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

Solution 1

Python Code
1
2
3
4
5
6
7
8
9

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)

Java Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13

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();
    }
}

C++ Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15

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);
    }
};

Go Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15

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)
}

TypeScript Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

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);
}