max_double_slice.py

dotfiles/lib/python/max_double_slice.py

@@ -0,0 +1,51 @@
+class Result(object):
+
+    def __init__(self, lb, excluded, rb, max):
+        self.lb = lb
+        self.excluded = excluded
+        self.rb = rb
+        self.max = max
+
+    def __repr__(self):
+        return "left bound: {0}, excluded {1}, right_bound {2}, max {3}".format(
+            self.lb,
+            self.excluded,
+            self.rb,
+            self.max,
+        )
+
+
+
+def max_double_slice(array):
+    left_slices = max_slice_at_index(array)
+    right_slices = max_slice_at_index(array[::-1])[::-1]
+    print left_slices
+    print right_slices
+    def slice_sum(index):
+        left_contribution = left_slices[index - 1][-1] if index > 0 else 0
+        right_contribution = right_slices[index + 1][-1] if index < len(array) - 2 else 0
+        return right_contribution + left_contribution
+    maximizing_slice_index = max((i for i in range(len(array))), key=slice_sum)
+    left_bound, lmax = left_slices[maximizing_slice_index - 1] if maximizing_slice_index > 0 else (0, 0)
+    rs, rmax = right_slices[maximizing_slice_index + 1] if maximizing_slice_index < len(array) - 2 else (len(array) - 1, 0)
+    right_bound = len(array) - 1 - rs
+    return Result(left_bound, maximizing_slice_index, right_bound, lmax + rmax)
+
+
+def max_double_slice_value(array):
+    left, right = max_double_slice(array)
+    return left[-1] + right[-1]
+
+
+def max_slice_at_index(array):
+    max_at_index = []
+    for index, array_value in enumerate(array):
+        last_start, last_max = max_at_index[-1] if max_at_index else (index, 0)
+        if last_max < 0:
+            current_max = array_value
+            current_start = index
+        else:
+            current_max = array_value + last_max
+            current_start = last_start
+        max_at_index.append((current_start, current_max))
+    return max_at_index