Nearly EqualThe Hamming distance between two pairs of strings of equal length is defined to be the number of positions at which they contain different characters.For example, the Hamming distance between strings "there""there" and "shire""shire" is 22 (their first and third characters are different), while the Hamming distance between "order""order" and "chaos""chaos" is 55, since they differ at every position.Chef has a string 𝐴A of length 𝑁N.Chef's favorite string is 𝐵B, which has length 𝑀M. It is known that 𝑀≤𝑁M≤N.Find the minimum Hamming distance between 𝐵B and some contiguous substring†† of 𝐴A that has length 𝑀M.†† A substring of a string is obtained by deleting some (possibly, zero) characters from its beginning and some (possibly, zero) characters from its end.For example, "abc", "bc", and "cd" are substrings of "abcd", but "ac" is not.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of three lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝑀M — the lengths of strings 𝐴A and 𝐵B, respectively.The second line contains the string 𝐴A, consisting of 𝑁N lowercase English letters.The third line contains the string 𝐵B, consisting of 𝑀M lowercase English letters.Output FormatFor each test case, output on a new line the minimum possible Hamming distance between 𝐵B and some length 𝑀M substring of 𝐴A.Constraints1≤𝑇≤1001≤T≤1001≤𝑀≤𝑁≤1001≤M≤N≤100𝐴A and 𝐵B contain only lowercase English letters, i.e, the characters 'a' through 'z'.Sample 1:InputOutput45 3stormorz7 6orangesapples4 1ohnop9 4pinotnoirtari1412
Question
Nearly EqualThe Hamming distance between two pairs of strings of equal length is defined to be the number of positions at which they contain different characters.For example, the Hamming distance between strings "there""there" and "shire""shire" is 22 (their first and third characters are different), while the Hamming distance between "order""order" and "chaos""chaos" is 55, since they differ at every position.Chef has a string 𝐴A of length 𝑁N.Chef's favorite string is 𝐵B, which has length 𝑀M. It is known that 𝑀≤𝑁M≤N.Find the minimum Hamming distance between 𝐵B and some contiguous substring†† of 𝐴A that has length 𝑀M.†† A substring of a string is obtained by deleting some (possibly, zero) characters from its beginning and some (possibly, zero) characters from its end.For example, "abc", "bc", and "cd" are substrings of "abcd", but "ac" is not.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of three lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝑀M — the lengths of strings 𝐴A and 𝐵B, respectively.The second line contains the string 𝐴A, consisting of 𝑁N lowercase English letters.The third line contains the string 𝐵B, consisting of 𝑀M lowercase English letters.Output FormatFor each test case, output on a new line the minimum possible Hamming distance between 𝐵B and some length 𝑀M substring of 𝐴A.Constraints1≤𝑇≤1001≤T≤1001≤𝑀≤𝑁≤1001≤M≤N≤100𝐴A and 𝐵B contain only lowercase English letters, i.e, the characters 'a' through 'z'.Sample 1:InputOutput45 3stormorz7 6orangesapples4 1ohnop9 4pinotnoirtari1412
Solution
The problem is asking to find the minimum Hamming distance between a string B and any contiguous substring of string A that has the same length as B. The Hamming distance is the number of positions at which two strings of equal length differ.
Here are the steps to solve this problem:
- Read the number of test cases, T.
- For each test case, do the following: a. Read the lengths of strings A and B, N and M respectively. b. Read the strings A and B. c. Initialize a variable, minHamming, to a large value. d. For each substring of A that has the same length as B, do the following: i. Calculate the Hamming distance between the substring and B. ii. If this Hamming distance is less than minHamming, update minHamming with this value.
- Print minHamming, which is the minimum possible Hamming distance between B and some length M substring of A.
This algorithm works by checking all possible substrings of A that have the same length as B and finding the one that has the minimum Hamming distance to B. The time complexity of this algorithm is O(N^2) as it needs to check all substrings of A.
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