462. Maximum Sum of Non-Adjacent Elements

Given an array of non-negative integers nums, find the maximum sum of a subsequence such that no two numbers in the subsequence are adjacent in the original array. This problem can be solved using Dynamic Programming, often exhibiting characteristics that suggest a greedy approach in state transitions.

Example:
Input: nums = [2, 7, 9, 3, 1]
Output: 12

Explanation: The maximum sum is achieved by selecting 2, 9, and 1, totaling 12.

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