伪代码中‘by’的含义是什么？以for k=0 to n-1 by m为例

Great question—let’s break this down simply!

• The by m part in this pseudocode defines the step size for the loop variable k.
• By default, a basic for loop (like for k = 0 to n-1) increments the variable by 1 each iteration. Adding by m overrides that: instead of adding 1, k increases by m every time the loop runs.

Example to Make It Concrete #

Let’s use actual numbers to see how it works:
Suppose n = 7 (so n-1 = 6) and m = 2:

• First iteration: k = 0
• Second iteration: k = 0 + 2 = 2
• Third iteration: k = 2 + 2 = 4
• Fourth iteration: k = 4 + 2 = 6
• After this, k would become 8, which is greater than 6, so the loop stops.
• The values of k we’ll see in the loop are: 0, 2, 4, 6.

Quick Note on Negative Step Sizes #

While your original statement uses a positive range (0 up to n-1), if m were negative (like by -1), the loop would decrement instead—starting at the upper bound and moving down to the lower one. But in most cases with this syntax, m is a positive integer, meant to skip ahead through the range.

This syntax is widely used in pseudocode to explicitly show we’re not iterating through every single value, but processing every m-th element (like chunking an array or implementing block-based algorithms).

内容的提问来源于stack exchange，提问作者abdulrahim almethiab