Added article for contains duplicate problem

articles/contains-duplicate.md

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+# Contains Duplicate
+
+## Problem Statement
+Given an integer array `nums`, return `true` if any value appears **at least twice** in the array, and return `false` if every element is **distinct**.
+
+## Intuition
+We're checking for repeated values in an array. There are several ways to approach this problem, each with different trade-offs between time and space complexity. We can either compare every pair of elements, sort the array and check adjacent elements, or use a hash set for efficient duplicate detection.
+
+## Approaches & Solutions
+
+### 1. Brute Force - Compare All Pairs
+**Logic:** Use two nested loops to compare every pair of elements in the array.
+
+```cpp
+class Solution {
+public:
+    bool hasDuplicate(vector<int>& nums) {
+        for (int i = 0; i < nums.size(); i++) {
+            for (int j = i + 1; j < nums.size(); j++) {
+                if (nums[i] == nums[j]) {
+                    return true;
+                }
+            }
+        }
+        return false;
+    }
+};
+```
+
+**Time Complexity:** O(n²)  
+**Space Complexity:** O(1)
+
+This approach is simple to understand but becomes inefficient for large arrays due to the quadratic time complexity.
+
+### 2. Sorting & Checking Adjacent Elements
+**Logic:** If duplicates exist, they will appear next to each other in a sorted array.
+
+```cpp
+class Solution {
+public:
+    bool hasDuplicate(vector<int>& nums) {
+        sort(nums.begin(), nums.end());
+        for (int i = 1; i < nums.size(); i++) {
+            if (nums[i] == nums[i - 1]) {
+                return true;
+            }
+        }
+        return false;
+    }
+};
+```
+
+**Time Complexity:** O(n log n)  
+**Space Complexity:** O(1) or O(n) depending on the sorting algorithm used
+
+This approach is more efficient than brute force and works well when you don't mind modifying the original array.
+
+### 3. Using Hash Set
+**Logic:** Store seen elements in a hash set and check if an element already exists before adding it.
+
+```cpp
+class Solution {
+public:
+    bool hasDuplicate(vector<int>& nums) {
+        unordered_set<int> seen;
+        for (int num : nums) {
+            if (seen.count(num)) {
+                return true;
+            }
+            seen.insert(num);
+        }
+        return false;
+    }
+};
+```
+
+**Time Complexity:** O(n)  
+**Space Complexity:** O(n)
+
+This is the most efficient approach in terms of time complexity and is widely used in practice.
+
+### 4. Using Set Length Comparison
+**Logic:** Convert the array to a set and compare the sizes. If they differ, duplicates exist.
+
+```cpp
+class Solution {
+public:
+    bool hasDuplicate(vector<int>& nums) {
+        return unordered_set<int>(nums.begin(), nums.end()).size() < nums.size();
+    }
+};
+```
+
+**Time Complexity:** O(n)  
+**Space Complexity:** O(n)
+
+This is a clean, one-liner solution that's both efficient and easy to read.
+
+## Summary
+
+| Approach | Time Complexity | Space Complexity | Notes |
+|----------|----------------|------------------|-------|
+| Brute Force | O(n²) | O(1) | Simple but slow for large inputs |
+| Sort & Check | O(n log n) | O(1)/O(n) | Good balance, modifies original array |
+| Hash Set | O(n) | O(n) | Most efficient, recommended approach |
+| Set Length Compare | O(n) | O(n) | Clean and fast implementation |
+
+The hash set approach is generally recommended as it provides the best time complexity while maintaining readable code. The set length comparison is also excellent for its simplicity and efficiency.
+