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Fix readme and duplicate (#967)

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* Fix typo

* Add all_permutations algorithm to backtracking directory

* Update backtracking and D&C algorithms in README

Update backtracking and divide_and_conquer algorithms in README

* Remove the duplicated file
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Erfan Alimohammadi 2019-07-06 19:02:06 +04:30 committed by Anup Kumar Panwar
parent 839160f83a
commit 781b7f86e7
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README.md
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@ -45,6 +45,8 @@ We're on [Gitter](https://gitter.im/TheAlgorithms)! Please join us.
- [N Queens](./backtracking/n_queens.py)
- [Sum Of Subsets](./backtracking/sum_of_subsets.py)
- [All Subsequences](./backtracking/all_subsequences.py)
- [All Permutations](./backtracking/all_permutations.py)
## Ciphers
@ -220,7 +222,6 @@ We're on [Gitter](https://gitter.im/TheAlgorithms)! Please join us.
## Divide And Conquer
- [Max Subarray Sum](./divide_and_conquer/max_subarray_sum.py)
- [Max Sub Array Sum](./divide_and_conquer/max_sub_array_sum.py)
- [Closest Pair Of Points](./divide_and_conquer/closest_pair_of_points.py)
## Strings

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divide_and_conquer/max_sub_array_sum.py
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"""
Given a array of length n, max_sub_array_sum() finds the maximum of sum of contiguous sub-array using divide and conquer method.
Time complexity : O(n log n)
Ref : INTRODUCTION TO ALGORITHMS THIRD EDITION (section : 4, sub-section : 4.1, page : 70)
"""
def max_sum_from_start(array):
""" This function finds the maximum contiguous sum of array from 0 index
Parameters :
array (list[int]) : given array
Returns :
max_sum (int) : maximum contiguous sum of array from 0 index
"""
array_sum = 0
max_sum = float("-inf")
for num in array:
array_sum += num
if array_sum > max_sum:
max_sum = array_sum
return max_sum
def max_cross_array_sum(array, left, mid, right):
""" This function finds the maximum contiguous sum of left and right arrays
Parameters :
array, left, mid, right (list[int], int, int, int)
Returns :
(int) : maximum of sum of contiguous sum of left and right arrays
"""
max_sum_of_left = max_sum_from_start(array[left:mid+1][::-1])
max_sum_of_right = max_sum_from_start(array[mid+1: right+1])
return max_sum_of_left + max_sum_of_right
def max_sub_array_sum(array, left, right):
""" This function finds the maximum of sum of contiguous sub-array using divide and conquer method
Parameters :
array, left, right (list[int], int, int) : given array, current left index and current right index
Returns :
int : maximum of sum of contiguous sub-array
"""
# base case: array has only one element
if left == right:
return array[right]
# Recursion
mid = (left + right) // 2
left_half_sum = max_sub_array_sum(array, left, mid)
right_half_sum = max_sub_array_sum(array, mid + 1, right)
cross_sum = max_cross_array_sum(array, left, mid, right)
return max(left_half_sum, right_half_sum, cross_sum)
array = [-2, -5, 6, -2, -3, 1, 5, -6]
array_length = len(array)
print("Maximum sum of contiguous subarray:", max_sub_array_sum(array, 0, array_length - 1))