level5/expanding-nebula/solution.py

@@ -0,0 +1,85 @@
+import numpy as np
+
+def solution(g):
+    #print_grid(g)
+    grid = np.array(g)
+    #print grid
+    height, width = grid.shape
+    #print height, width
+
+    memo = {}
+    prev_cases = {}
+    for i in range(2**(height+1)):
+        prev_cases[i] = 1
+        memo[i] = {}
+        for j in range(2**(height+1)):
+            memo[i][j] = calculate_c_column(i, j, height)
+    #print memo
+
+    #print prev_cases
+    for column in range(width):
+        cases = {}
+        for i in range(2**(height+1)):
+            cases[i] = 0
+        #print grid[:,column], list_to_int(grid[:,column])
+        for i in range(2**(height+1)):
+            if prev_cases[i] == 0:
+                continue
+            for j in range(2**(height+1)):
+                if memo[i][j] == list_to_int(grid[:,column]):
+                    cases[j] += prev_cases[i]
+        #print cases
+        prev_cases = cases
+    return sum(prev_cases.values())
+
+def print_grid(g):
+    for row in g:
+        line = ""
+        for elem in row:
+            if elem:
+                line+="O"
+            else:
+                line+="."
+        print line
+
+def calculate_c_column(i, j, length):
+    mask = 2**(length)-1
+    multi_ones = ((i&j)|((i&j)>>1)) & mask
+    odd_ones = ((i^j)^((i^j)>>1)) & mask
+    single_one = (~multi_ones & odd_ones) & mask
+    #print ' '.join(('{:0'+str(length)+'b}').format(k) for k in [i, j]), ' '.join(('{:0'+str(length-1)+'b}').format(k) for k in [multi_ones, odd_ones, single_one])
+    return single_one
+
+#l=3
+#memo = {}
+#for i in range(2**(l-1)):
+#    memo[i] = 0
+#for i in range(2**l):
+#    for j in range(2**l):
+#        t = calculate_c_column(i, j, l)
+#        memo[t] += 1
+#print memo
+#exit(0)
+
+def list_to_int(l):
+    value = 0
+    for v in l:
+        value |= v
+        value <<= 1
+    return value >> 1
+
+tests = [
+            ([[True, True, False, True, False, True, False, True, True, False], [True, True, False, False, False, False, True, True, True, False], [True, True, False, False, False, False, False, False, False, True], [False, True, False, False, False, False, True, True, False, False]], 11567),
+            ([[True, False, True], [False, True, False], [True, False, True]], 4),
+            ([[True, False, True, False, False, True, True, True], [True, False, True, False, False, False, True, False], [True, True, True, False, False, False, True, False], [True, False, True, False, False, False, True, False], [True, False, True, False, False, True, True, True]] ,254),
+            ([[True]], 4),
+            ([[False]], 12),
+            ([[True, True]], 6),
+            ([[True, False]], 10),
+            ([[False, True]], 10),
+            ([[False, False]], 38),
+        ]
+
+for (i, o) in tests:
+    result = solution(i)
+    print(i, result == o, result, o)