Add Search in Rotated Sorted Array implementation in C++

Author: Adi-3108

CPP/algorithms/searching/search_rotated_sorted_array.cpp

@@ -0,0 +1,128 @@
+/*
+ * Algorithm: Search in Rotated Sorted Array
+ * Language: C++
+ * Description: 
+ * Searches for an integer 'target' in a sorted array 'nums' that has been 
+ * left-rotated at an unknown pivot point 'k'. The algorithm must achieve 
+ * O(log n) runtime complexity, which requires a modified Binary Search.
+ * * Problem Constraints:
+ * - nums is sorted ascendingly with distinct values.
+ * - The array structure is [nums[k], ..., nums[n-1], nums[0], ..., nums[k-1]].
+ * - Example: [4,5,6,7,0,1,2] (rotated at k=4 from [0,1,2,4,5,6,7]).
+ * * Time Complexity: O(log n) // Achieved via single-pass Binary Search
+ * Space Complexity: O(1)   // In-place search using only a few pointers
+ * Author: Adi-3108
+ 
+ */
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+
+/**
+ * @brief Searches for a target value in a possibly rotated sorted array using O(log n) time.
+ * * The core idea is that in a rotated sorted array, at least one half (left or right) 
+ * defined by the 'mid' point MUST be sorted. We identify the sorted half and check 
+ * if the 'target' falls within that sorted range. If it does, we move our search 
+ * boundary (low/high) into that sorted half. Otherwise, the target must be in the 
+ * unsorted/rotated half, and we move the search there.
+ * * @param nums The rotated sorted array of unique integers.
+ * @param target The integer value to search for.
+ * @return int The index of the target if found, or -1 otherwise.
+ */
+int searchRotatedSortedArray(const std::vector<int>& nums, int target) {
+    // Input validation (Constraint: nums.length >= 1, but safe to check)
+    if (nums.empty()) {
+        return -1;
+    }
+
+    int low = 0;
+    int high = nums.size() - 1;
+
+    while (low <= high) {
+        int mid = low + (high - low) / 2;
+
+        if (nums[mid] == target) {
+            return mid;
+        }
+
+        // --- Core Binary Search Logic ---
+
+        // 1. Check if the left half is sorted (comparison between the extremes)
+        if (nums[low] <= nums[mid]) {
+            // Left half [low...mid] is sorted.
+            
+            // Check if the target is within the sorted left half
+            if (target >= nums[low] && target < nums[mid]) {
+                // Target is in the sorted left half; search there.
+                high = mid - 1;
+            } else {
+                // Target must be in the rotated right half; search there.
+                low = mid + 1;
+            }
+        } 
+        
+        // 2. Otherwise, the right half must be sorted (from nums[mid] to nums[high])
+        else {
+            // Right half [mid...high] is sorted.
+
+            // Check if the target is within the sorted right half
+            if (target > nums[mid] && target <= nums[high]) {
+                // Target is in the sorted right half; search there.
+                low = mid + 1;
+            } else {
+                // Target must be in the rotated left half; search there.
+                high = mid - 1;
+            }
+        }
+    }
+
+    // Target not found after exhausting the array.
+    return -1;
+}
+
+// Test Function
+void testSearchRotatedSortedArray() {
+    std::cout << "--- Testing Search in Rotated Sorted Array ---\n";
+
+    // Example 1: Input: [4,5,6,7,0,1,2], target = 0, Output: 4
+    std::vector<int> nums1 = {4, 5, 6, 7, 0, 1, 2};
+    int target1 = 0;
+    int expected1 = 4;
+    int result1 = searchRotatedSortedArray(nums1, target1);
+    std::cout << "Test 1: Input: [4,5,6,7,0,1,2], Target: 0\n";
+    std::cout << "Expected: " << expected1 << ", Actual: " << result1 << " | " 
+              << (result1 == expected1 ? "PASS" : "FAIL") << std::endl;
+
+    // Example 2: Input: [4,5,6,7,0,1,2], target = 3, Output: -1
+    std::vector<int> nums2 = {4, 5, 6, 7, 0, 1, 2};
+    int target2 = 3;
+    int expected2 = -1;
+    int result2 = searchRotatedSortedArray(nums2, target2);
+    std::cout << "Test 2: Input: [4,5,6,7,0,1,2], Target: 3\n";
+    std::cout << "Expected: " << expected2 << ", Actual: " << result2 << " | "
+              << (result2 == expected2 ? "PASS" : "FAIL") << std::endl;
+
+    // Example 3: Input: [1], target = 0, Output: -1
+    std::vector<int> nums3 = {1};
+    int target3 = 0;
+    int expected3 = -1;
+    int result3 = searchRotatedSortedArray(nums3, target3);
+    std::cout << "Test 3: Input: [1], Target: 0\n";
+    std::cout << "Expected: " << expected3 << ", Actual: " << result3 << " | "
+              << (result3 == expected3 ? "PASS" : "FAIL") << std::endl;
+
+    // Edge Case: No rotation (Target found)
+    std::vector<int> nums4 = {1, 2, 3, 4, 5};
+    int target4 = 4;
+    int expected4 = 3;
+    int result4 = searchRotatedSortedArray(nums4, target4);
+    std::cout << "Test 4: Input: [1,2,3,4,5], Target: 4\n";
+    std::cout << "Expected: " << expected4 << ", Actual: " << result4 << " | "
+              << (result4 == expected4 ? "PASS" : "FAIL") << std::endl;
+}
+
+int main() {
+    testSearchRotatedSortedArray();
+    return 0;
+}