Add a Solution for Search in Rotated Sorted Arrayy (LeetCode Problem 33)

dsa-solutions/lc-solutions/0000-0099/0033-search-in-rotated-sorted-array.md

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+---
+id: search-in-rotated-sorted-array
+title: Search in Rotated Sorted Array (LeetCode)
+sidebar_label: 0033-SearchInRotatedSortedArray
+description: Search for a target element in a rotated sorted array with distinct values using an algorithm with O(log n) runtime complexity.
+---
+
+## Problem Description
+
+| Problem Statement | Solution Link | LeetCode Profile |
+| :---------------- | :------------ | :--------------- |
+| [Merge Two Sorted Lists](https://leetcode.com/problems/search-in-rotated-sorted-array/) | [Merge Two Sorted Lists Solution on LeetCode](https://leetcode.com/problems/search-in-rotated-sorted-array/solutions/) |  [VijayShankerSharma](https://leetcode.com/u/darkknight648/) |
+
+## Problem Description
+
+There is an integer array nums sorted in ascending order (with distinct values).
+
+Prior to being passed to your function, nums is possibly rotated at an unknown pivot index k (0 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed).
+
+Given the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.
+
+You must write an algorithm with $O(log n)$ runtime complexity.
+
+### Examples
+
+#### Example 1
+
+- **Input:** nums = [4,5,6,7,0,1,2], target = 0
+- **Output:** 4
+- **Explanation:** 0 is located at index 4 in the rotated sorted array [4,5,6,7,0,1,2].
+
+#### Example 2
+
+- **Input:** nums = [4,5,6,7,0,1,2], target = 3
+- **Output:** -1
+- **Explanation:** 3 is not in nums, so return -1.
+
+#### Example 3
+
+- **Input:** nums = [1], target = 0
+- **Output:** -1
+- **Explanation:** 0 is not in nums, so return -1.
+
+### Constraints
+
+- $v1 <= nums.length <= 5000$
+- $-10^4 <= nums[i] <= 10^4$
+- All values of $nums$ are unique.
+- nums is an ascending array that is possibly rotated.
+- $-10^4 <= target <= 10^4$
+
+### Approach
+
+To search for a target element in a rotated sorted array with distinct values with $O(log n)$ runtime complexity, we can use the binary search algorithm.
+
+1. **Find the Pivot Point:**
+   - Perform binary search to find the pivot element, which is the smallest element in the array. This element divides the array into two sorted subarrays.
+
+2. **Perform Binary Search:**
+   - Based on the pivot element, determine which half of the array the target might be in.
+   - Perform binary search in the appropriate half to find the target element.
+
+### Solution Code
+
+#### Python
+
+```py
+class Solution:
+    def search(self, nums: List[int], target: int) -> int:
+        left, right = 0, len(nums) - 1
+        while left <= right:
+            mid = (left + right) // 2
+            if nums[mid] == target:
+                return mid
+            elif nums[left] <= nums[mid]:
+                if nums[left] <= target < nums[mid]:
+                    right = mid - 1
+                else:
+                    left = mid + 1
+            else:
+                if nums[mid] < target <= nums[right]:
+                    left = mid + 1
+                else:
+                    right = mid - 1
+        return -1
+```
+
+#### Java
+
+```java
+class Solution {
+    public int search(int[] nums, int target) {
+        int left = 0, right = nums.length - 1;
+        while (left <= right) {
+            int mid = (left + right) / 2;
+            if (nums[mid] == target)
+                return mid;
+            else if (nums[left] <= nums[mid]) {
+                if (nums[left] <= target && target < nums[mid])
+                    right = mid - 1;
+                else
+                    left = mid + 1;
+            } else {
+                if (nums[mid] < target && target <= nums[right])
+                    left = mid + 1;
+                else
+                    right = mid - 1;
+            }
+        }
+        return -1;
+    }
+}
+```
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    int search(vector<int>& nums, int target) {
+        int left = 0, right = nums.size() - 1;
+        while (left <= right) {
+            int mid = (left + right) / 2;
+            if (nums[mid] == target)
+                return mid;
+            else if (nums[left] <= nums[mid]) {
+                if (nums[left] <= target && target < nums[mid])
+                    right = mid - 1;
+                else
+                    left = mid + 1;
+            } else {
+                if (nums[mid] < target && target <= nums[right])
+                    left = mid + 1;
+                else
+                    right = mid - 1;
+            }
+        }
+        return -1;
+    }
+};
+```
+
+### Conclusion
+
+The above solution effectively searches for a target element in a rotated sorted array with distinct values using the binary search algorithm with $O(log n)$ runtime complexity. It handles all edge cases and constraints specified in the problem statement.