], lower[size - 1], *r_it) >= 0)
88.                 lower.pop_back();
89.
90.             lower.emplace_back(*r_it);
91.         }
92.
93.         std::copy(lower.begin(), lower.end(), std::back_inserter(upper));
94.
95.         return upper;
96.     }
97.
98.     inline
99.     void pe(const char* msg) {
100.         std::cout << msg << std::endl;
101.
102.         std::exit(EXIT_FAILURE);
103.     }
104. }
105.
106. int main() {
107.     std::ios_base::sync_with_stdio(false);
108.
109.     std::pair<double, char> key;
110.
111.     std::cout << "key in form of double, char pair: ";
112.     std::cin >> key.first >> key.second;
113.
114.     std::string pass;
115.
116.     std::cout << "pass with atleast 16 chars: ";
117.     std::cin >> pass;
118.
119.     if (pass.length() < 16)
120.         pr::pe("pass is too short");
121.
122.     pass = pass.length() % 2 ? std::move(pass.substr(1)) : pass;
123.
124.     std::vector<pr::Point> points;
125.                            points.reserve(pass.length() / 2);
126.
127.     for (std::size_t i = 0; i < pass.length(); i += 2)
128.         points.emplace_back(
129.             (double) (pass[i] - key.second) * key.first,
130.             (double) (pass[i + 1] - key.second) * key.first
131.         );
132.
133.     points = std::move(pr::ch(points));
134.     auto perimeter =  pr::perimeter(points);
135.
136.     std::cout << (
137.         points.size() == 5 && pr::is_prime(perimeter) ?
138.             "success"
139.                 :
140.             "failure"
141.     ) << std::endl;
142. }
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