`sum()`, `min()`, and `max()`

Introduction

These three aggregation functions are the most commonly used built-ins in algorithmic interviews. Never write manual for loops to calculate these values unless the interviewer explicitly asks you to.

`sum()`

Returns the total of all items in an iterable.

nums = [1, 2, 3, 4]
print(sum(nums)) # 10

With a starting value

sum() takes an optional second argument: the starting value. This is occasionally useful when you want to sum elements and add them to a baseline offset.

print(sum(nums, 100)) # 110

(Note: Do not use sum() to concatenate strings. Use "".join() instead).

`min()` and `max()`

Returns the smallest or largest item in an iterable, or among two or more arguments.

nums = [5, 1, 9, 3]

# From an iterable
print(min(nums)) # 1

# From multiple arguments (useful in DP)
print(max(10, 20)) # 20

Using the `key` argument

Just like sort(), you can pass a key function to customize how min() and max() determine the value of an element.

This is highly requested in interviews involving strings or complex objects.

words = ["apple", "banana", "kiwi"]

# Find the longest word
longest = max(words, key=len)
print(longest) # "banana"

points = [(1, 5), (3, 2), (8, 10)]

# Find the point with the smallest Y coordinate
lowest_point = min(points, key=lambda p: p[1])
print(lowest_point) # (3, 2)

Providing a `default`

If you call min() or max() on an empty iterable, Python raises a ValueError. To prevent this, you can provide a default keyword argument.

empty_list = []

# print(max(empty_list)) # ValueError!

print(max(empty_list, default=0)) # 0

Interview Application: Dynamic Programming

In Top-Down DP or recursive Backtracking, min and max are used constantly to find the optimal path.

# DP state transition example
def min_coins(amount):
    if amount == 0: return 0
    if amount < 0: return math.inf

    # Try all coins and take the minimum result
    return 1 + min(min_coins(amount - coin) for coin in coins)

Time and Space Complexity

Time Complexity: \(O(N)\) for iterables of length \(N\).
Space Complexity: \(O(1)\).

Summary

Use sum() to add numbers.
Use min() and max() to find extremes.
Use the key argument to find extremes based on custom properties (e.g., key=len).
Use default=0 to prevent ValueErrors on empty lists.

sum(), min(), and max()