WIP: changing algorithm from linear to divide and conquer

others/dodge-the-lasers/solution.py

@@ -1,2 +1,65 @@
+import math
+from decimal import *
+
+getcontext().prec = 102
+sqrt_2 = Decimal(2).sqrt()
+
 def solution(s):
-    # Your code here
+    total = 0
+    for i in range(int(s)+1):
+        total += int(math.floor(i*sqrt_2))
+        #print i, total
+    return str(total)
+
+def check_known_pattern(start, end, memo):
+    if '0'*(end-start+1) in memo: # TODO: checkk value in the memo
+        return '0'*(end-start+1)
+    return False
+
+def generate_dfs(start, end, memo):
+    pattern = check_known_pattern(start, end, memo)
+    if pattern:
+        yield pattern, memo[pattern]
+    else:
+        new_pattern = ''
+        new_value = 0 # TODO: calculate new_value
+        pivot = int(math.floor((start+end)/2)) # TODO: power of 2 is optimal
+        for pattern, value in generate_dfs(start, pivot, memo):
+            new_pattern += pattern
+            new_value += value
+            yield pattern, value
+        for pattern, value in generate_dfs(pivot + 1, end, memo):
+            new_pattern += pattern
+            new_value += value
+            yield pattern, value
+        memo[new_pattern] = new_value
+
+memo = {'0': 1, '1': 1} # TODO: upgrade memo
+total = 0
+for pattern, value in generate_dfs(1, 5, memo):
+    total += value
+    print pattern, value
+print total, memo
+
+exit(0)
+
+
+
+tests = [
+        ['77', '4208'],
+        ['1', '1'],
+        ['2', '3'],
+        ['3', '7'],
+        ['4', '12'],
+        ['5', '19'],
+        ['6', '27'],
+        ['7', '36'],
+        ['8', '47'],
+        ['9', '59'],
+        ['10', '73'],
+        ]
+
+
+for test in tests:
+    result = solution(test[0])
+    print(test[0], result == test[1], result, test[1])