You finally decode the Elves' message. HI, the message says. You continue searching for the sleigh keys.

Ahead of you is what appears to be a large ocean trench. Could the keys have fallen into it? You'd better send a probe to investigate.

Read the full puzzle.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace AdventOfCode.Y2021.Day17;

[ProblemName("Trick Shot")]
class Solution : Solver {

    public object PartOne(string input) => Solve(input).Max();
    public object PartTwo(string input) => Solve(input).Count();

    // For each vx0, vy0 combination that reaches the target, yield the highest y value of the trajectory:
    IEnumerable<int> Solve(string input) {
        // Parse the (signed) integers
        var m = Regex.Matches(input, "-?[0-9]+").Select(m => int.Parse(m.Value)).ToArray();

        // Get the target rectangle
        var (xMin, xMax) = (m[0], m[1]);
        var (yMin, yMax) = (m[2], m[3]);

        // Bounds for the initial horizontal and vertical speeds:
        var vx0Min = 0;     // Because vx is non negative
        var vx0Max = xMax;  // For bigger values we jump too much to the right in the first step
        var vy0Min = yMin;  // For smaller values we jump too deep in the first step
        var vy0Max = -yMin; // 🍎 Newton says that when the falling probe reaches y = 0, it's speed is -vy0.
                            // In the next step we go down to -vy0, which should not be deeper than yMin.
        
        // Run the simulation in the given bounds, maintaining maxY
        for (var vx0 = vx0Min; vx0 <= vx0Max; vx0++) {
            for (var vy0 = vy0Min; vy0 <= vy0Max; vy0++) {

                var (x, y, vx, vy) = (0, 0, vx0, vy0);
                var maxY = 0;

                // as long as there is any chance to reach the target rectangle:
                while (x <= xMax && y >= yMin) {
                   
                    x += vx;
                    y += vy;
                    vy -= 1;
                    vx = Math.Max(0, vx - 1);
                    maxY = Math.Max(y, maxY);

                    // if we are within target, yield maxY:
                    if (x >= xMin && x <= xMax && y >= yMin && y <= yMax) {
                        yield return maxY;
                        break;
                    }
                }
            }
        }
    }
}

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