Pascal's Triangle

Pascal'sTriangle.cpp

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+You are given an integer N. Your task is to return a 2-D ArrayList 
+containing the pascal’s triangle till the row N.
+
+A Pascal's triangle is a triangular array constructed by summing adjacent elements 
+in preceding rows. Pascal's triangle contains the values of the binomial coefficient. 
+For example in the figure below.
+
+For example, given integer N= 4 then you have to print.
+
+1  
+1 1 
+1 2 1 
+1 3 3 1
+
+Here for the third row, you will see that the second element 
+is the summation of the above two-row elements i.e. 2=1+1, 
+and similarly for row three 3 = 1+2 and 3 = 1+2.
+
+//code
+/*
+	Time Complexity: O(2^N)
+	Space complexity: O(N)
+	
+	Where N denotes the number of Rows.
+*/
+
+//Recursive Approach
+#include<vector>
+
+long long int calPascal(long long int i, long long int j) {
+    if (j == 0 || j == i) {
+        return 1;
+    } else {
+        return calPascal(i - 1, j - 1) + calPascal(i - 1, j);
+    }
+}
+
+vector < vector < long long int >> printPascal(int n) {
+    vector < vector < long long int >> triangle;
+    for (int i = 0; i < n; i++) {
+        vector < long long int > temp;
+        for (int j = 0; j <= i; j++) {
+            temp.push_back(calPascal((long long int) i, (long long int) j));
+        }
+        triangle.push_back(temp);
+    }
+    return triangle;
+}
+
+//optimized approach
+
+#include <bits/stdc++.h>
+#include<vector>
+
+vector<vector<long long int>> printPascal(int n) 
+{
+    vector<vector<long long int > > triangle;
+    vector<long long int > temp;
+
+    for(int i=1;i<=n;i++){
+      long long int rCe = 1;
+      temp.clear();
+      for(int  j=1;j <= i; j++){
+        temp.push_back(rCe);
+        rCe = rCe * (i-j)/j;
+      }
+      triangle.push_back(temp);
+    } 
+    return triangle;
+}
+