Create 0202-Happy-Numbers.md

dsa-solutions/lc-solutions/0200-0299/0202-Happy-Numbers.md

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+---
+id: Happy-Number
+title: Happy Number
+sidebar_label: Happy Number
+tags: 
+    - Math
+    - Hash Table
+    - Two Pointers
+---
+
+## Problem Description
+
+| Problem Statement                                       | Solution Link                                                              | LeetCode Profile                                        |
+| :------------------------------------------------------ | :------------------------------------------------------------------------- | :------------------------------------------------------ |
+| [Happy-Number](https://leetcode.com/problems/Happy-Number/description/) | [Happy-Number Solution on LeetCode](https://leetcode.com/problems/Happy-Number/solutions/) | [Nikita Saini](https://leetcode.com/u/Saini_Nikita/) |
+
+## Problem Description
+
+A happy number is a number defined by the following process:
+Starting with any positive integer, replace the number by the sum of the squares of its digits.
+Repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.
+Those numbers for which this process ends in 1 are happy.
+
+Given a positive integer `n`, determine if it is a happy number.
+
+### Example 1:
+
+Input: `n = 19`
+Output: `true`
+Explanation:
+1^2 + 9^2 = 82
+8^2 + 2^2 = 68
+6^2 + 8^2 = 100
+1^2 + 0^2 + 0^2 = 1
+
+### Example 2:
+
+Input: `n = 2`
+Output: `false`
+Explanation:
+2^2 = 4
+4^2 = 16
+1^2 + 6^2 = 37
+3^2 + 7^2 = 58
+5^2 + 8^2 = 89
+8^2 + 9^2 = 145
+1^2 + 4^2 + 5^2 = 42
+4^2 + 2^2 = 20
+2^2 + 0^2 = 4 (cycle repeats endlessly)
+
+## Constraints
+
+- `1 <= n <= 2^31 - 1`
+
+## Approach
+
+To determine if a number `n` is a happy number:
+1. Use a set to keep track of numbers seen during the process to detect cycles.
+2. Repeat the process of replacing `n` by the sum of the squares of its digits until `n` becomes 1 or a cycle is detected (a number repeats).
+3. If `n` becomes 1, return true; otherwise, return false.
+
+## Solution in Python
+
+```python
+def isHappy(n: int) -> bool:
+    seen = set()
+    while n != 1 and n not in seen:
+        seen.add(n)
+        n = sum(int(digit)**2 for digit in str(n))
+    return n == 1
+```
+
+## Solution in Java
+```java
+import java.util.HashSet;
+import java.util.Set;
+
+class Solution {
+    public boolean isHappy(int n) {
+        Set<Integer> seen = new HashSet<>();
+        while (n != 1 && !seen.contains(n)) {
+            seen.add(n);
+            int sum = 0;
+            while (n > 0) {
+                int digit = n % 10;
+                sum += digit * digit;
+                n /= 10;
+            }
+            n = sum;
+        }
+        return n == 1;
+    }
+}
+```
+
+## Solution in C++
+```cpp
+class Solution {
+public:
+    bool isHappy(int n) {
+        unordered_set<int> seen;
+        while (n != 1 && seen.find(n) == seen.end()) {
+            seen.insert(n);
+            int sum = 0;
+            while (n > 0) {
+                int digit = n % 10;
+                sum += digit * digit;
+                n /= 10;
+            }
+            n = sum;
+        }
+        return n == 1;
+    }
+};
+```
+
+## Solution in C
+```c
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+bool isHappy(int n) {
+    int seen[1000] = {0};
+    while (n != 1 && !seen[n]) {
+        seen[n] = 1;
+        int sum = 0;
+        while (n > 0) {
+            int digit = n % 10;
+            sum += digit * digit;
+            n /= 10;
+        }
+        n = sum;
+    }
+    return n == 1;
+}
+```
+
+## Solution in JavaScript
+```js
+var isHappy = function(n) {
+    let seen = new Set();
+    while (n !== 1 && !seen.has(n)) {
+        seen.add(n);
+        n = String(n).split('').reduce((sum, digit) => sum + digit * digit, 0);
+    }
+    return n === 1;
+};
+```
+
+## Step-By_Step Algorithm
+1. Initialize an empty set `seen` to keep track of numbers encountered.
+2. While `n` is not 1 and `n` is not in `seen`:
+    - Add `n` to `seen`.
+    - Compute the sum of the squares of its digits for `n`.
+    - Update `n` to this computed sum.
+3. Check if `n` equals 1. If yes, return true (it is a happy number). If no, return false (it is not a happy number).
+
+## Conclusion
+The provided solutions use a similar approach to solve the happy number problem across different programming languages. They efficiently detect cycles and determine if a number eventually leads to 1 or loops endlessly. The use of a set ensures that the algorithm runs in linear time relative to the number of digits in `n`, making it suitable for the given constraints.
+