This code will take as output any string (long, empty, with spaces...) and will return its reverse. Can I improve this algorithm so that it can be faster?

Right now its complexity is $O(n)$.

def reverse(stri):
 output = ''
 length = len(stri)
 while length > 0:
 output += stri[-1]
 stri, length = (stri[0:length - 1], length - 1)
 return output

Yes, this can be faster. Adding strings using + is usually a bad idea in Python, since strings are immutable. This means that whenever you add two strings, a new string needs to be allocated with the size of the resulting strings and then both string contents need to be copied there. Instead you usually want to build a list of strings and ''.join them at the end (where you pay this cost only once).

But here you can just use the fact that strings can be sliced and you can specify a negative step:

def reverse_g(s):
 return s[::-1]

Here is a timing comparison for random strings of length up to 1M characters, where reverse is your function and reverse_g is this one using slicing. Note the double-log scale, for the largest string your function is almost a hundred thousand times slower.

The reverse_s function uses the reversed built-in, as suggested in the answer by @sleblanc and assumes you actually need the reversed string and not just an iterator over it:

def reverse_s(s):
 return ''.join(reversed(s))

In terms of pure complexity, the answer is simple: No, it is not possible to reverse a string faster than O(n). That is the theoretical limit when you look at the pure algorithm.

However, your code does not achieve that because the operations in the loop are not O(1). For instance, output += stri[-1] does not do what you think it does. Python is a very high level language that does a lot of strange things under the hood compared to languages such as C. Strings are immutable in Python, which means that each time this line is executed, a completely new string is created.

If you really need the speed, you could consider writing a C function and call it from Python. Here is an example:

rev.c:

#include <stddef.h>
void reverse(char * stro, char * stri, size_t length) 
 for(size_t i=0; i<length; i++) stro[i]=stri[length-1-i];
 stro[length]='';

Compile the above function with this command:

gcc -o rev.so -shared -fPIC rev.c

And here is a python script using that function.

rev.py:

from ctypes import *

revlib = cdll.LoadLibrary("rev.so");
reverse = revlib.reverse
reverse.argtypes = [c_char_p, c_char_p, c_size_t]

hello = "HelloWorld"
stri = create_string_buffer(hello)
stro = create_string_buffer(b'00' * (len(hello)+1))

reverse(stro, stri, len(stri)-1)

print(repr(stri.value))
print(repr(stro.value))

Please note that I'm by no means an expert on this. I tested this with string of length 10⁸, and I tried the method from Graipher, calling the C function from Python and calling the C function from C. I used -O3 optimization. When I did not use any optimization it was slower to call the C function from Python. Also note that I did NOT include the time it took to create the buffers.

stri[::-1] : 0.98s
calling reverse from python : 0.59s
calling reverse from c: 0.06s

It's not a huge improvement, but it is an improvement. But the pure C program was WAY faster. The main function I used was this one:

int __attribute__((optimize("0"))) // Disable optimization for main
main(int argc, char ** argv) // so that reverse is not inlined

 const size_t size = 1e9;
 char * str = malloc(size+1);

 static const char alphanum[] =
 "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
 // Take data from outside the program to fool the optimizer 
 alphanum[atoi(argv[1])]='7';

 // Load string with random data to fool the optimizer 
 srand(time(NULL));
 for (size_t i = 0; i < size; ++i) 
 str[i] = alphanum[rand() % (sizeof(alphanum) - 1)];
 

 char *o = malloc(size+1);
 reverse(o, str, strlen(str));

 // Do something with the data to fool the optimizer 
 for(size_t i=0; i<size; i++) 
 if(str[i] != o[size-i-1]) 
 printf("Errorn");
 exit(1);
 

Then, to get the runtime I ran:

gcc -O3 -pg rev.c; ./a.out; gprof a.out gmon.out | head -n8

Here's a very short code I would use to reverse any string.

a = 'Coding is fun'

rev = print("Reverse of this statement is "+ a[::-1])