Finding the largest sum subarray is a intermediate problem in coding interviews. In this guide, we’ll explore how to locate the maximum sum of a continuous subarray using Kadane’s Algorithm. Don’t worry if this sounds complex at first—we’ll break it down step by step.
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Why Kadane’s Algorithm ?
As a programmer, you might wonder why Kadane’s Algorithm is so popular. Well, let me share a story. While searching for a better approach to solve the continuous subarray problem, I came across Kadane’s Algorithm.
This technique uses dynamic programming to efficiently find the maximum sum of a continuous subarray. It operates in linear time, making it ideal for handling large datasets. The main idea is to go through the array, keeping track of both the maximum sum encountered so far and the current subarray sum. Let’s delve into how it works!
How Kadane’s Algorithm Works ?
Initialize Variables: Start with two variables, max_so_far and max_ending_here, both set to the first element of the array. The max_so_far keeps the record of the maximum sum found, and max_ending_here keeps the sum of the current subarray.
Iterate through the Array: For each element in the array, update max_ending_here to be the maximum of the current element itself or the current element plus max_ending_here. Update max_so_far to be the maximum of max_so_far and max_ending_here.
Return the Result: After processing all elements, max_so_far will contain the largest sum of a subarray.
Please follow Detailed page How Kadane’s Algorithm Works ?
Implement Kadane’s Algorithm in Python
def find_largest_sum_subarray(arr):
max_so_far = arr[0]
max_ending_here = arr[0]
for num in arr[1:]:
max_ending_here = max(num, max_ending_here + num)
max_so_far = max(max_so_far, max_ending_here)
return max_so_far
# Example usage
array = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
print("The largest sum of a subarray is:", find_largest_sum_subarray(array))
Using Kadane’s Algorithm is a straightforward and efficient way to find the largest sum of a continuous subarray. By maintaining a running tally of the current subarray sum and updating the maximum sum encountered, the algorithm ensures an optimal solution in linear time. This approach is widely applicable in various fields, including finance, data analysis, and more, where locating maximum sum subarrays is essential.
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