Merge pull request #158 from TheAlgorithms/pascal-triangle-ii-dd-approach

DIRECTORY.md

@@ -78,6 +78,7 @@
   * [Coin Change](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/coin_change.rb)
   * [Count Sorted Vowel Strings](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/count_sorted_vowel_strings.rb)
   * [Fibonacci](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/fibonacci.rb)
+  * [Pascal Triangle Ii](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/pascal_triangle_ii.rb)
 
 ## Maths
   * [Abs](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs.rb)

dynamic_programming/pascal_triangle_ii.rb

@@ -0,0 +1,138 @@
+# 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]
+
+#
+# Approach 1: Brute Force
+#
+
+# Complexity Analysis
+#
+# Time complexity: O(k^2).
+# Space complexity: O(k) + O(k) ~ O(k)
+
+def get_num(row, col)
+  return 1 if row == 0 || col == 0 || row == col
+
+  get_num(row - 1, col - 1) + get_num(row - 1, col)
+end
+
+def get_row(row_index)
+  result = []
+
+  (row_index + 1).times do |i|
+    result.push(get_num(row_index, i))
+  end
+
+  result
+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]
+
+#
+# Approach 2: Dynamic Programming
+#
+
+# Complexity Analysis
+#
+# Time complexity: O(k^2).
+# Space complexity: O(k) + O(k) ~ O(k).
+
+# @param {Integer} row_index
+# @return {Integer[]}
+def get_row(row_index)
+  result = generate(row_index)
+  result[result.count - 1]
+end
+
+def generate(num_rows)
+  return [[1]] if num_rows < 1
+  result = [[1], [1, 1]]
+
+  (2...num_rows + 1).each do |row|
+    prev = result[row - 1]
+    current = [1]
+    med = prev.count / 2
+
+    (1...prev.count).each do |i|
+      current[i] = prev[i - 1] + prev[i]
+    end
+
+    current.push(1)
+    result.push(current)
+  end
+
+  result
+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]
+
+#
+# Approach 3: Memory-efficient Dynamic Programming
+#
+
+# Complexity Analysis
+#
+# Time complexity: O(k^2).
+# Space complexity: O(k).
+
+# @param {Integer} row_index
+# @return {Integer[]}
+def get_row(row_index)
+  pascal = [[1]]
+
+  (1..row_index).each do |i|
+    pascal[i] = []
+    pascal[i][0] = pascal[i][i] = 1
+
+    (1...i).each do |j|
+      pascal[i][j] = pascal[i - 1][j - 1] + pascal[i - 1][j]
+    end
+  end
+
+  pascal[row_index]
+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]