Create 0118-pascal's-triangle.md

Author: Ayushmaanagarwal1211

dsa-solutions/lc-solutions/0100-0199/0118-pascal's-triangle.md

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+---
+id: 118-pascals-triangle
+title: Pascal's Triangle
+sidebar_label: 0118-Pascal's Triangle
+tags:
+
+Java
+Python
+C++
+description: "Generate the first n rows of Pascal's Triangle."
+---
+
+## Problem Description
+
+Given an integer numRows, return the first numRows of Pascal's triangle.
+
+In Pascal's triangle, each number is the sum of the two numbers directly above it.
+
+### Examples
+
+**Example 1:**
+
+```
+Input: numRows = 5
+Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
+```
+
+**Example 2:**
+
+```
+Input: numRows = 1
+Output: [[1]]
+```
+
+### Constraints
+
+- $1 <= numRows <= 30$
+
+---
+
+## Solution for Binary Tree Problem
+
+### Intuition And Approach
+
+To generate Pascal's triangle, we start with the first row [1]. Each subsequent row is generated by adding the number above and to the left with the number above and to the right. We append 1 at the beginning and end of each row.
+
+<Tabs>
+ <tabItem value="Recursive" label="Recursive">
+
+
+#### Code in Different Languages
+
+<Tabs>
+  <TabItem value="Java" label="Java" default>
+  <SolutionAuthor name="@Vipullakum007"/>
+   ```java
+   class Solution {
+    public List<List<Integer>> generate(int numRows) {
+        List<List<Integer>> triangle = new ArrayList<>();
+
+        if (numRows == 0) {
+            return triangle;
+        }
+
+        // First row
+        triangle.add(new ArrayList<>());
+        triangle.get(0).add(1);
+
+        for (int rowNum = 1; rowNum < numRows; rowNum++) {
+            List<Integer> row = new ArrayList<>();
+            List<Integer> prevRow = triangle.get(rowNum - 1);
+
+            // First element is always 1
+            row.add(1);
+
+            // Each triangle element (except the first and last of each row)
+            for (int j = 1; j < rowNum; j++) {
+                row.add(prevRow.get(j - 1) + prevRow.get(j));
+            }
+
+            // Last element is always 1
+            row.add(1);
+
+            triangle.add(row);
+        }
+
+        return triangle;
+    }
+}
+    ```
+
+  </TabItem>
+  <TabItem value="Python" label="Python">
+  <SolutionAuthor name="@Vipullakum007"/>
+   ```python
+    class Solution:
+    def generate(self, numRows: int) -> List[List[int]]:
+        triangle = []
+
+        for row_num in range(numRows):
+            row = [1] * (row_num + 1)
+
+            for j in range(1, row_num):
+                row[j] = triangle[row_num - 1][j - 1] + triangle[row_num - 1][j]
+
+            triangle.append(row)
+
+        return triangle
+    ```
+
+  </TabItem>
+  <TabItem value="C++" label="C++">
+  <SolutionAuthor name="@Vipullakum007"/>
+   ```cpp
+    class Solution {
+public:
+    vector<vector<int>> generate(int numRows) {
+        vector<vector<int>> triangle;
+
+        for (int row_num = 0; row_num < numRows; row_num++) {
+            vector<int> row(row_num + 1, 1);
+
+            for (int j = 1; j < row_num; j++) {
+                row[j] = triangle[row_num - 1][j - 1] + triangle[row_num - 1][j];
+            }
+
+            triangle.push_back(row);
+        }
+
+        return triangle;
+    }
+};
+    ```
+
+  </TabItem>
+</Tabs>
+
+#### Complexity Analysis
+
+- Time Complexity:  $O(n^2)$ where n is the number of rows. This is because we are generating each element in the triangle, and there are $\frac{n(n+1)}{2}$ elements in total.
+- Space Complexity: $O(n^2)$, the space required to store the triangle.
+
+</tabItem>
+</Tabs>
+
+
+---