Recursion

1
Recursion
2
Sum a list of numbers

• Iterative
• def sum(L)
• total 0
• for i in L
• total i
• return total

• Recursive
• def sum(L)
• if len(L) 0
• return 0
• else
• return L0 sum(L1)

3
How iteration works

• def sum(L)
• total 0
• for i in L
• total i
• return total

• sum(4,5,6)
• total 0
• i 4
• total 0 4 4
• i 5
• total 4 5 9
• i 6
• total 9 6 15
• 15

4
How recursion works

• def sum(L)
• if len(L) 0
• return 0
• else
• return L0 sum(L1

• sum(4,5,6)
• 4sum(5,6)
• 5sum(6)
• 6sum( )
• 0
• 6 0 6
• 5 6 11
• 4 11 15
• 15

5
Side by side

• sum(4,5,6)
• total 0
• i 4
• total 0 4 4
• i 5
• total 4 5 9
• i 6
• total 9 6 15
• 15

• sum(4,5,6)
• 4sum(5,6)
• 5sum(6)
• 6sum( )
• 0
• 6 0 6
• 5 6 11
• 4 11 15
• 15

6
Fact

• Iteration and recursion are equivalent.
• Any iteration can be replaced by recursion.
• Any recursion can be replaced by iteration.

7
Why use Recursion?

• Clarity The logic of certain task can sometimes
  be clarified.
• Elegance The coding is sometimes more elegant.

8
A recursive algorithm must

• have a base case.

• def sum(L)
• if len(L) 0
• return 0
• else
• return L0 sum(L1)

Empty list is the base case
9
A recursive algorithm must

• have a base case.
• change its state and move toward the base case.

• def sum(L)
• if len(L) 0
• return 0
• else
• return L0 sum(L1)

L ? L1 Closer to
10
A recursive algorithm must

• have a base case.
• change its state and move toward the base case.
• call itself, recursively.

• def sum(L)
• if len(L) 0
• return 0
• else
• return L0 sum(L1)

11
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

12
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list

13
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list

14
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number

15
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list

16
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list
• 11 number

17
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list
• 11 number
• 411 number

18
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list
• 11 number
• 411 number

?
19
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list
• 11 number
• 411 number

?
?
20
Recursion Worksheet

• def sum(L)
• if len(L) 0
• return 0
• else
• return \
• L0sum(L1)
• a sum(4,5,6)

• 4,5,6 list
•   list
• 0 number
• 5,6 list
• 11 number
• 411 number

?
?
?