HihoCoder genetic engineering

Original title link  http://hihocoder.com/problemset/problem/1052

Problems: to set length of the composition of N ATCG string S, solving the least number of changes, so that the K character sequence after the first K character sequence identity, where 1 <= K <= N

analysis:

1) for the same length of the two strings A and B, the character string you want two become the same, all changes only where Ai = Bi, so that Ai = Bi or Bi = Ai can!;

2) When K <= N / 2, the first K character sequence with the K character sequence is no intersection, thus according to a) can be treated;

3) When K> N / 2, the first K character sequence with the character sequence of K intersection exists, as shown below:

For convenience of description, taking m = n - k, the same as the first K character sequence with the sequence of characters to meet the K, S the element must satisfy the relationship shown below is equal to:

These constraints equivalence relation corresponds to the set S is divided into the following characters U0 = {S0, Sm, ..., Sj * m}, U1 = {S1, Sm + 1, ..., Sj * m + 1 }, ..., Ui = {Si, Sm + i ... Sj * m + i}, where i <m and Sj * m + i <N. For each set Ui, just keep the same characters appear most frequently to replace other characters into the character can be, you need to modify the number of times = total number of characters - Maximum number of characters appear. Obviously, when K> N / 2, may also be so treated, but this time each set contains only two elements Ui.

Rules are as follows:

1) successively through each set U0 = {S0, Sm, ..., Sj * m}, U1 = {S1, Sm + 1, ..., Sj * m + 1}, ..., Ui = { si, Sm + i ... Sj * m + i}, where i <min (m, k) and Sj * m + i <N

2) For each set, you need to modify the number of times = total number of characters - the maximum number of characters appear

3) the accumulated number of modifications required to each set

code show as below:

 1 def solve():
 2     T = int(input())
 3     for i in range(T):
 4         S = raw_input()
 5         K = int(raw_input())
 6         ret = do_solve(S.strip(" "), K)
 7         print(str(ret))
 8 
 9 
10 def do_solve(S, K):
11     ret = 0
12     step = len(S) - K
13     cnt = [0, 0, 0, 0]
14     for i in range(min(K, step)):
15         cnt[0] = cnt[1] = cnt[2] = cnt[3] = 0
16         j = i
17         while j < len(S):
18             if S[j] == 'A':
19                 cnt[0] = cnt[0] + 1
20             elif S[j] == 'T':
21                 cnt[1] = cnt[1] + 1
22             elif S[j] == 'C':
23                 cnt[2] = cnt[2] + 1
24             elif S[j] == 'G':
25                 cnt[3] = cnt[3] + 1
26             j += step
27         ret += sum(cnt) - max(cnt)
28     return ret
29 
30 
31 solve()