Maximum Sum of 3 Non-Overlapping Subarrays | Detailed For Beginners | Leetcode 689 | codstorywithMIK
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Hi Everyone, this is the 106th video of our Playlist "Dynamic Programming : Popular Interview Problems".
In this video we will solve a very good knapsack variant of DP - Maximum Sum of 3 Non-Overlapping Subarrays | Detailed For Begginers | Leetcode 689 | codstorywithMIK
The video is detailed for beginners as well so that they can understand it easily.
Problem Name : Maximum Sum of 3 Non-Overlapping Subarrays | Detailed For Beginners | Leetcode 689 | codstorywithMIK
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My solutions on Github(C++ & JAVA) - https://github.com/MAZHARMIK/Interview_DS_Algo/blob/master/DP/Maximum Sum of 3 Non-Overlapping Subarrays.cpp
Leetcode Link : https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays
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Video Summary :
The solution uses Dynamic Programming (DP) to find the maximum sum of three non-overlapping subarrays of size k. The approach is divided into three key steps:
Precomputing Subarray Sums:
A sliding window technique is used to compute the sums of all possible subarrays of size k in the input array.
These sums are stored in a separate array, sums, to simplify further calculations.
Dynamic Programming to Maximize Sum:
A recursive function (helper) with memoization is used to compute the maximum sum of up to 3 subarrays.
The state is defined by:
idx: Current position in the sums array.
rem: Remaining number of subarrays to include.
The function explores two choices:
Include the current subarray and skip k indices.
Skip the current subarray and move to the next index.
Reconstructing the Solution:
Another recursive function (solve) reconstructs the indices of the subarrays contributing to the maximum sum.
It uses the precomputed DP table to decide whether to include or skip a subarray at each step.
✨ Timelines✨
00:00 - Introduction
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