Functions - Python Programming

Sum of list function

Wrap the sum logic in a reusable function.

                            sum.py
                        
Replay: real traced execution (multi-file project)

                            def sum(arr):
    total = 0
    for i in range(len(arr)):
        total = total + arr[i]

    return total

nums1 = [10, 20, 30]
nums2 = [1, 2, 3, 4, 5]

print("nums1=" + str(nums1))
result1 = sum(nums1)

print("nums2=" + str(nums2))
result2 = sum(nums2)


                        
1nums1 ← [10, 20, 30], nums2 ← [1, 2, 3, 4, 5]⋯8nums1→ [10, 20, 30] = [10, 20, 30]9nums2→ [1, 2, 3, 4, 5] = [1, 2, 3, 4, 5]1011print("nums1=" + str(nums1[10, 20, 30]))12result1 = sum(nums1[10, 20, 30])⋯outputnums1=[10, 20, 30]
2total ← 0pass 1 of 21def sum(arr[10, 20, 30]):2    total→ 0 = 03    for i in range(len(arr)):⋯
3total ← 10pass 1 of 8⋯2total = 03for i0 in range(len(arr[10, 20, 30])):4    total→ 10 = total + arr[i]105#?return_value⋯All 8 passes — pass 1 is the card abovepassiarrarr[i]total
10[10, 20, 30]100 → 10
21[10, 20, 30]2010 → 30
32[10, 20, 30]3030 → 60
40[1, 2, 3, 4, 5]10 → 1
51[1, 2, 3, 4, 5]21 → 3
62[1, 2, 3, 4, 5]33 → 6
73[1, 2, 3, 4, 5]46 → 10
84[1, 2, 3, 4, 5]510 → 15
4return total⋯5#?return_value6return total60⋯
5result1 ← 60⋯11print("nums1=" + str(nums1))12result1→ 60 = sum(nums1[10, 20, 30])1314print("nums2=" + str(nums2[1, 2, 3, 4, 5]))15result2 = sum(nums2[1, 2, 3, 4, 5])⋯outputnums2=[1, 2, 3, 4, 5]
6total ← 0pass 2 of 21def sum(arr[1, 2, 3, 4, 5]):2    total→ 0 = 03    for i in range(len(arr)):⋯
7return total⋯5#?return_value6return total15⋯
8result2 ← 15⋯14print("nums2=" + str(nums2))15result2→ 15 = sum(nums2[1, 2, 3, 4, 5])⋯

All 8 passes — pass 1 is the card above
pass	`i`	`arr`	`arr[i]`	`total`
1	0	[10, 20, 30]	10	0 → 10
2	1	[10, 20, 30]	20	10 → 30
3	2	[10, 20, 30]	30	30 → 60
4	0	[1, 2, 3, 4, 5]	1	0 → 1
5	1	[1, 2, 3, 4, 5]	2	1 → 3
6	2	[1, 2, 3, 4, 5]	3	3 → 6
7	3	[1, 2, 3, 4, 5]	4	6 → 10
8	4	[1, 2, 3, 4, 5]	5	10 → 15

The function takes a list, returns the sum.

def `def name(parameters):` defines a function in Python.

parameter Input values passed to a function when calling it.

return The value a function sends back to the caller.

Temperature conversion

Convert between Fahrenheit and Celsius. Two functions, opposite directions.

example f1 = 98.6, c2 = 0 (default)f1 = 32f1 = 212c2 = 37c2 = 100

temperature.py

Replay: real traced execution (multi-file project)

def fahrenheit_to_celsius(f):
    return (f - 32) * 5 / 9

def celsius_to_fahrenheit(c):
    return c * 9 / 5 + 32

f1 = 98.6
c1 = fahrenheit_to_celsius(f1)

c2 = 0
f2 = celsius_to_fahrenheit(c2)

def fahrenheit_to_celsius(f):
    return (f - 32) * 5 / 9

def celsius_to_fahrenheit(c):
    return c * 9 / 5 + 32

f1 = 32
c1 = fahrenheit_to_celsius(f1)

c2 = 0
f2 = celsius_to_fahrenheit(c2)

def fahrenheit_to_celsius(f):
    return (f - 32) * 5 / 9

def celsius_to_fahrenheit(c):
    return c * 9 / 5 + 32

f1 = 212
c1 = fahrenheit_to_celsius(f1)

c2 = 0
f2 = celsius_to_fahrenheit(c2)

def fahrenheit_to_celsius(f):
    return (f - 32) * 5 / 9

def celsius_to_fahrenheit(c):
    return c * 9 / 5 + 32

f1 = 98.6
c1 = fahrenheit_to_celsius(f1)

c2 = 37
f2 = celsius_to_fahrenheit(c2)

def fahrenheit_to_celsius(f):
    return (f - 32) * 5 / 9

def celsius_to_fahrenheit(c):
    return c * 9 / 5 + 32

f1 = 98.6
c1 = fahrenheit_to_celsius(f1)

c2 = 100
f2 = celsius_to_fahrenheit(c2)

f1 ← 98.6

⋯7f1→ 98.6 = 98.6  #@f1=32, 2128c1 = fahrenheit_to_celsius(f198.6)⋯

def fahrenheit_to_celsius(f):

1def fahrenheit_to_celsius(f98.6):2    return (f98.6 - 32) * 5 / 9⋯

c1 ← 37.0, c2 ← 0

⋯7f1 = 98.6  #@f1=32, 2128c1→ 37.0 = fahrenheit_to_celsius(f198.6)910c2→ 0 = 0  #@c2=100, 3711f2 = celsius_to_fahrenheit(c20)⋯

def celsius_to_fahrenheit(c):

⋯4def celsius_to_fahrenheit(c0):5    return c0 * 9 / 5 + 32⋯

f2 ← 32.0

⋯10c2 = 0  #@c2=100, 3711f2→ 32.0 = celsius_to_fahrenheit(c20)⋯

f1 ← 32

⋯7f1→ 32 = 328c1 = fahrenheit_to_celsius(f132)⋯

def fahrenheit_to_celsius(f):

1def fahrenheit_to_celsius(f32):2    return (f32 - 32) * 5 / 9⋯

c1 ← 0.0, c2 ← 0

⋯7f1 = 328c1→ 0.0 = fahrenheit_to_celsius(f132)910c2→ 0 = 011f2 = celsius_to_fahrenheit(c20)⋯

def celsius_to_fahrenheit(c):

⋯4def celsius_to_fahrenheit(c0):5    return c0 * 9 / 5 + 32⋯

f2 ← 32.0

⋯10c2 = 011f2→ 32.0 = celsius_to_fahrenheit(c20)⋯

f1 ← 212

⋯7f1→ 212 = 2128c1 = fahrenheit_to_celsius(f1212)⋯

def fahrenheit_to_celsius(f):

1def fahrenheit_to_celsius(f212):2    return (f212 - 32) * 5 / 9⋯

c1 ← 100.0, c2 ← 0

⋯7f1 = 2128c1→ 100.0 = fahrenheit_to_celsius(f1212)910c2→ 0 = 011f2 = celsius_to_fahrenheit(c20)⋯

def celsius_to_fahrenheit(c):

⋯4def celsius_to_fahrenheit(c0):5    return c0 * 9 / 5 + 32⋯

f2 ← 32.0

⋯10c2 = 011f2→ 32.0 = celsius_to_fahrenheit(c20)⋯

f1 ← 98.6

⋯7f1→ 98.6 = 98.68c1 = fahrenheit_to_celsius(f198.6)⋯

def fahrenheit_to_celsius(f):

1def fahrenheit_to_celsius(f98.6):2    return (f98.6 - 32) * 5 / 9⋯

c1 ← 37.0, c2 ← 37

⋯7f1 = 98.68c1→ 37.0 = fahrenheit_to_celsius(f198.6)910c2→ 37 = 3711f2 = celsius_to_fahrenheit(c237)⋯

def celsius_to_fahrenheit(c):

⋯4def celsius_to_fahrenheit(c37):5    return c37 * 9 / 5 + 32⋯

f2 ← 98.6

⋯10c2 = 3711f2→ 98.6 = celsius_to_fahrenheit(c237)⋯

f1 ← 98.6

⋯7f1→ 98.6 = 98.68c1 = fahrenheit_to_celsius(f198.6)⋯

def fahrenheit_to_celsius(f):

1def fahrenheit_to_celsius(f98.6):2    return (f98.6 - 32) * 5 / 9⋯

c1 ← 37.0, c2 ← 100

⋯7f1 = 98.68c1→ 37.0 = fahrenheit_to_celsius(f198.6)910c2→ 100 = 10011f2 = celsius_to_fahrenheit(c2100)⋯

def celsius_to_fahrenheit(c):

⋯4def celsius_to_fahrenheit(c100):5    return c100 * 9 / 5 + 32⋯

f2 ← 212.0

⋯10c2 = 10011f2→ 212.0 = celsius_to_fahrenheit(c2100)⋯

Functions can take one value and return another. Each function does one specific job.

Fibonacci function

Get the first n Fibonacci numbers.

                            n
                            n = 10 (default)n = 5n = 15
                        

                            fibonacci.py
                        
Replay: real traced execution (multi-file project)

                            def fibonacci(n):
    fib = [0] * n
    fib[0] = 0
    fib[1] = 1

    for i in range(2, n):
        fib[i] = fib[i - 1] + fib[i - 2]

    return fib

n = 10
result = fibonacci(n)
print("result=" + str(result))
def fibonacci(n):
    fib = [0] * n
    fib[0] = 0
    fib[1] = 1

    for i in range(2, n):
        fib[i] = fib[i - 1] + fib[i - 2]

    return fib

n = 5
result = fibonacci(n)
print("result=" + str(result))
def fibonacci(n):
    fib = [0] * n
    fib[0] = 0
    fib[1] = 1

    for i in range(2, n):
        fib[i] = fib[i - 1] + fib[i - 2]

    return fib

n = 15
result = fibonacci(n)
print("result=" + str(result))

                        
1n ← 10⋯11n→ 10 = 10  #@n=5, 1512result = fibonacci(n10)13print("result=" + str(result))⋯
2fib ← [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], fib[0] ← 0, fib[1] ← 11def fibonacci(n10):2    fib→ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] = [0] * n103    fib[0]→ 0 = 04    fib[1]→ 1 = 1⋯
3fib[i] ← 1pass 1 of 8⋯6for i2 in range(2, n10):7    fib[i]→ 1 = fib[i - 1]1 + fib[i - 2]0⋯All 8 passes — pass 1 is the card abovepassifib[i - 1]fib[i - 2]fib[i]
12101
23112
34213
45325
56538
678513
7813821
89211334
4return fib⋯9return fib[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]⋯
5result ← [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]⋯11n = 10  #@n=5, 1512result→ [0, 1, 1, 2, 3, 5, 8, 13, 21, 34] = fibonacci(n10)13print("result=" + str(result[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]))⋯outputresult=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
1n ← 5⋯11n→ 5 = 512result = fibonacci(n5)13print("result=" + str(result))⋯
2fib ← [0, 0, 0, 0, 0], fib[0] ← 0, fib[1] ← 11def fibonacci(n5):2    fib→ [0, 0, 0, 0, 0] = [0] * n53    fib[0]→ 0 = 04    fib[1]→ 1 = 1⋯
3fib[i] ← 1pass 1 of 3⋯6for i2 in range(2, n5):7    fib[i]→ 1 = fib[i - 1]1 + fib[i - 2]0⋯All 3 passes — pass 1 is the card abovepassifib[i - 1]fib[i - 2]fib[i]
12101
23112
34213
4return fib⋯9return fib[0, 1, 1, 2, 3]⋯
5result ← [0, 1, 1, 2, 3]⋯11n = 512result→ [0, 1, 1, 2, 3] = fibonacci(n5)13print("result=" + str(result[0, 1, 1, 2, 3]))⋯outputresult=[0, 1, 1, 2, 3]
1n ← 15⋯11n→ 15 = 1512result = fibonacci(n15)13print("result=" + str(result))⋯
2fib ← [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], fib[0] ← 01def fibonacci(n15):2    fib→ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] = [0] * n153    fib[0]→ 0 = 04    fib[1]→ 1 = 1⋯
3fib[i] ← 1pass 1 of 13⋯6for i2 in range(2, n15):7    fib[i]→ 1 = fib[i - 1]1 + fib[i - 2]0⋯13 passes — pass 1 is the card abovepassifib[i - 1]fib[i - 2]fib[i]
12101
23112
34213
45325
56538
678513
7813821
89211334
910342155
⋯ 2 more passes ⋯
121314489233
1314233144377
4return fib⋯9return fib[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]⋯
5result ← [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]⋯11n = 1512result→ [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377] = fibonacci(n15)13print("result=" + str(result[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]))⋯outputresult=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

All 8 passes — pass 1 is the card above
pass	`i`	`fib[i - 1]`	`fib[i - 2]`	`fib[i]`
1	2	1	0	1
2	3	1	1	2
3	4	2	1	3
4	5	3	2	5
5	6	5	3	8
6	7	8	5	13
7	8	13	8	21
8	9	21	13	34

All 3 passes — pass 1 is the card above
pass	`i`	`fib[i - 1]`	`fib[i - 2]`	`fib[i]`
1	2	1	0	1
2	3	1	1	2
3	4	2	1	3

13 passes — pass 1 is the card above
pass	`i`	`fib[i - 1]`	`fib[i - 2]`	`fib[i]`
1	2	1	0	1
2	3	1	1	2
3	4	2	1	3
4	5	3	2	5
5	6	5	3	8
6	7	8	5	13
7	8	13	8	21
8	9	21	13	34
9	10	34	21	55
⋯ 2 more passes ⋯
12	13	144	89	233
13	14	233	144	377

The function handles all the list setup and calculation internally. The caller just says "give me 10 Fibonacci numbers."

Find maximum function

Wrap the "find max" logic in a reusable function.

                            max.py
                        
Replay: real traced execution (multi-file project)

                            def max(arr):
    result = arr[0]
    for i in range(1, len(arr)):
        if arr[i] > result:
            result = arr[i]
    return result

nums = [23, 45, 12, 67, 34, 89, 41]

print("nums=" + str(nums))
m = max(nums)

                        
1nums ← [23, 45, 12, 67, 34, 89, 41]⋯8nums→ [23, 45, 12, 67, 34, 89, 41] = [23, 45, 12, 67, 34, 89, 41]910print("nums=" + str(nums[23, 45, 12, 67, 34, 89, 41]))11m = max(nums[23, 45, 12, 67, 34, 89, 41])⋯outputnums=[23, 45, 12, 67, 34, 89, 41]
2result ← 231def max(arr[23, 45, 12, 67, 34, 89, 41]):2    result→ 23 = arr[0]233    for i in range(1, len(arr)):⋯
3for i in range(1, len(arr)):pass 1 of 6⋯2result = arr[0]3for i1 in range(1, len(arr[23, 45, 12, 67, 34, 89, 41])):4    if arr[i] > result:5        result = arr[i]⋯All 6 passes — pass 1 is the card abovepassi
11
22
33
44
55
66
4result ← 45pass 1 of 3⋯3for i in range(1, len(arr)):4    if arr[i]45 > result23:5        result→ 45 = arr[i]456return result⋯All 3 passes — pass 1 is the card abovepassarr[i]result
14523 → 45
26745 → 67
38967 → 89
5return result⋯5        result = arr[i]6return result89⋯
6m ← 89⋯10print("nums=" + str(nums))11m→ 89 = max(nums[23, 45, 12, 67, 34, 89, 41])⋯

All 6 passes — pass 1 is the card above
pass	`i`
1	1
2	2
3	3
4	4
5	5
6	6

All 3 passes — pass 1 is the card above
pass	`arr[i]`	`result`
1	45	23 → 45
2	67	45 → 67
3	89	67 → 89

Now any code can find the maximum of a list with a single call.

Multiple function calls

Use functions together to solve a problem.

                            combined.py
                        
Replay: real traced execution (multi-file project)

                            def sum(arr):
    total = 0
    for i in range(len(arr)):
        total = total + arr[i]
    return total

def average(arr):
    return sum(arr) / len(arr)

scores = [85, 92, 78, 95, 88]

print("scores=" + str(scores))
total = sum(scores)
avg = average(scores)

                        
1scores ← [85, 92, 78, 95, 88]⋯10scores→ [85, 92, 78, 95, 88] = [85, 92, 78, 95, 88]1112print("scores=" + str(scores[85, 92, 78, 95, 88]))13total = sum(scores[85, 92, 78, 95, 88])14avg = average(scores)⋯outputscores=[85, 92, 78, 95, 88]
2total ← 0pass 1 of 21def sum(arr[85, 92, 78, 95, 88]):2    total→ 0 = 03    for i in range(len(arr)):⋯
3total ← 85pass 1 of 10⋯2total = 03for i0 in range(len(arr[85, 92, 78, 95, 88])):4    total→ 85 = total + arr[i]855return total⋯All 10 passes — pass 1 is the card abovepassiarr[i]total
10850 → 85
219285 → 177
3278177 → 255
4395255 → 350
5488350 → 438
60850 → 85
719285 → 177
8278177 → 255
9395255 → 350
10488350 → 438
4return total⋯4    total = total + arr[i]5return total438⋯
5total ← 438⋯12print("scores=" + str(scores))13total→ 438 = sum(scores[85, 92, 78, 95, 88])14avg = average(scores[85, 92, 78, 95, 88])⋯
6def average(arr):⋯7def average(arr[85, 92, 78, 95, 88]):8    return sum(arr[85, 92, 78, 95, 88]) / len(arr)⋯
7total ← 0pass 2 of 21def sum(arr[85, 92, 78, 95, 88]):2    total→ 0 = 03    for i in range(len(arr)):⋯
8return total⋯4    total = total + arr[i]5return total438⋯
9avg ← 87.6⋯13total = sum(scores)14avg→ 87.6 = average(scores[85, 92, 78, 95, 88])⋯

All 10 passes — pass 1 is the card above
pass	`i`	`arr[i]`	`total`
1	0	85	0 → 85
2	1	92	85 → 177
3	2	78	177 → 255
4	3	95	255 → 350
5	4	88	350 → 438
6	0	85	0 → 85
7	1	92	85 → 177
8	2	78	177 → 255
9	3	95	255 → 350
10	4	88	350 → 438

Functions can call other functions. Build complex logic from simple pieces - this is called composition.