day24: adding python z3, example

day24/notes.org

@@ -20,16 +20,86 @@ so, what do i do? to get the ends of the lines?
 i try to calcluate with both x & y in 2 min\max. then if the other is ok, than that's the ends?
 wait, what happens when i do x = 7, and x = 27 and y is outside? it means no intesections, i guess
 or it could be outside from different sides, so not all x are ok, but there's still line there
-* Using homogeneous coordinates
+** Using homogeneous coordinates
 https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
 no, i don't understant that
-* https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Given_two_points_on_each_line
+** https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Given_two_points_on_each_line
 with 2 points. i guess
 but also - check if the point in future of the hail, by comparing with speeds?
 should be easy
-* and i got wrong result
+** and i got wrong result
 day24 result: 8406
-* another formula gives
+** another formula gives
 day24 result: 8406
-* another formula
+** another formula
 12938
+*
+* ok, part 2.
+what if.
+i start checking t = 0, 1, etc.
+for each t, i need two points of the two hail lines.
+
+it would constitute the trajectory.
+then condition for the solution that all other hail lines will intersect it at some t.
+so check for intersection (maybe not necessarily in the field?)
+
+go though lines, if any fail to intersect - continue with t
+
+if all intersect, find where the rock has to be in time 0
+
+oh. no.
+it's not just intersect. it's that the movement of the rock with t would be there at correct time? yuck?
+
+would there really be more than i line that intersects all of the hail lines?
+
+i'll just need to also figure out t=0 from other coords.
+
+i don't like this at all.
+
+And intersections have to be over (X, Y, Z)
+** so 'hail mary' approach would be
+scan first 1k nanoseconds. so already 1M calculations
+( this is first part of desperation, that at least 2 hails will intercept in first 1k ticks )
+
+for collision 1, assume HailA is on path.
+then iterate for all other assumint they are intercepted on t 2 etc ?
+
+no. the intersections could be on non-integer times?
+( this would be second part of the 'hail mary' )
+
+from that i should be able to construct the 'trajectory' line.
+and then check with all other points - do the intersect?
+( and check of intersection in future would be nice )
+
+then if line confirmed, will need to calc for t = 0, t = 1, and get speeds
+*** not hoping for all integer intersections
+or what if i will hope for that?
+let's try?
+* ok, what if i could do system of equasions?
+    #+begin_src
+    yuck_test.go:12:
+        x + Dx * t0 == 19 + -2 * t0
+        y + Dy * t0 == 13 + 1 * t0
+        z + Dz * t0 == 19 + -2 * t0
+        x + Dx * t1 == 18 + -1 * t1
+        y + Dy * t1 == 19 + -1 * t1
+        z + Dz * t1 == 18 + -2 * t1
+        x + Dx * t2 == 20 + -2 * t2
+        y + Dy * t2 == 25 + -2 * t2
+        z + Dz * t2 == 20 + -4 * t2
+        solve for x, y, z, Dx, Dy, Dz, t1, t2, t3. ti > 0
+    #+end_src
+
+    #+begin_src
+    yuck_test.go:18:
+        x + Dx * t0 == 147847636573416 + 185 * t0
+        y + Dy * t0 == 190826994408605 + 49 * t0
+        z + Dz * t0 == 147847636573416 + 219 * t0
+        x + Dx * t1 == 287509258905812 + -26 * t1
+        y + Dy * t1 == 207449079739538 + 31 * t1
+        z + Dz * t1 == 287509258905812 + 8 * t1
+        x + Dx * t2 == 390970075767404 + -147 * t2
+        y + Dy * t2 == 535711685410735 + -453 * t2
+        z + Dz * t2 == 390970075767404 + -149 * t2
+        solve for x, y, z, Dx, Dy, Dz, t1, t2, t3. ti > 0
+    #+end_src