intial commit

Author: ndsvw

max_sum_subarray.py

@@ -0,0 +1,64 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+# max_sum_dac solves the max-sum-subarray-problem with Divide and Conquer
+# in O(m*log(m))
+
+# example 1: max_sum_dac( [3,-5,0,2,100,-2,-5,9] )
+# max-sum-subarray: [2,100,-2,-5,9]
+# max-sum: 2+100-2-5+9 = 104
+
+# example 2: max_sum_dac( [-3,5,-1,2,-5,3] )
+# max-sum-subarray: [5,-1,2]
+# max-sum: 5-1+2 = 6
+
+def max_prefix_sum(a):
+  i = 0
+  accumulator, maxval = a[i], a[i]
+  
+  for j in range(1,len(a)):
+    accumulator += a[j]
+    maxval = max(maxval, accumulator)
+  return maxval
+
+def max_sum_dac(a):
+  m = len(a)
+
+  # trivial case
+  if m == 1:
+    return a[0]
+
+  # divide
+  a1 = a[:len(a)//2]
+  a2 = a[len(a1):]
+
+  # recursion
+  l = max_sum_dac(a1)
+  r = max_sum_dac(a2)
+
+  # conquer
+  left_max = max_prefix_sum([a1[i] for i in range(len(a1)-1, -1, -1)]) #reversed a1
+  right_max = max_prefix_sum(a2)
+  max_sum_over_middle = left_max + right_max
+  return max(max_sum_over_middle, l, r)
+  
+# Tests
+print("Tests:")
+a = [3,-5,0,2,100,-2,-5,9]
+print(max_sum_dac(a) == 104)
+a = [-3,5,-1,2,-5,3]
+print(max_sum_dac(a) == 6)
+a = [13,-5,-1,7,-5,4]
+print(max_sum_dac(a) == 14)
+a = [3,-5,0,1,10,-2,-5,6]
+print(max_sum_dac(a) == 11)
+a = [3,-5,0,1,0,-2,-5,6]
+print(max_sum_dac(a) == 6)
+a = [-3,-9,-4,-5,-2,-1]
+print(max_sum_dac(a) == -1)
+a = [3,5,10,9,2,3]
+print(max_sum_dac(a) == 32)
+a = [3,-5,-10,-9,-2,-3]
+print(max_sum_dac(a) == 3)
+a = [3,-5,10,9,-2,-3]
+print(max_sum_dac(a) == 19)