什麼是遞迴？

Python 程式面試題實作練習

Kirill Smirnov

Data Science Consultant, Altran

定義

遞迴是一種用自身來定義問題的方式
遞迴是函式把自己當作子程序呼叫的過程

範例：階乘 $n!$

$n! = n\cdot(n-1)\cdot(n-2)\cdot...\cdot1$

$n = 4$：

$4! = 4\cdot3\cdot2\cdot1$

4! = 24

階乘－迭代法

$n! = n\cdot(n-1)\cdot(n-2)\cdot...\cdot1 = $

$ = 1\cdot2\cdot3\cdot...\cdot n$

迭代解法：

# iterative factorial
def fact_iter(n):
    result = 1
    # looping over numbers from 1 to n
    for num in range(1, n+1)
        result = num * result

    return result

$n = 4$：

result = 1

result = 1 * result(1) = 1
result = 2 * result(1) = 2
result = 3 * result(2) = 6
result = 4 * result(4) = 24

$4! = 1 \cdot 2 \cdot 3 \cdot 4 = 24$

階乘－遞迴法

$n!$ $=n\cdot(n-1)!$

def fact_rec(n):
    return n * fact_rec(n-1)

那段程式哪裡有問題？

fact_rec(4)

RecursionError

必須定義基底情況！

$n! = n\cdot(n-1)\cdot(n-2)\cdot...\cdot1$

停止條件／基底情況：$1! = 1$

def fact_rec(n):
    if n == 1:
        return 1
    return n * fact_rec(n-1)

fact_rec(4)

重點總結

遞迴函式有兩個重點：

對較小子問題的遞迴呼叫
防止無限呼叫的基底情況

範例－決策樹

決策樹

用決策樹做分類

走訪決策樹

x－新樣本 $(x_1, x_2)$

# Pseudo algorithm for finding out the category:

category = pred(node, x):

  # Check if there is a split  
  if node.hasSplitting:

    # Check which child node to take
    if node.goToLeftChild(x):
      return pred(node.leftChild, x)   
    if node.goToRightChild(x):
      return pred(node.rightChild, x)

走訪決策樹

用決策樹做預測

x－新樣本 $(x_1, x_2)$

# Pseudo algorithm for finding out the category:

category = pred(node, x):

  # Check if there is a split  
  if node.hasSplitting:

    # Check which child node to take
    if node.goToLeftChild(x):
      return pred(node.leftChild, x) 
    if node.goToRightChild(x):
      return pred(node.rightChild, x)

  # Returning the category
  return node.category

一起來練習吧！

Python 程式面試題實作練習