Partition Array for Maximum Sum | Why DP | Recursion | Memo | Bottom Up | Leetcode 1043
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This is the 85th Video of our Playlist "Dynamic Programming : Popular Interview Problems".
In this video we will try to solve a very good and classic DP problem based on array partition - Partition Array for Maximum Sum | Leetcode 1043
I will explain the intuition so easily that you will never forget and start seeing this as cakewalk EASYYY.
We will do live coding after explanation and see if we are able to pass all the test cases.
Also, please note that my Github solution link below contains both C++ as well as JAVA code.
Problem Name : Partition Array for Maximum Sum | Leetcode 1043
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My solutions on Github(C++ & JAVA) : https://github.com/MAZHARMIK/Interview_DS_Algo/blob/master/DP/Partition%20Array%20for%20Maximum%20Sum.cpp
Leetcode Link : https://leetcode.com/problems/partition-array-for-maximum-sum/description
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Approach-1 Summary : The approach uses a recursive dynamic programming strategy with memoization to avoid redundant calculations. The function solve recursively explores different partitioning options, keeping track of the maximum sum encountered. The memoization array t is used to store and retrieve previously computed results, reducing the time complexity. The main function initializes necessary variables, sets up memoization, and calls the recursive solve function to obtain the maximum sum after partitioning.
Approach-2 Summary : The approach uses dynamic programming to iteratively compute the maximum sum for each partition. The array t is used to store intermediate results, where t[i] represents the maximum sum for the partition arr[0 to i]. The code iterates through each position in the array, considering partitions of size at most k. It calculates the current maximum within the partition and updates the maximum sum for the current position based on the best result from previous partitions. The final result is the maximum sum for the entire array, stored in t[n]. This approach avoids recursion and efficiently computes the maximum sum after partitioning.
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✨ Timelines✨
00:00 - Introduction
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