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dsa-solutions/lc-solutions/1600-1699/1646-get-maximum-in-generated-array.md

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+---
+id: get-maximum-in-generated-array
+title: Get Maximum in Generated Array
+sidebar_label: 1646-Get Maximum in Generated Array
+tags:
+  - Brute Force
+  - Dynamic Programming
+  - LeetCode
+  - Java
+  - Python
+  - C++
+description: "This is a solution to the Get Maximum in Generated Array problem on LeetCode."
+sidebar_position: 2
+---
+
+## Problem 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`.
+
+### Examples
+
+**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`
+
+---
+
+## Solution for Get Maximum in Generated Array Problem
+
+### Approach: Dynamic Programming
+
+The problem can be solved efficiently using a dynamic programming approach. We generate the array according to the given rules and keep track of the maximum value.
+
+#### Code in Different Languages
+
+<Tabs>
+<TabItem value="C++" label="C++" default>
+<SolutionAuthor name="@ImmidiSivani"/>
+
+```cpp
+class Solution {
+public:
+    int getMaximumGenerated(int n) {
+        if (n == 0) return 0;
+        if (n == 1) return 1;
+
+        vector<int> nums(n + 1);
+        nums[0] = 0;
+        nums[1] = 1;
+        int maxVal = 1;
+
+        for (int i = 2; i <= n; ++i) {
+            if (i % 2 == 0) {
+                nums[i] = nums[i / 2];
+            } else {
+                nums[i] = nums[i / 2] + nums[i / 2 + 1];
+            }
+            maxVal = max(maxVal, nums[i]);
+        }
+
+        return maxVal;
+    }
+};
+```
+
+</TabItem>
+<TabItem value="Java" label="Java">
+<SolutionAuthor name="@ImmidiSivani"/>
+
+```java
+class Solution {
+    public int getMaximumGenerated(int n) {
+        if (n == 0) return 0;
+        if (n == 1) return 1;
+
+        int[] nums = new int[n + 1];
+        nums[0] = 0;
+        nums[1] = 1;
+        int maxVal = 1;
+
+        for (int i = 2; i <= n; ++i) {
+            if (i % 2 == 0) {
+                nums[i] = nums[i / 2];
+            } else {
+                nums[i] = nums[i / 2] + nums[i / 2 + 1];
+            }
+            maxVal = Math.max(maxVal, nums[i]);
+        }
+
+        return maxVal;
+    }
+}
+```
+
+</TabItem>
+<TabItem value="Python" label="Python">
+<SolutionAuthor name="@ImmidiSivani"/>
+
+```python
+class Solution:
+    def getMaximumGenerated(self, n: int) -> int:
+        if n == 0:
+            return 0
+        if n == 1:
+            return 1
+
+        nums = [0] * (n + 1)
+        nums[0] = 0
+        nums[1] = 1
+        max_val = 1
+
+        for i in range(2, n + 1):
+            if i % 2 == 0:
+                nums[i] = nums[i // 2]
+            else:
+                nums[i] = nums[i // 2] + nums[i // 2 + 1]
+            max_val = max(max_val, nums[i])
+
+        return max_val
+```
+
+</TabItem>
+</Tabs>
+
+#### Complexity Analysis
+
+- **Time Complexity**: $O(n)$
+  - We iterate through the array once to fill in the values.
+- **Space Complexity**: $O(n)$
+  - We use additional space to store the array `nums` of length `n + 1`.
+
+---
+
+<h2>Authors:</h2>
+
+<div style={{display: 'flex', flexWrap: 'wrap', justifyContent: 'space-between', gap: '10px'}}>
+{['ImmidiSivani'].map(username => (
+ <Author key={username} username={username} />
+))}
+</div>