Two Piles of Equal Weight

Medium

You have a set of weights whose masses are listed in the array weights. Can all of them be split into two piles with the same total mass? Every weight must go into exactly one pile. Return True if this is possible and False otherwise.

Example 1

weights=[3, 8, 2, 7] → True

The total weight is 20: the piles {3, 7} and {8, 2} weigh 10 each.

Example 2

weights=[6, 1, 1, 2] → False

The total is 10, yet any pile holding the 6 is already over 5, and without it the most you can gather is 4.

Example 3

weights=[5, 4] → False

Constraints

1 ≤ len(weights) ≤ 200
1 ≤ weights[i] ≤ 100

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Topics

Array Dynamic Programming

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Input

weights=[3, 8, 2, 7]

Expected

True

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