String sorting vs integer sorting

If I store integer in string then if I sort these string then will the time be same as when I will sort the number while storing them in int?

Actually I need to solve the question sorting bank accounts in spoj
And my approach is to store the ints in a string and sort them therefore I need to know whether its faster or not

Time taken to sort a list of strings will be O(length of longest string * size of list * log (size of list) ), which will be slower than sorting a list of integers, as strings won’t have to be compared.

That is assuming that you are using a O(n*log(n)) sorting algorithm.

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