day 13

day13/sample1.in

@@ -0,0 +1,15 @@
+Button A: X+94, Y+34
+Button B: X+22, Y+67
+Prize: X=8400, Y=5400
+
+Button A: X+26, Y+66
+Button B: X+67, Y+21
+Prize: X=12748, Y=12176
+
+Button A: X+17, Y+86
+Button B: X+84, Y+37
+Prize: X=7870, Y=6450
+
+Button A: X+69, Y+23
+Button B: X+27, Y+71
+Prize: X=18641, Y=10279

day13/sol.py

@@ -0,0 +1,78 @@
+def parse(file):
+    while True:
+        a = file.readline()
+        if not a:
+            break
+        b = file.readline()
+        pr = file.readline()
+        blank = file.readline()
+
+        ax, ay = parse_numbers(a)
+        bx, by = parse_numbers(b)
+        px, py = parse_numbers(pr)
+        yield ax,ay, bx,by, px,py
+
+import re
+def parse_numbers(s):
+    return [int(x) for x in re.findall(r"\d+", s)]
+
+from fractions import Fraction as F
+
+import numpy
+def solve(file):
+    total = 0
+    total2 = 0
+    for record in parse(file):
+        #print(record)
+        ax, ay, bx, by, px, py = record
+
+        # k_a ax + k_b * bx = px
+        # k_a ay + k_b * by = py
+        
+        M = numpy.array([[ax, bx], [ay, by]])
+        V = numpy.array([px, py])
+        sol = numpy.linalg.solve(M,V)
+        k1 = int(round(sol[0]))
+        k2 = int(round(sol[1]))
+        if k1*ax + k2*bx == px and k1*ay + k2*by == py:
+            print("yes", k1, k2)
+            total += 3*k1 + k2
+
+
+        m00 = ax
+        m01 = bx
+        m10 = ay
+        m11 = by
+        v1 = px+ 10000000000000
+        v2 = py+ 10000000000000
+        
+        c = F(m10,m00)
+        m10 -= c*m00
+        m11 -= c*m01
+        v2  -= c*v1
+
+        c = F(1,m11)
+        v2 *= c
+        m11 *= c
+
+        c = F(m01,m11)
+        m01 -= c*m11
+        v1  -= c*v2
+
+        c = F(1,m00)
+        v1  *= c
+        m00 *= c
+
+        print(m00, m01, m10, m11, v1, v2)
+        if v1.denominator == 1 and v2.denominator == 1 and v1 > 0 and v2 > 0:
+            #if v1*ax + v2*bx == px and v1*ay + v2*by == py:
+                print("yes2", v1, v2)
+                total2 += 3*v1 + v2
+
+        
+    print(total)
+    print(total2)
+
+
+solve(open("sample1.in"))
+solve(open("input"))