A substring of a string is a contiguous sequence of characters from the string. For example, BC
Question:
A substring of a string is a contiguous sequence of characters from the string. For example, BC is a substring of ABCD which starts from the second character of ABCD. Another example, ABC is a substring of ABCD which starts from the first character of ABCD. Note that ABCD itself is also a substring of ABCD.
In this problem, we define a special substring as a non-empty substring that contains only the same character. For example, B and CC are special substrings of ABBCCC, while ABBC and BC are not special substrings.
You are given a string S of length N and an integer K. Your task is to determine the minimum number of characters of S that need to be changed such that there exists a special substring of length K in S.
For example, let N = 6, K = 4, and S = ABBCCC. In this example, we only need to change the third character of S to C (i.e. ABBCCC → ABCCCC) so that we have a special substring CCCC of length 4.
Format Input
Input begins with a line containing two integers: N K (1 ≤ K ≤ N ≤ 100000) representing the length of the string and the length of a special substring that should be produced, respectively. The next line contains a string S containing N uppercase alphabetical character, i.e. Si ∈ [A-Z].
Format Output
Output in a line an integer representing the minimum number of characters of S that need to be changed such that there exists a special substring of length K in the given S.
Constraints
- 1 ≤ K ≤ N ≤ 100000
- S containing N uppercase alphabetical character, i.e. Si ∈ [A-Z].
Sample Input 1 (Standard Input)
6 4
ABBCCC
Sample Output 1 (Standard Output)
1
Sample Input 2 (Standard Input)
9 6
AABCABBBA
Sample Output 2 (Standard Output)
2
Sample Input 3 (Standard Input)
10 7
BAABAABAAB
Sample Output 3 (Standard Output)
2
Sample Input 4 (Standard Input)
6 2
INNCCC
Sample Output 4 (Standard Output)
0
Explanation:
Explanation for the sample input/output #1
This is the example from the problem description.
Explanation for the sample input/output #2
If we change the fourth and fifth characters of S to B, i.e. AABCABBBA → AABBBBBBA, then S will have a special substring of length 6 which is BBBBBB (AABBBBBBA). In this case, it is not possible to have a special substring of length 6 in S by changing fewer than 2 characters.
Explanation for the sample input/output #3
If we change the fourth and seventh characters of S to A, i.e. BAABAABAAB → BAAAAAAAAB, then S will have a special substring of length 7 which is AAAAAAA (either BAAAAAAAAB or BAAAAAAAAB). In this case, it is not possible to have a special substring of length 7 in S by changing fewer than 2 characters.
Explanation for the sample input/output #4
The string INNCCC already has a special substring of length 2, e.g., NN or CC.
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell