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package g1601_1700.s1646_get_maximum_in_generated_array;

// #Easy #Array #Dynamic_Programming #Simulation
// #2022_04_21_Time_0_ms_(100.00%)_Space_41.6_MB_(12.23%)

/**
 * 1646 - Get Maximum in Generated Array\.
 *
 * Easy
 *
 * 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`
**/
public class Solution {
    public int getMaximumGenerated(int n) {
        if (n == 0) {
            return 0;
        }
        int[] nums = new int[n + 1];
        nums[0] = 0;
        nums[1] = 1;
        int max = 1;
        for (int i = 1; i <= n / 2; i++) {
            nums[(i * 2)] = nums[i];
            max = Math.max(max, nums[i]);
            if ((i * 2) + 1 <= n) {
                nums[(i * 2) + 1] = nums[i] + nums[i + 1];
                max = Math.max(max, nums[(i * 2) + 1]);
            }
        }
        return max;
    }
}