Add 2021 day 17 puzzles

2021/puzzle-17-01.cc

@@ -0,0 +1,75 @@
+#include <iostream>
+#include <regex>
+#include <string>
+
+template<typename T>
+constexpr auto triangle_sum(T t) noexcept -> T
+{
+  return t * (t + 1) / 2;
+}
+
+auto main() -> int
+{
+  static std::regex re{R"(target area: x=(-?\d+)\.\.(-?\d+), y=(-?\d+)\.\.(-?\d+))"};
+  std::smatch m;
+  std::string line;
+
+  if (!std::getline(std::cin, line)) {
+    std::cerr << "Unable to read line";
+    return 1;
+  }
+  if (!std::regex_search(line, m, re)) {
+    std::cerr << "Unable to interpret: " << line << '\n';
+    return 1;
+  }
+
+  auto x0{std::stol(m.str(1))};
+  auto x1{std::stol(m.str(2))};
+  auto y0{std::stol(m.str(3))};
+  auto y1{std::stol(m.str(4))};
+
+  auto x_max{std::max(std::abs(x0), std::abs(x1))};
+  auto [y_min, y_max] = std::minmax(std::abs(y0), std::abs(y1));
+  /* We want to go at most x_max away.  To do this in the most steps we want to be going vertical
+   * at or before the last step.  So vx0 must be such that:
+   *   vx0 + (vx0 - 1) + ... + 1 + 0 ... 0 <= x_max. (Look triangular number we know a formula...)
+   *   => vx0 * (vx0 + 1) / 2 <= x_max
+   *
+   * I'm lazy - the input is small enough that I can find this by iteration...
+   */
+  long vx0{1};
+  while (triangle_sum(vx0) < x_max) {
+    ++vx0;
+  }
+  /* And correct vx0 here. */
+  --vx0;
+
+  std::cout << "vx0: " << vx0 << '\n';
+
+  /* Going the vertically is harder.  Let's do it by iteration.  We know the total number of steps
+   * we want to take is at least vx0.
+   *
+   * Actually - we pass y=0 on the way down, with velocity -vy0.  So we want:
+   * triangle_sum(vy_end) - triangle_sum(vy0) <= y_max;
+   */
+  long candidate_vy0{1};
+  long vy0{1};
+  while (candidate_vy0 <= y_max) {
+    long ypos{0};
+    long vy{candidate_vy0};
+    while (ypos < y_max) {
+      ypos += (vy++);
+    }
+    ypos -= (--vy);
+    if (ypos >= y_min) {
+      /* This speed works - let's use update the candidate.  */
+      vy0 = candidate_vy0;
+    }
+    ++candidate_vy0;
+  }
+
+  std::cout << "vy0: " << vy0 << '\n';
+  std::cout << "Max height:" << triangle_sum(vy0) << '\n';
+
+  return 0;
+}