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Project Description
Kadane's Algorithm: Maximum Subarray Problem Statement: Kadane's Algorithm is used to find the maximum sum of a contiguous subarray in a given array of integers. The goal is to identify a subarray (one or more elements) that has the largest sum.
Key Concepts: Contiguous Subarray: A subarray is a slice of the original array that consists of consecutive elements. Kadane’s Algorithm ensures that it considers every possible subarray to find the one with the maximum sum.
Kadane’s Algorithm uses a approach by maintaining two variables:
max_current: The maximum sum of the subarray that ends at the current position. max_global: The maximum sum found so far across all subarrays.
Steps: Initialization:
Set both max_current and max_global to the first element of the array. Iterate Over the Array:
For each subsequent element, update max_current by choosing the maximum of either: The current element itself (arr[i]), which implies starting a new subarray. The current element plus the previous max_current, meaning the subarray continues. Update max_global if max_current exceeds the previously recorded max_global. Return Result: After traversing the entire array, max_global will hold the largest sum of any contiguous subarray.
Kadane's Algorithm: Maximum Subarray Problem Statement: Kadane's Algorithm is used to find the maximum sum of a contiguous subarray in a given array of integers. The goal is to identify a subarray (one or more elements) that has the largest sum.
Key Concepts: Contiguous Subarray: A subarray is a slice of the original array that consists of consecutive elements. Kadane’s Algorithm ensures that it considers every possible subarray to find the one with the maximum sum.
Dynamic Programming Approach: Kadane’s Algorithm uses a dynamic programming approach by maintaining two variables:
max_current: The maximum sum of the subarray that ends at the current position. max_global: The maximum sum found so far across all subarrays. Steps: Initialization:
Set both max_current and max_global to the first element of the array. Iterate Over the Array:
For each subsequent element, update max_current by choosing the maximum of either: The current element itself (arr[i]), which implies starting a new subarray. The current element plus the previous max_current, meaning the subarray continues. Update max_global if max_current exceeds the previously recorded max_global. Return Result: After traversing the entire array, max_global will hold the largest sum of any contiguous subarray.
Time Complexity: O(n) where n is the number of elements in the array. Kadane's Algorithm runs in linear time since it processes each element of the array exactly once. Space Complexity: O(1) as the algorithm only uses a few extra variables to track the maximum sums.
Full Name
Mithanshu Rajesh Hedau
Participant Role
Gssoc-ext , hacktoberfest