Codeforces Round #656 (Div. 3)D. a-Good String【搜索】

it2023-09-26  64

题目

传送门 You are given a string s[1…n] consisting of lowercase Latin letters. It is guaranteed that n=2k for some integer k≥0.

The string s[1…n] is called c-good if at least one of the following three conditions is satisfied:

The length of s is 1, and it consists of the character c (i.e. s1=c); The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s1=s2=⋯=sn2=c) and the second half of the string (i.e. the string sn2+1sn2+2…sn) is a (c+1)-good string; The length of s is greater than 1, the second half of the string consists of only the character c (i.e. sn2+1=sn2+2=⋯=sn=c) and the first half of the string (i.e. the string s1s2…sn2) is a (c+1)-good string. For example: “aabc” is ‘a’-good, “ffgheeee” is ‘e’-good.

In one move, you can choose one index i from 1 to n and replace si with any lowercase Latin letter (any character from ‘a’ to ‘z’).

Your task is to find the minimum number of moves required to obtain an ‘a’-good string from s (i.e. c-good string for c= ‘a’). It is guaranteed that the answer always exists.

You have to answer t independent test cases.

Another example of an ‘a’-good string is as follows. Consider the string s=“cdbbaaaa”. It is an ‘a’-good string, because:

the second half of the string (“aaaa”) consists of only the character ‘a’; the first half of the string (“cdbb”) is ‘b’-good string, because: the second half of the string (“bb”) consists of only the character ‘b’; the first half of the string (“cd”) is ‘c’-good string, because: the first half of the string (“c”) consists of only the character ‘c’; the second half of the string (“d”) is ‘d’-good string. Input The first line of the input contains one integer t (1≤t≤2⋅104) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1≤n≤131 072) — the length of s. It is guaranteed that n=2k for some integer k≥0. The second line of the test case contains the string s consisting of n lowercase Latin letters.

It is guaranteed that the sum of n does not exceed 2⋅105 (∑n≤2⋅105).

Output For each test case, print the answer — the minimum number of moves required to obtain an ‘a’-good string from s (i.e. c-good string with c= ‘a’). It is guaranteed that the answer exists.

输入 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac 输出 0 7 4 5 1 1

题意:额,这题的题意不太好描述,定义一个串为‘a’-good,当且仅当前n/2个字符为a且后半个串为‘b’good,或后n/2个字符为a且前半个串为‘b’good,依次往下推,具体还是应该看题…,你可以改动字符串中的字符为任意一个小写字母,问:最少操作多少次可以使串为‘a’-good;

思路:本来是想用贪心来着,但后来想了想不对,参考大佬的博客之后发现还是应该用搜索

AC code

#include<iostream> #include<algorithm> #include<cstring> #include<cmath> #include<sstream> #include<queue> #include<stack> #include<vector> #define inf 0x3f3f3f3f using namespace std; string a; int solve(int l,int r,char q) { if(l==r)return a[l]!=q; int mid=(l+r)/2; int s1=0,s2=0; for(int i=l;i<=mid;i++) if(a[i]!=q)s1++; for(int i=mid+1;i<=r;i++) if(a[i]!=q)s2++; return min(s1+solve(mid+1,r,q+1),s2+solve(l,mid,q+1)); } int main() { ios::sync_with_stdio(0); int t; cin>>t; while(t--) { int n; cin>>n; cin>>a; a=" "+a; cout<<solve(1,n,'a')<<endl; } }
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