update files

Author: Ali7040

pascalsTriangle/PascalsTriangle.md

@@ -0,0 +1,63 @@
+
+# Pascal's Triangle - LeetCode Solution 🚀
+
+## Problem Statement
+Given an integer `numRows`, return the first `numRows` of Pascal's triangle.
+
+## Approach
+
+To generate Pascal's Triangle, follow these steps:
+
+1. **Initialization**:
+   - Create a 2D vector `result` to store the rows of Pascal's Triangle.
+
+2. **Iterate through the rows**:
+   - Loop from `0` to `numRows - 1` to generate each row.
+   - For each row `i`, initialize a vector `row` with `i + 1` elements, all set to `1` because the first and last elements of each row are always `1`.
+
+3. **Fill in the values**:
+   - For each element `j` in the row, except for the first and last elements, set `row[j]` to the sum of the two elements directly above it from the previous row:
+     \[
+     row[j] = result[i - 1][j - 1] + result[i - 1][j]
+     \]
+
+4. **Add the row to the result**:
+   - Append the fully populated row to the `result` vector.
+
+5. **Return the result**:
+   - After generating all rows, return the `result` vector.
+
+### Time Complexity ⏱️
+- The time complexity is **O(numRows^2)** because we are iterating through each element of each row once.
+
+### Space Complexity 💾
+- The space complexity is **O(numRows^2)** due to the space required to store the entire triangle in memory.
+
+## Code Implementation in C++
+
+```cpp
+class Solution {
+public:
+    vector<vector<int>> generate(int numRows) {
+        std::vector<std::vector<int>> result;
+        for(int i=0; i < numRows; i++){
+            std::vector<int> row(i + 1, 1);
+            for(int j = 1; j < i; j++){
+                row[j] = result[i - 1][j - 1] + result[i - 1][j];
+            }
+            result.push_back(row);
+        }
+        return result;
+    }
+};
+```
+
+### LeetCode Performance 💯
+- **Time Complexity**: `0ms` (As fast as possible)
+- **Space Complexity**: `0ms` (Optimal memory usage)
+  
+> 🚀 **Conclusion**: This solution efficiently generates Pascal's Triangle with minimal time and space complexity. Enjoy coding!
+
+---
+
+**Keep Coding!** 💻✨

pascalsTriangle/pascalsTriangle.cpp

@@ -0,0 +1,15 @@
+class Solution {
+public:
+    vector<vector<int>> generate(int numRows) {
+        std::vector<std::vector<int>> result;
+        for(int i=0; i < numRows; i++){
+            std::vector<int> row(i + 1, 1);
+            for(int j = 1; j < i; j++){
+                row[j] = result[i - 1][j - 1] + result[i - 1][j];
+            }
+            result.push_back(row);
+        }
+        return result;
+    }
+};
+