如何证明算法的正确性和运行时间？
例如，假设我要求证明算法的正确性和运行时间本质上是计算排序..我知道它在最坏的情况下运行O（n），但是idk如何证明正确性或证明运行时为O（n）。
问题：描述一种算法，在O（n）时间内对n个整数进行排序，每个整数的范围为[0..n4 - 1]。证明算法的正确性和运行时间。
工作：
Algorithm to sort n integers in the range [0..(n^4)-1] in O(n)
Use countSort with respect to the least significant digit
countSort with respect to the next least significant digit
Represent each int x in the list as its 4 digits in base n
let k = (n^4)-1 the max value in the range
Since values range from 0..k, create k+1 buckets
Iterate through the list and increment counter each time a value appears
Fill input list with the data from the buckets where each key is a value in the list
From smallest to largest key, add bucket index to the input array
Variables:
array: list of ints to be sorted
result: output array (indexes from 0..n-1)
n: length of the input
k: value such that all keys are in range 0..k-1
count: array of ints with indexes 0..k-1 (starts with all = 0)
x: single input value
total/oCount: control variables
total=0
for x in array
count[key of x] ++
for i < length of k-1
oCount = count[i]
count[i] = total
total += oCount
for x in array
result[count[key of x]] = x
count[key of x] ++
return result
该算法使用简单循环而不递归。初始化计数数组和计算数组上的和的中间for循环最多迭代k + 1次。 1是常数，因此需要O（k）。循环初始化结果数组和输入数组将花费O（n）时间。这些总计为O（n + k）时间。 k被认为是常数，因此最终运行时间为O（n）
我需要一些帮助才能指出正确的方向。谢谢！