# 1646. Get Maximum in Generated Array

## Description

You are given an integer n. A 0-indexed integer 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 max(0,1,1,2,1,3,2,3) = 3.


Example 2:

Input: n = 2
Output: 1
Explanation: According to the given rules, nums = [0,1,1]. The maximum is max(0,1,1) = 1.


Example 3:

Input: n = 3
Output: 2
Explanation: According to the given rules, nums = [0,1,1,2]. The maximum is max(0,1,1,2) = 2.


Constraints:

• 0 <= n <= 100

## Solutions

• class Solution {
public int getMaximumGenerated(int n) {
if (n < 2) {
return n;
}
int[] nums = new int[n + 1];
nums[1] = 1;
for (int i = 2; i <= n; ++i) {
nums[i] = i % 2 == 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
}
return Arrays.stream(nums).max().getAsInt();
}
}

• class Solution {
public:
int getMaximumGenerated(int n) {
if (n < 2) {
return n;
}
int nums[n + 1];
nums[0] = 0;
nums[1] = 1;
for (int i = 2; i <= n; ++i) {
nums[i] = i % 2 == 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
}
return *max_element(nums, nums + n + 1);
}
};

• class Solution:
def getMaximumGenerated(self, n: int) -> int:
if n < 2:
return n
nums = [0] * (n + 1)
nums[1] = 1
for i in range(2, n + 1):
nums[i] = nums[i >> 1] if i % 2 == 0 else nums[i >> 1] + nums[(i >> 1) + 1]
return max(nums)


• func getMaximumGenerated(n int) int {
if n < 2 {
return n
}
nums := make([]int, n+1)
nums[1] = 1
for i := 2; i <= n; i++ {
if i%2 == 0 {
nums[i] = nums[i/2]
} else {
nums[i] = nums[i/2] + nums[i/2+1]
}
}
return slices.Max(nums)
}

• function getMaximumGenerated(n: number): number {
if (n === 0) {
return 0;
}
const nums: number[] = new Array(n + 1).fill(0);
nums[1] = 1;
for (let i = 2; i < n + 1; ++i) {
nums[i] = i % 2 === 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
}
return Math.max(...nums);
}