In-place versus extra-space transformations

What is an array?

An array stores values in a sequence of numbered positions. A position is called an index. Indices usually start at 0: the first value is at index 0, the second at index 1. Knowing the index lets you go directly to that position; finding an unknown value may require checking many positions.

Example: In [4, 8, 15], index 1 contains 8. There are three elements, so the valid indices are 0, 1, and 2. A Python list is a dynamic array: its storage can grow when you append values.

Helpful before this chapter

If these ideas are new, begin with:

Programming foundations Time and space complexity

Understand the idea

In-place transformation reuses input storage. Separate output simplifies reasoning but allocates memory. Compaction uses write≤read so writing cannot destroy future unread input.

Work through an example

The lab returns length 3 and leaves a valid prefix [1,2,3]. The suffix is unspecified. Sorted input is required because duplicates must be adjacent.

Time and space complexity

O(n) time/O(1) auxiliary space; a separate result needs O(k) output storage.

Why it works

Before each read, values[:write] is exactly the distinct processed values in order.

Common mistakes

Only the returned prefix is meaningful.
Sorting first changes cost and original order.

Chapter lab · Python implementation

Arrays make positions directly accessible. Our lab compacts a sorted list: read examines input; write marks the next output slot. Python lists are resizable arrays of references. Fixed-width address diagrams illustrate slots, rather than promising contiguous Python objects.

This shared lab connects the chapter's topics. Follow the current lesson's worked example first, then trace the complete implementation. Additional algorithms described in topic exercises are variations you can implement independently.

def compact_sorted(values):
    write = 0
    for read in range(len(values)):
        if write == 0 or values[read] != values[write-1]:
            values[write] = values[read]
            write += 1
    return write

def transpose(matrix):
    if not matrix:
        return []
    cols = len(matrix[0])
    if any(len(row) != cols for row in matrix):
        raise ValueError('rectangular matrix required')
    return [[matrix[r][c] for r in range(len(matrix))]
            for c in range(cols)]

Run and test the lab

Copy the implementation and these assertions into a Python 3 file and run it. An assertion failure means the actual result differs from the expectation. Add the current topic's exercise and boundary tests to deepen your understanding.

a=[1,1,2,2,3]; k=compact_sorted(a)
assert a[:k]==[1,2,3]
assert compact_sorted([])==0
assert transpose([[1,2,3],[4,5,6]])==[[1,4],[2,5],[3,6]]
assert transpose([])==[]

CHECK YOUR UNDERSTANDING