Kadane's algorithm for finding the maximum subarray sum in an array

int best = 0, sum = 0;

for (int k = 0; k < n; k++) { sum = max(array[k],sum+array[k]); best = max(best,sum); } cout << best << "\n";

The program implements Kadane's algorithm, which is an efficient algorithm for finding the maximum subarray sum in an array. The algorithm works by iterating through the array and keeping track of the maximum sum encountered so far.

Here's a step-by-step explanation of how the algorithm works:

  1. Initialize two variables, "best" and "sum", to 0:
    • The variable "best" will store the maximum subarray sum.
    • The variable "sum" will store the current sum of the subarray being considered.
  1. Iterate through the array from index 0 to n-1:
    • The loop variable "k" represents the current index being considered.
  1. For each element at index k, calculate the new sum:
    • The new sum is calculated by taking the maximum of two values:
      • The current element at index k (array[k])
      • The sum of the previous elements plus the current element (sum + array[k])
  • This step is crucial because it determines whether to start a new subarray or continue with the previous subarray. If the current element is greater than the sum of the previous elements plus the current element, it means that starting a new subarray from the current element will yield a larger sum.
  1. Update the "best" variable:
    • After calculating the new sum, update the "best" variable by taking the maximum of the current "best" and the new "sum".
    • This ensures that the "best" variable always stores the maximum subarray sum encountered so far.
  1. Repeat steps 3 and 4 for all elements in the array.
  1. After the loop, the "best" variable will contain the maximum subarray sum.
  1. Finally, print the value of "best" using the cout statement.

The algorithm works because it considers all possible subarrays and keeps track of the maximum sum encountered so far. By updating the "sum" and "best" variables at each iteration, the algorithm efficiently finds the maximum subarray sum without the need for nested loops or additional data structures.


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