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Merge pull request #761 from mahletseyoum101/kadanes_algorithm
kadanes_algorithm
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def kadanes_algorithm(arr): | ||
"""Standard Kadane's Algorithm for maximum sum subarray.""" | ||
max_ending_here = max_so_far = arr[0] | ||
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for num in arr[1:]: | ||
max_ending_here = max(num, max_ending_here + num) | ||
max_so_far = max(max_so_far, max_ending_here) | ||
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return max_so_far | ||
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def max_circular_subarray(arr): | ||
"""Kadane's Algorithm variation for circular arrays.""" | ||
max_kadane = kadanes_algorithm(arr) | ||
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# Compute total array sum | ||
total_sum = sum(arr) | ||
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# Invert the array elements | ||
inverted_arr = [-x for x in arr] | ||
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# Find the maximum sum of the inverted array (minimum subarray sum) | ||
max_inverted_kadane = kadanes_algorithm(inverted_arr) | ||
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# The maximum circular sum is total_sum + max_inverted_kadane | ||
# If max_inverted_kadane is equal to total_sum, it means all elements are negative | ||
max_circular = total_sum + max_inverted_kadane if max_inverted_kadane != -total_sum else max_kadane | ||
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return max(max_kadane, max_circular) | ||
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# Example usage | ||
arr = [1, -2, 4, -3] | ||
print("Maximum sum subarray (circular):", max_circular_subarray(arr)) |