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Day 15 - Get Maximum in Generated Array

ruarfff profile image Ruairí O'Brien ・2 min read

The Problem

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.
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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.
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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.
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Constraints:

  • 0 <= n <= 100

My Tests

import pytest
from .Day14_GetMaximumInGeneratedArray import Solution

s = Solution()


@pytest.mark.parametrize(
    "n,expected",
    [
        (7, 3),
        (2, 1),
        (3, 2),
        (0, 0),
    ],
)
def test_get_maximum_generated(n, expected):
    assert s.getMaximumGenerated(n) == expected
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My Solution

class Solution:
    def getMaximumGenerated(self, n: int) -> int:
        l = n + 1
        if n == 0:
            return 0
        nums = [0] * l
        nums[1] = 1
        current_max = 1

        for i in range(1, l):
            x = 2 * i
            if x > 1 and x <= n:
                nums[x] = nums[i]
            if x + 1 > 1 and x + 1 <= n:
                nums[x + 1] = nums[i] + nums[i + 1]
            current_max = max(current_max, nums[i])

        return current_max
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Analysis

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My Commentary

This one was probably the easiest yet. I just followed the instructions in the description. I am sure there's a lot of optimisation I could have done but leaving this one here for today.

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