Add No_119: Pascal's Triangle II

Author: brianchiang-tw

No_119_Pascal's Triangle II/No_119_Pascal's Triangle II_description.md

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+'''
+
+Description:
+
+Given a non-negative index k where k ≤ 33, return the kth index row of the Pascal's triangle.
+
+Note that the row index starts from 0.
+
+In Pascal's triangle, each number is the sum of the two numbers directly above it.
+
+Example:
+
+Input: 3
+Output: [1,3,3,1]
+Follow up:
+
+Could you optimize your algorithm to use only O(k) extra space?
+
+'''

No_119_Pascal's Triangle II/pascal_triangle_by_math.py

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+'''
+
+Description:
+
+Given a non-negative index k where k ≤ 33, return the kth index row of the Pascal's triangle.
+
+Note that the row index starts from 0.
+
+In Pascal's triangle, each number is the sum of the two numbers directly above it.
+
+Example:
+
+Input: 3
+Output: [1,3,3,1]
+Follow up:
+
+Could you optimize your algorithm to use only O(k) extra space?
+
+'''
+
+
+from math import factorial
+from typing import List
+
+class Solution:
+    
+    def comb(self, n, m):
+        
+        if n == m or m == 0:
+            return 1
+        else:
+            return factorial(n) // ( factorial(m) * factorial(n-m) )
+
+        
+    def getRow(self, rowIndex: int) -> List[int]:
+        
+        # the coefficient of level k is as folling
+        #
+        # C(k,0), C(k,1), ... , C(k,k)
+        
+        return [ self.comb(rowIndex,i) for i in range(0, rowIndex+1) ]
+
+
+
+# k : the input value of rowIndex
+
+## Time Complexity: O( k ) 
+#
+# The major overhead in time is the length of list comprehension on i, which is of O( k )
+
+## Space Complexity: O( k )
+#
+# The major overhead in space is the storge for output list, which is of O( k )
+
+
+
+
+def test_bench():
+
+    test_data = [ 0, 1, 2, 3, 4, 5 ]
+
+    # expected output:
+    '''
+    [1]
+    [1, 1]
+    [1, 2, 1]
+    [1, 3, 3, 1]
+    [1, 4, 6, 4, 1]
+    [1, 5, 10, 10, 5, 1]
+    '''
+
+    for n in test_data:
+
+        print( Solution().getRow(n) )
+
+    return
+
+
+
+if __name__ == '__main__':
+
+    test_bench()