docs: clarify the operation-counting convention

This commit is contained in:
krahets
2026-10-11 02:51:20 +08:00
parent 817a24d7ef
commit 9c928face6
5 changed files with 15 additions and 15 deletions
@@ -717,7 +717,7 @@ For code, count from top to bottom line by line. However, since the constant coe
2. **Omit all coefficients**. For example, looping $2n$ times, $5n + 1$ times, etc., can all be simplified as $n$ times, because the coefficient before $n$ does not affect time complexity.
3. **Use multiplication for nested loops**. The total number of operations equals the product of the number of operations in the outer and inner loops, with each layer of loop still able to apply techniques `1.` and `2.` separately.
Given a function, we can use the above techniques to count the number of operations:
In the following example, each execution of an assignment or print statement counts as one operation. We omit loop-variable initialization, condition checks, and increments, which do not affect the asymptotic time complexity of this example. We can use the above techniques to further simplify the count:
=== "Python"
@@ -964,9 +964,9 @@ The following formula shows the counting results before and after using the abov
$$
\begin{aligned}
T(n) & = 2n(n + 1) + (5n + 1) + 2 & \text{Complete count (-.-|||)} \newline
T(n) & = 2n(n + 1) + (5n + 1) + 2 & \text{Before simplification (-.-|||)} \newline
& = 2n^2 + 7n + 3 \newline
T(n) & = n^2 + n & \text{Simplified count (o.O)}
T(n) & = n^2 + n & \text{After simplification (o.O)}
\end{aligned}
$$