There's an interesting problem I recently solved on leetcode based on dynamic programming. My Github repository contains list of all problems that I have solved.
Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum. A subarray is a contiguous part of an array.1
We can commence with a brute force algorithm. For every element of array, we compare its sum with the rest of the element to calculate maximum sum.
Time complexity is O(n2) and the execution time is 110 ms on leetcode.
We can use Kadane algorithm to solve. It cans the given array A[1..n] from left to right. In the jth step, it computes the subarray with the largest sum ending at j; this sum is maintained in variable cSum. It computes the subarray with the largest sum anywhere in A[1..j], maintained in variable oSum;
The time complexity is O(n). The execution time took 0 ms on leetcode.