Given a string which contains lower alphabetic characters, we need to find out such a substring of this string whose product of length and frequency in string is maximum among all possible choices of substrings.
Input : String str = “abddab” Output : 6 All unique substring with product of their frequency and length are, Val["a"] = 2 * 1 = 2 Val["ab"] = 2 * 2 = 4 Val["abd"] = 1 * 3 = 3 Val["abdd"] = 1 * 4 = 4 Val["abdda"] = 1 * 5 = 5 Val["abddab"] = 1 * 6 = 6 Val["b"] = 2 * 1 = 2 Val["bd"] = 1 * 2 = 2 Val["bdd"] = 1 * 3 = 3 Val["bdda"] = 1 * 4 = 4 Val["bddab"] = 1 * 5 = 5 Val["d"] = 2 * 1 = 2 Val["da"] = 1 * 2 = 2 Val["dab"] = 1 * 3 = 3 Val["dd"] = 1 * 2 = 2 Val["dda"] = 1 * 3 = 3 Val["ddab"] = 1 * 4 = 4 Input : String str = “zzzzzz” Output : 12 In above string maximum value 12 can be obtained with substring “zzzz”
A simple solution is to consider all substrings one by one. For every substring, count number of occurrences of it in whole string.
An efficient solution to solve this problem by first constructing longest common prefix array, now suppose value of lcp[i] is K then we can say that i-th and (i+1)-th suffix has K length prefix in common i.e. there is a substring of length K which is repeating twice. In the same way, let three consecutive values of lcp are (K, K-2, K+1) then we can say that there is a substring of length (K-2) which is repeating three times in the string.
Now after above observation, we can see that our result will be such a range of lcp array whose smallest element times number of elements in the range is maximum because range will correspond to the frequency of string and smallest element of range will correspond to length of repeating string now this reformed problem can be solved similar to largest rectangle in histogram problem.
In below code lcp array is constructed by Kasai’s algorithm.
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- Frequency of a substring in a string
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- Length of the longest valid substring
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