Solution of Print Pattern is added

dsa-solutions/gfg-solutions/Easy problems/Print-Pattern.md

@@ -0,0 +1,119 @@
+---
+id: print-pattern
+title: Print Pattern
+sidebar_label: Print-Pattern
+tags:
+  - Recursion
+  - Algorithms
+description: "This tutorial covers the solution to the Print Pattern problem from the GeeksforGeeks."
+---
+## Problem Description
+Print a sequence of numbers starting with nn, without using a loop. Replace `nn` with `n−5n - 5n−5` until `n≤0n` `\leq 0n≤0`. Then, replace n with `n+5n + 5n+5` until `nn` regains its initial value. Complete the function pattern(n) which takes n as input and returns a list containing the pattern.
+
+## Examples
+
+**Example 1:**
+
+```
+Input: n = 16
+Output: 16 11 6 1 -4 1 6 11 16
+Explanation: The value decreases until it is greater than 0. After that it increases and stops when it becomes 16 again.
+```
+
+**Example 2:**
+
+```
+Input: n = 10
+Output: 10 5 0 5 10
+Explanation: It follows the same logic as per the above example.
+```
+
+
+
+Expected Time Complexity: $O(n)$
+
+Expected Auxiliary Space: $O(n)$ for dynamic programming 
+
+## Constraints
+
+* `-10^5 ≤ n ≤ 10^5`
+
+## Problem Explanation
+Print a sequence of numbers starting with nn, without using a loop. Replace `nn` with `n−5n - 5n−5` until `n≤0n` `\leq 0n≤0`. Then, replace n with `n+5n + 5n+5` until nn regains its initial value. Complete the function pattern(n) which takes n as input and returns a list containing the pattern.
+
+## Code Implementation
+
+<Tabs>
+  <TabItem value="Python" label="Python" default>
+  <SolutionAuthor name="@Ishitamukherjee2004"/>
+
+  ```py
+ def pattern(n, initial=None, result=None):
+    if result is None:
+        result = []
+    if initial is None:
+        initial = n
+    if n > 0:
+        result.append(n)
+        return pattern(n - 5, initial, result)
+    elif n < initial:
+        result.append(n)
+        return pattern(n + 5, initial, result)
+    return result
+
+  ```
+
+  </TabItem>
+  <TabItem value="C++" label="C++">
+  <SolutionAuthor name="@Ishitamukherjee2004"/>
+
+  ```cpp
+ vector<int> pattern(int n) {
+    vector<int> result;
+    while (n > 0) {
+        result.push_back(n);
+        n -= 5;
+    }
+    while (n < result[0]) {
+        result.push_back(n);
+        n += 5;
+    }
+    return result;
+}
+
+
+  ```
+
+  </TabItem>
+
+
+  <TabItem value="Java" label="Java" default>
+  <SolutionAuthor name="@Ishitamukherjee2004"/>
+
+  ```java
+public List<Integer> pattern(int n) {
+    List<Integer> result = new ArrayList<>();
+    while (n > 0) {
+        result.add(n);
+        n -= 5;
+    }
+    while (n < result.get(0)) {
+        result.add(n);
+        n += 5;
+    }
+    return result;
+}
+
+  ```
+
+  </TabItem>
+</Tabs>
+
+
+## Time Complexity
+
+* The iterative approach has a time complexity of $O(n)$ because we are iterating through the sequence of numbers twice: once from n to 0, and once from 0 to n.
+
+## Space Complexity
+
+* The space complexity is O(n) because we are storing the sequence of numbers in the result list.