Kadane’s algorithm python: The maximum sub-array sum situation needs you to identify a continuous sub-array that has the highest sum.
Take a look at the following array:
The sum of a continuous array of green cells, i.e., 6, gives the greatest sum in this array of length 7 that is Any other possible sub-array generates a sum that is less than or equal to 6.
The Maximum Subarray Problem is a well-known dynamic programming problem. Kadane’s algorithm is the algorithm we utilize to tackle this problem. It is a bit difficult algorithm to grasp, but don’t worry. In this tutorial, we will go over the algorithm in a simple manner.
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Examples:
Example1:
Input:
given array = [-3, 4, 1, 2, -1, -4, 3]
Output:
The maximum subarray sum of the given list [-3, 4, 1, 2, -1, -4, 3] : 7
Example2:
Input:
given array = [2, -1, 46, 9, -3, -2, 10, 11, -9, 23, -3]
Output:
The maximum subarray sum of the given list [2, -1, 46, 9, -3, -2, 10, 11, -9, 23, -3] : 86
Program to solve Maximum Subarray Problem using Kadane’s Algorithm in Python
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1)Algorithm
Kadane’s algorithm java: Kadane’s approach is the best solution for finding the maximum sub-array; it utilizes two variables:
current_maximum to keep track of whether the value at the current index raises the maximum total.
maximum_so_far to keep track of the total maximum propagated along with the array.
- Set both of the variables specified above to the value at the first index, i.e., arr[0].
- Store the maximum of arr[i] and current_maximum + arr[i] in the current_maximum for the following index i.
- Maximum_so_far stores the maximum of maximum_so_far and current_maximum.
- Repeat the preceding two procedures for the remaining indices.
- Return the maximum_so_far value.
2)Implementation(Static Array)
Approach:
- Give the array/list as static input and store it in a variable.
- Calculate the length of the given list using the len() function and store it in a variable.
- Pass the given list and length of the given list as an argument to the findKadane function which implements the kadane’s algorithm.
- It returns the maximum subarray sum for the given list.
- Print the maximum sum.
- The Exit of the Program
Below is the implementation:
def findKadane(givnList, listleng): # Set both of the variablesto the value at the first index, i.e., givnList[0]. cur_maxi = givnList[0] maxi_so_far = givnList[0] for i in range(1, listleng): # Store the maximum of givnList[i] and cur_maxi + givnList[i] # in the cur_maxi for the following index i. cur_maxi = max(givnList[i], cur_maxi + givnList[i]) # maxi_so_far stores the maximum of maxi_so_far and cur_maxi. maxi_so_far = max(maxi_so_far, cur_maxi) # return the maxi_so_far return maxi_so_far # Give the array/list as static input and store it in a variable. givnList = [-3, 4, 1, 2, -1, -4, 3] # Calculate the length of the given list # using the len() function and store it in a variable. listleng = len(givnList) # Pass the given list and length of the given # list as an arguments to the findKadane function which implements the kadane's algorithm. resltsum = findKadane(givnList, listleng) # Print the maximum sum. print('The maximum subarray sum of the given list', givnList, ':') print(resltsum)
Output:
The maximum subarray sum of the given list [-3, 4, 1, 2, -1, -4, 3] : 7
Here it takes O(n) Time Complexity as we traversed only once in the given list. So it is the best and efficient way to find the maximum sum of a subarray in the given list.
3)Implementation(User Input)
Approach:
- Give the array/list as user input using list(),map(),split() and input() functions.
- Here the given numbers will get divided by space using the split() function.
- The string numbers get converted to an integer using map and int functions.
- Calculate the length of the given list using the len() function and store it in a variable.
- Pass the given list and length of the given list as an argument to the findKadane function which implements the kadane’s algorithm.
- It returns the maximum subarray sum for the given list.
- Print the maximum sum.
- The Exit of the Program
Below is the implementation:
def findKadane(givnList, listleng): # Set both of the variablesto the value at the first index, i.e., givnList[0]. cur_maxi = givnList[0] maxi_so_far = givnList[0] for i in range(1, listleng): # Store the maximum of givnList[i] and cur_maxi + givnList[i] # in the cur_maxi for the following index i. cur_maxi = max(givnList[i], cur_maxi + givnList[i]) # maxi_so_far stores the maximum of maxi_so_far and cur_maxi. maxi_so_far = max(maxi_so_far, cur_maxi) # return the maxi_so_far return maxi_so_far # Give the array/list as user input using list(),map(),split() and input() functions. # Here the given numbers will get divided by space using the split() function. # The string numbers get converted to integer using map and int functions. givnList = list( map(int, input('Enter some random list numbers separated by spaces = ').split())) # Calculate the length of the given list # using the len() function and store it in a variable. listleng = len(givnList) # Pass the given list and length of the given # list as an arguments to the findKadane function which implements the kadane's algorithm. resltsum = findKadane(givnList, listleng) # Print the maximum sum. print('The maximum subarray sum of the given list', givnList, ':') print(resltsum)
Output:
Enter some random list numbers separated by spaces = 2 -1 4 9 -3 -2 10 11 -9 23 -3 The maximum subarray sum of the given list [2, -1, 46, 9, -3, -2, 10, 11, -9, 23, -3] : 86
Time Complexity :O(n)
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