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Grokking Dynamic Programming Interview

Equal Sum Subarrays

Explore how to partition an array into two subarrays with equal sums by applying dynamic programming techniques, specifically the 0/1 Knapsack pattern. Learn to optimize naive recursive solutions using memoization and tabulation, improving efficiency and managing time and space complexity. This lesson guides you through implementing these approaches step-by-step to solve equal sum subarray problems.

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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][1, 2, 3]:

  • The total length of this array can be denoted as nn that is 33.

  • 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=61 + 2 + 3 = 6, so two equal sum subarrays can be obtained here, as [1,2][1, 2] and [3][3], both having an equal sum of 33.

  • 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≤1 \leqnums.length ≤200\leq 200

  • 1≤1 \leq nums[i] ...