Python3 Program for Size of The Subarray With Maximum Sum
Last Updated :
05 Sep, 2024
An array is given, find length of the subarray having maximum sum.
Examples :
Input : a[] = {1, -2, 1, 1, -2, 1}
Output : Length of the subarray is 2
Explanation: Subarray with consecutive elements
and maximum sum will be {1, 1}. So length is 2
Input : ar[] = { -2, -3, 4, -1, -2, 1, 5, -3 }
Output : Length of the subarray is 5
Explanation: Subarray with consecutive elements
and maximum sum will be {4, -1, -2, 1, 5}. This problem is mainly a variation of Largest Sum Contiguous Subarray Problem.
The idea is to update starting index whenever sum ending here becomes less than 0.
Python3
# Python3 program to print largest contiguous array sum
from sys import maxsize
# Function to find the maximum contiguous subarray
# and print its starting and end index
def maxSubArraySum(a,size):
max_so_far = -maxsize - 1
max_ending_here = 0
start = 0
end = 0
s = 0
for i in range(0,size):
max_ending_here += a[i]
if max_so_far < max_ending_here:
max_so_far = max_ending_here
start = s
end = i
if max_ending_here < 0:
max_ending_here = 0
s = i+1
return (end - start + 1)
# Driver program to test maxSubArraySum
a = [-2, -3, 4, -1, -2, 1, 5, -3]
print(maxSubArraySum(a,len(a)))
Time Complexity: O(N) where N is the size of the input array. This is because a for loop is executed from 1 to the size of the array.
Auxiliary Space: O(1) as no extra space has been taken.
Approach#2: Using Kadane’s algorithm
This approach implements Kadane’s algorithm to find the maximum subarray sum and returns the size of the subarray with the maximum sum.
Algorithm:
- Initialize max_sum, current_sum, start, end, max_start, and max_end to the first element of the array.
- Iterate through the array from the second element.
- If the current element is greater than the sum of the current element and current_sum, update start to the current index.
- Update current_sum as the maximum of the current element and the sum of current element and current_sum.
- If current_sum is greater than max_sum, update max_sum, end to the current index, and max_start and max_end to start and end respectively.
- Return max_end – max_start + 1 as the size of the subarray with maximum sum.
Below is the implementation of the approach:
Python
# Python3 implementation of the approach
# Function to find the maximum subarray sum
def max_subarray_sum(a):
n = len(a)
# Initializing initial and final sum to 0
max_sum = a[0]
current_sum = a[0]
start = 0
end = 0
max_start = 0
max_end = 0
# Traverse the array
for i in range(1, n):
# If the current element is greater than the sum so
# far plus the current element, then update the
# start index to the current index
if a[i] > current_sum + a[i]:
start = i
# Update the current sum to be either the current
# element or the sum so far plus the current
# element
current_sum = max(a[i], current_sum + a[i])
# If the current sum is greater than the maximum
# sum so far, then update the maximum sum and its
# start and end indices
if current_sum > max_sum:
max_sum = current_sum
end = i
max_start = start
max_end = end
# Return the length of the maximum subarray
return max_end - max_start + 1
# Initializing array
if __name__ == "__main__":
a = [-2, -3, 4, -1, -2, 1, 5, -3]
# Function call
print(max_subarray_sum(a))
Time Complexity: O(n), where n is length of array
Auxiliary Space: O(1)
Note: The above code assumes that there is at least one positive element in the array. If all the elements are negative, the code needs to be modified to return the maximum element in the array.
Please refer complete article on Size of The Subarray With Maximum Sum for more details!
Similar Reads
Javascript Program for Size of The Subarray With Maximum Sum An array is given, find length of the subarray having maximum sum.Examples : Input : a[] = {1, -2, 1, 1, -2, 1}Output : Length of the subarray is 2Explanation: Subarray with consecutive elements and maximum sum will be {1, 1}. So length is 2Input : ar[] = { -2, -3, 4, -1, -2, 1, 5, -3 }Output : Leng
2 min read
Python Program for Maximum size square sub-matrix with all 1s Write a Python program for a given binary matrix, the task is to find out the maximum size square sub-matrix with all 1s. Recommended: Please solve it on "PRACTICE" first, before moving on to the solution.Approach: Let the given binary matrix be M[R][C]. The idea of the algorithm is to construct an
4 min read
Maximum sum subarray of size range [L, R] Given an integer array arr[] of size N and two integer L and R. The task is to find the maximum sum subarray of size between L and R (both inclusive). Example: Input: arr[] = {1, 2, 2, 1}, L = 1, R = 3 Output: 5 Explanation: Subarray of size 1 are {1}, {2}, {2}, {1} and maximum sum subarray = 2 for
8 min read
Maximum sum subarray of size K with sum less than X Given an array arr[] and two integers K and X, the task is to find the maximum sum among all subarrays of size K with the sum less than X. Examples: Input: arr[] = {20, 2, 3, 10, 5}, K = 3, X = 20Output: 18Explanation: Subarray of size 3 having maximum sum less than 20 is {3, 10, 5}. Therefore, requ
7 min read
Maximum sum two non-overlapping subarrays of given size Given an array, we need to find two subarrays with a specific length K such that sum of these subarrays is maximum among all possible choices of subarrays. Examples: Input : arr[] = [2, 5, 1, 2, 7, 3, 0] K = 2 Output : 2 5 7 3 We can choose two arrays of maximum sum as [2, 5] and [7, 3], the sum of
12 min read
Length of the smallest subarray with maximum possible sum Given an array arr[] consisting of N non-negative integers, the task is to find the minimum length of the subarray whose sum is maximum. Example: Input: arr[] = {0, 2, 0, 0, 12, 0, 0, 0}Output: 4Explanation: The sum of the subarray {2, 0, 0, 12} = 2 + 0 + 0 + 12 = 14, which is maximum sum possible a
6 min read