Target Sum | Two Ways Of Memoization | Detailed | Leetcode 494 | Explanation + Code

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Hi Everyone, this is the 105th video of our Playlist "Dynamic Programming : Popular Interview Problems".
In this video we will solve a very classic knapsack variant of DP - Target Sum | Two Ways Of Memoization | Detailed | Leetcode 494 | Explanation + Code
We will also see two different ways of doing memoization.

Problem Name : Target Sum | Two Ways Of Memoization | Detailed | Leetcode 494 | Explanation + Code
Company Tags : Google, META
My solutions on Github(C++ & JAVA) - https://github.com/MAZHARMIK/Interview_DS_Algo/blob/master/DP/Target%20Sum.cpp
Leetcode Link : https://leetcode.com/problems/target-sum
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My Graph Concepts Playlist : https://youtu.be/5JGiZnr6B5w
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Video Summary :
Approach-1: Normal Recursion & Memoization using unordered_map

Description:
This approach uses recursion to explore all possible combinations of adding or subtracting elements to achieve the target sum. Memoization is implemented using an unordered_map to store intermediate results, where the key is a string representation of the current state (index, sum).

Advantages:

Flexible and dynamic as it doesn't require predefining the memoization table size.
Efficient for sparse states.
Disadvantages:

Slightly slower due to string manipulation and hashing overhead.
Approach-2: Normal Recursion & Memoization using vector

Description:
Similar to the first approach, this uses recursion to explore all possible combinations. However, memoization is implemented using a 2D vector, where the dimensions are based on the number of elements (n) and the range of sums (2 * totalSum + 1). A shift (S) is used to handle negative sums by offsetting the indices.

Advantages:

Faster access compared to unordered_map due to direct indexing.
No overhead of key creation and hashing.
Disadvantages:

Memory-intensive as the entire table is preallocated, even for unused states.
Not suitable for very large inputs or sparse state spaces.
✨ Timelines✨
00:00 - Introduction
0:45 - Motivation
1:47 - Problem Explanation
4:51 - Notice
5:46 - Thought Process + Tree Diagram
14:27 - Coding Brute Force
16:51 - 2 Ways to Memoize
28:37 - Coding Memoization

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