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+# 1394. Find Lucky Integer in an Array
+
+**Difficulty:** Easy  
+**Category:** Arrays, Hashing  
+**Leetcode Link:** https://leetcode.com/problems/find-lucky-integer-in-an-array/ 
+
+---
+
+## 📝 Introduction
+
+You are given an integer array `arr`.  
+A *lucky integer* is defined as an integer whose **value is equal to its frequency** in the array.  
+The task is to return the **largest** lucky integer, or `-1` if no such integer exists. 
+
+Key points and constraints:  
+- `1 <= arr.length <= 500`  
+- `1 <= arr[i] <= 500`  
+- Need to compare each value with how many times it appears and pick the maximum such value. 
+
+---
+
+## 💡 Approach & Key Insights
+
+Main idea:  
+1. Count how many times each number appears in the array (its frequency).  
+2. A number is *lucky* if `value == frequency`.  
+3. Among all lucky numbers, return the **largest** one.
+
+Insights:  
+- A brute force solution can compute frequency for each element by scanning the array repeatedly (nested loops).  
+- An optimal solution uses a frequency structure (hash map or counting array) to count in linear time, then scans the frequency structure to find the largest value satisfying `value == frequency`. 
+---
+
+## 🛠️ Breakdown of Approaches
+
+### 1️⃣ Brute Force / Naive Approach
+
+- **Explanation:**  
+  - For each element `arr[i]`, iterate over the entire array and count how many times this value appears.  
+  - After counting, if `count == arr[i]`, then `arr[i]` is a lucky integer candidate.  
+  - Track the **maximum** such candidate across all elements. 
+- **Time Complexity:**  
+  - Outer loop runs `n` times, inner loop runs `n` times for each outer iteration.  
+  - Overall \(O(n^2)\) time. 
+
+- **Space Complexity:**  
+  - Uses only a few integer variables (`temp`, `count`, `lucky`).  
+  - Overall \(O(1)\) extra space. 
+
+- **Example/Dry Run:**
+
+Example input: `arr = [2, 2, 3, 4]`  
+
+- Step 1: `i = 0`, `temp = 2`  
+  - Count frequency of `2` by scanning entire array → `count = 2`.  
+  - Check `count == temp` → `2 == 2` → lucky candidate = 2, `lucky = 2`.  
+
+- Step 2: `i = 1`, `temp = 2` again  
+  - Frequency still 2, `count == temp` → `lucky` remains 2.  
+
+- Step 3: `i = 2`, `temp = 3`  
+  - Count frequency of `3` → `count = 1`, `count != temp`, ignore.  
+
+- Step 4: `i = 3`, `temp = 4`  
+  - Count frequency of `4` → `count = 1`, `count != temp`, ignore.  
+
+Output: `2`.
+
+---
+
+### 2️⃣ Optimized Approach
+
+- **Explanation:**  
+  - Instead of recounting each value with nested loops, use a **frequency map/array**.  
+  - First pass: build `freq[x] = frequency of x` for all elements in `arr`.  
+  - Second pass: iterate over possible values and check where `value == freq[value]`.  
+  - Track the **maximum** value that satisfies this condition. [web:16][web:4][web:40]
+
+  Because constraints are small (`arr[i] <= 500`), a simple integer array of size `501` is enough for frequencies. 
+
+- **Time Complexity:**  
+  - Count frequencies in \(O(n)\).  
+  - Scan possible values (at most 500) in \(O(K)\) where `K = 500`.  
+  - Total \(O(n + K)\), effectively \(O(n)\) for given constraints. 
+
+- **Space Complexity:**  
+  - Frequency array of fixed size `501`.  
+  - Overall \(O(K)\), which is \(O(1)\) relative to `n` (because K is bounded by constraints). 
+
+- **Example/Dry Run:**
+
+Example input: `arr = [1, 2, 2, 3, 3, 3]` 
+
+- Step 1: Count frequencies:  
+  - `freq[1] = 1`, `freq[2] = 2`, `freq[3] = 3`, all others 0.  
+- Step 2: Check values from high to low:  
+  - `i = 6, 5, 4` → `freq[i]` not equal to `i`.  
+  - `i = 3` → `freq[3] = 3` → lucky, candidate = 3.  
+  - `i = 2` → `freq[2] = 2` → also lucky, but smaller than 3.  
+  - `i = 1` → `freq[1] = 1` → also lucky, but smaller than 3.  
+- Step 3: Return the largest lucky integer seen → `3`.
+
+Output: `3`.
+
+---
+
+### 3️⃣ Best / Final Optimized Approach (if applicable)
+
+For this problem, the **counting array or hashmap frequency solution** is already optimal in both time and space under the given constraints. 
+
+- **Explanation:**  
+  - Use a hash map or fixed-size array to count all frequencies in a single pass.  
+  - Then either:
+    - Scan from largest possible value to smallest (guarantees the first match is the answer), or
+    - Collect all lucky integers and take their maximum.  
+  - This approach is simple, fast, and directly encodes the problem definition `value == frequency`. 
+
+- **Time Complexity:**  
+  - \(O(n)\) to build frequencies + \(O(K)\) to scan, where `K` is bounded (≤ 500).  
+  - Overall \(O(n)\) for practical purposes.
+
+- **Space Complexity:**  
+  - \(O(K)\) for the frequency structure, effectively constant. 
+
+- **Example/Dry Run:**
+
+Example input: `arr = [2, 2, 2, 3, 3]` 
+
+- Step 1: Build frequency:  
+  - `freq[2] = 3`, `freq[3] = 2`.  
+- Step 2: Scan from high to low:  
+  - `i = 5, 4` → `freq[i] = 0`, not equal to `i`.  
+  - `i = 3` → `freq[3] = 2`, `2 != 3` → not lucky.  
+  - `i = 2` → `freq[2] = 3`, `3 != 2` → not lucky.  
+  - `i = 1` → `freq[1] = 0`, not lucky.  
+- No lucky integer found → return `-1`.
+
+Output: `-1`.
+
+---
+
+## 📊 Complexity Analysis
+
+| Approach      | Time Complexity   | Space Complexity |
+| ------------- | -----------------| ---------------- |
+| Brute Force   | O(n²)            | O(1)             |
+| Optimized     | O(n + K) ≈ O(n)  | O(K) (K ≤ 500)   |
+| Best Approach | O(n + K) ≈ O(n)  | O(K) (K ≤ 500)   | 
+
+---
+
+## 📉 Optimization Ideas
+
+- Because `arr[i]` is at most 500, using a **fixed-size array** is more cache-friendly and simpler than a generic hash map. 
+- Scanning from the **maximum possible value downwards** allows early exit as soon as the largest lucky integer is found.   
+- In languages with built-in frequency utilities (like `Counter` in Python), code can be both concise and efficient while still following the same logic. 
+
+---
+
+## 📌 Example Walkthroughs & Dry Runs
+```
+Example 1:
+Input:​
+
+Frequencies:
+2 -> 2 times
+3 -> 1 time
+4 -> 1 time
+
+Lucky check:
+2: value 2, frequency 2 -> lucky
+3: value 3, frequency 1 -> not lucky
+4: value 4, frequency 1 -> not lucky
+
+Largest lucky integer = 2
+Output: 2
+
+Example 2:
+Input:​
+
+Frequencies:
+1 -> 1 time
+2 -> 2 times
+3 -> 3 times
+
+Lucky integers: 1, 2, 3 (all satisfy value == frequency)
+Largest lucky integer = 3
+Output: 3
+```
+
+---
+
+## 🔗 Additional Resources
+
+- [LeetCode Problem 1394 – Find Lucky Integer in an Array](https://leetcode.com/problems/find-lucky-integer-in-an-array/)  
+- [In-depth explanation with frequency map and code examples](https://algo.monster/liteproblems/1394)  
+- [Alternative editorial and multi-language solutions](https://progiez.com/1394-find-lucky-integer-in-an-array-leetcode-solution)
+
+---
+
+Author: *Samuel Joseph S*  
+Date: *01/12/2025*
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diff --git a/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.cpp b/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.cpp
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+++ b/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.cpp	
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+class Solution {
+public:
+    int findLucky(vector<int>& arr) {
+        int temp = 0, lucky = -1, count = 0;
+
+        for (int i = 0; i < arr.size(); i++) {
+            count = 0;
+            temp = arr[i];
+
+            for (int j = 0; j < arr.size(); j++) {
+                if (arr[j] == temp)
+                    count++;
+            }
+
+            if (count == arr.size())
+                lucky = temp;
+        }
+
+        return lucky;
+    }
+};
diff --git a/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.java b/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.java
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+class Solution {
+    public int findLucky(int[] arr)
+    {
+      int temp=0,lucky=-1,count=0;
+      for(int i=0;i<arr.length;i++)
+      {
+       count=0;
+       temp=arr[i];
+       for(int j=0;j<arr.length;j++)
+       {
+        if(arr[j]==temp)
+        count++;
+       }
+       if(count==temp&&temp>lucky)
+       lucky=temp;
+      }  
+      return lucky;
+    }
+}
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diff --git a/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.py b/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.py
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+++ b/Arrays & Strings/#1394 - Lucky integer in an Array - Easy/solution.py	
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+class Solution:
+    def findLucky(self, arr):
+        temp = 0
+        lucky = -1
+        count = 0
+
+        for i in range(len(arr)):
+            count = 0
+            temp = arr[i]
+
+            for j in range(len(arr)):
+                if arr[j] == temp:
+                    count += 1
+
+            if count == len(arr):
+                lucky = temp
+
+        return lucky
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