Equal Sum Subarrays

Explore how to identify if an array can be divided into two subarrays with equal sums using dynamic programming. Understand the naive recursive solution and improve it with top-down memoization and bottom-up tabulation approaches based on the 0/1 Knapsack pattern, optimizing time and space efficiency.

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Statement
Examples
Try it yourself
Solution
- Naive approach
  - Time complexity
  - Space complexity
- Optimized solution using dynamic programming
  - Top-down solution
    - Time complexity
    - Space complexity
  - Bottom-up solution
    - Time complexity
    - Space complexity

Statement

For a given array nums, determine if the array can be divided into two subarrays such that the sum of both the subarrays is equal.

For example, we have an array $[1, 2, 3]$ :

The total length of this array can be denoted as $n$ that is $3$ .
An array can only be divided into two equal subarrays if the total sum of the array is even. In this case, the total sum of array elements is $1 + 2 + 3 = 6$ , so two equal sum subarrays can be obtained here, as $[1, 2]$ and $[3]$ , both having an equal sum of $3$ .
In this case, TRUE will be returned as the array can be divided into two equal sum subarrays.
In case, the sum of array elements is odd or the array can not be divided into two equal sum subarrays, FALSE will be returned.

Constraints:

$1 \leq$ nums.length $\leq 200$
$1 \leq$ nums[i] ...

1.Getting Started

2.0/1 Knapsack

3.Unbounded Knapsack

4.Recursive Numbers

5.Longest Common Substring

6.Palindromic Subsequence

7.Conclusion

Equal Sum Subarrays

Statement