xiaoxin juju needs help

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題意：給你一個字符串，求打亂字符后，有多少種回文串。????????????????????? （題于文末）

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知識點：

??? n個元素，其中a1，a2，····，an互不相同，進行全排列，可得n!個不同的排列。

??? 若其中某一元素ai重復了ni次，全排列出來必有重復元素，其中真正不同的排列數應為 ，即其重復度為ni!

??? 同理a1重復了n1次，a2重復了n2次，····，ak重復了nk次，n1+n2+····+nk=n。

??? 對于這樣的n個元素進行全排列，可得不同排列的個數實際上是

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題解：

字符串長度為len,若每個元素的重復次數ni為奇數的個數count>1,則無法形成回文串。

當能構成回文串時，我們只需考慮這個回文串左半部分的情況，所以這個問題也就變成了求一半字符串的有重復的全排列。

因為涉及到除法取模的問題，所以用到逆元。

逆元可以用擴展歐幾里得，或費馬小定理。/*6.逆元*/

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#include<iostream> #include<cstdio> #include<cstring> using namespace std; typedef long long LL; const LL MOD=1e9+7; int cnt[260]; char ch[1005];LL jiecheng(int n) {if(n==0)return 1;LL ans=1;for(int i=1;i<=n;i++)ans=ans*i%MOD;return ans; }LL x,y; LL gcd(LL a,LL b) {LL t,d;if(b==0){x=1,y=0;return a;}d=gcd(b,a%b);t=x, x=y, y=t-(a/b)*y;return d;}int main() {int t;cin>>t;while(t--){memset(cnt,0,sizeof(cnt));scanf("%s",ch);int len=strlen(ch);for(int i=0;i<len;i++){cnt[ch[i]-' ']++;}int count=0;for(int i=0;i<260;i++){if(cnt[i]&1)count++;cnt[i]/=2;}if(count>1){cout<<0<<endl;continue;}LL ans=jiecheng(len/2)%MOD;for(int i=0;i<260;i++){if(cnt[i]>0){gcd(jiecheng(cnt[i]),MOD);if(x<0)x+=MOD;ans=ans*x%MOD;}}cout<<ans<<endl;} }

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xiaoxin juju needs help

Time Limit:1000MS???? Memory Limit:65536KB???? 64bit IO Format:%I64d & %I64u

Submit Status

Description

As we all known, xiaoxin is a brilliant coder. He knew **palindromic** strings when he was only a six grade student at elementry school.
This summer he was working at Tencent as an intern. One day his leader came to ask xiaoxin for help. His leader gave him a string and he wanted xiaoxin to generate palindromic strings for him. Once xiaoxin generates a different palindromic string, his leader will give him a watermelon candy. The problem is how many candies xiaoxin's leader needs to buy?

Input

This problem has multi test cases. First line contains a single integer $T(T\leq 20)$ which represents the number of test cases.
For each test case, there is a single line containing a string $S(1 \leq length(S) \leq 1,000)$.

Output

For each test case, print an integer which is the number of watermelon candies xiaoxin's leader needs to buy after mod $1,000,000,007$.

Sample Input

3 aa aabb a

Sample Output

1 2 1

轉載于:https://www.cnblogs.com/shentr/p/5349489.html

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