Counting common substrings effectively

Abstract

This article presents effective (dynamic) algorithm for solving a problem of counting the number of substrings of given string which are also substrings of second string. Presented algorithm can be used for example for quick calculation of strings similarity measure using generalized $n$-gram method (Niewiadomski measure), which are shown. Correctness and complexity analyses are included. ----- W artykule przedstawiono efektywny (dynamiczny) algorytm wyznaczaj\k{a}cy miar\k{e} podobie\'nstwa wyraz\'ow za pomoc\k{a} uog\'olnionej metody $n$-gram\'ow (miary Niewiadomskiego). Uzasadniono tak\.ze poprawno\'s\'c dzia{\l}ania algorytmu i oszacowano jego z{\l}o\.zono\'s\'c obliczeniow\k{a}.