15. Get Maximum in Generated Array.cpp

/*
Get Maximum in Generated Array
===============================

You are given an integer n. An array nums of length n + 1 is generated in the following way:

nums[0] = 0
nums[1] = 1
nums[2 * i] = nums[i] when 2 <= 2 * i <= n
nums[2 * i + 1] = nums[i] + nums[i + 1] when 2 <= 2 * i + 1 <= n
Return the maximum integer in the array nums​​​.

Example 1:
Input: n = 7
Output: 3
Explanation: According to the given rules:
  nums[0] = 0
  nums[1] = 1
  nums[(1 * 2) = 2] = nums[1] = 1
  nums[(1 * 2) + 1 = 3] = nums[1] + nums[2] = 1 + 1 = 2
  nums[(2 * 2) = 4] = nums[2] = 1
  nums[(2 * 2) + 1 = 5] = nums[2] + nums[3] = 1 + 2 = 3
  nums[(3 * 2) = 6] = nums[3] = 2
  nums[(3 * 2) + 1 = 7] = nums[3] + nums[4] = 2 + 1 = 3
Hence, nums = [0,1,1,2,1,3,2,3], and the maximum is 3.

Example 2:
Input: n = 2
Output: 1
Explanation: According to the given rules, the maximum between nums[0], nums[1], and nums[2] is 1.

Example 3:
Input: n = 3
Output: 2
Explanation: According to the given rules, the maximum between nums[0], nums[1], nums[2], and nums[3] is 2.

Constraints:
0 <= n <= 100

Hint #1  
Try generating the array.

Hint #2  
Make sure not to fall in the base case of 0.
*/

class Solution
{
public:
  int getMaximumGenerated(int n)
  {
    n++;
    if (n <= 2)
      return n - 1;
    vector<int> arr(n, -1);
    arr[0] = 0;
    arr[1] = 1;
    int ans = INT_MIN;

    for (int i = 2; i < n; ++i)
    {
      if (i % 2 == 0)
      {
        arr[i] = arr[i / 2];
      }
      else
        arr[i] = arr[(i - 1) / 2] + arr[(i + 1) / 2];
      ans = max(ans, arr[i]);
    }

    return ans;
  }
};