Pascal triangle ii: math approach

maths/pascal_triangle_ii.rb

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+# Challenge name: Pascal's triangle ii
+#
+# Given an integer row_index, return the rowIndexth (0-indexed) row of the Pascal's triangle.
+# Example 1:
+#
+# Input: row_index = 3
+# Output: [1,3,3,1]
+#
+# Example 2:
+#
+# Input: row_index = 0
+# Output: [1]
+#
+# Example 3:
+#
+# Input: row_index = 1
+# Output: [1,1]
+
+# Complexity Analysis
+# Time complexity: O(k).
+# Each term is calculated once, in constant time.
+
+# Space complexity: O(k).
+# No extra space required other than that required to hold the output.
+
+def get_row(row_index)
+  (0..row_index).map {|num| combination(row_index, num) }
+end
+
+def combination(num1, num2)
+  factorial(num1) / (factorial(num2) * factorial(num1 - num2))
+end
+
+def factorial(num)
+  (1..num).inject(1) {|res, i| res * i }
+end
+
+row_index = 3
+print(get_row(row_index))
+# => [1,3,3,1]
+
+row_index = 0
+print(get_row(row_index))
+# => [1]
+
+row_index = 1
+print(get_row(row_index))
+# => [1,1]