1 files changed, 87 insertions, 0 deletions
diff --git a/2021/day17/day17.cpp b/2021/day17/day17.cpp
new file mode 100644
index 0000000..305900a
--- /dev/null
+++ b/2021/day17/day17.cpp
@@ -0,0 +1,87 @@
+#include <iostream>
+#include <string>
+#include <vector>
+#include <map>
+
+// -- notes
+// if vy(0) > 0 the trajectory always reaches y=0 at time t 
+//     and vy(t) = -vy(0), vy(t+1) = -vy(0)-1
+// sum {i:1..n} (n) = ((n)(n+1))/2
+// triangle = { i in N | exist an n in N s.t. i = sum(n) }
+// if probe reaches y=0 with vx(t)=0, vx(0) is in triangle
+// so for every vx(0) in sumn and sum(vx(0)) in target
+//     get the largest vy(t) in target
+// this approach only works if vy(0)>0
+
+std::vector<int> parse_range(std::string raw) {
+	std::vector<int> range;
+	std::string nolabel = raw.substr(2);
+	auto dotdot = nolabel.find("..");
+	std::string r = nolabel.substr(0, dotdot);
+	std::string l = nolabel.substr(dotdot+2);
+	range.push_back(std::stoi(r));
+	range.push_back(std::stoi(l));
+	return range; 
+}
+
+int get_trig (int n) {
+	return ((n)*(n+1))/2;
+}
+
+int validate (int vx, int vy, std::vector<int> range, int maxt) {
+	int x = 0, y = 0;
+	for (int t=0; t<maxt; t++) {
+		x += vx; y += vy;
+		if (vx > 0) vx--; 
+		vy--;
+		if (range[0] <= x && x <= range[1])
+			if (range[2] <= y && y <= range[3])
+				return 1;
+		if (y < range[2]) return 0;
+	}
+	return 0;
+}
+
+int main (int argc, char *argv[]) {
+	std::string raw = std::string({ argv[1] });
+	std::string nolabel = raw.substr(13);
+	auto comma = nolabel.find(", ");
+	std::string rangex = nolabel.substr(0, comma);
+	std::string rangey = nolabel.substr(comma+2);
+	auto range = parse_range(rangex);
+	auto ry = parse_range(rangey);
+	range.insert(std::end(range), std::begin(ry), std::end(ry));
+	// range is x1, x2, y1, y2
+	
+	std::map<int, int> triangles {};
+	for (int i=0; i<100; i++) {
+		triangles[get_trig(i)] = i;
+	}
+
+	int vx = 0;
+	int vy = 0;
+	for (int i=range[0]; i<range[1]; i++) {
+		if (triangles.contains(i)) {
+			for (int j=range[2]; j<range[3]; j++) {
+				if (-j > vy) {
+					vy = -j-1;
+					vx = triangles[i];
+				}
+			}
+		}
+	}
+
+	std::cout << "velocity: vx=" << vx << ", vy=" << vy << std::endl;
+	std::cout << "max height: " << get_trig(vy) << std::endl;
+
+	int sum = 0;
+	for (int i=0; i<range[1]*2; i++) {
+		for (int j=range[2]; j<vy+1; j++) {
+			sum += validate(i, j, range, 1000);
+		}
+	}
+
+	std::cout << "total intial velocities: " << sum << std::endl;
+
+	return 0;
+}