hdoj 5459 Jesus Is Here 【求公式 递推】
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Jesus Is Here
Time Limit: 1500/1000 MS (Java/Others) Memory Limit: 65535/102400 K (Java/Others)Total Submission(s): 87 Accepted Submission(s): 57
Problem Description
I've sent Fang Fang around 201314 text messages in almost 5 years. Why can't she make sense of what I mean?
``But Jesus is here!" the priest intoned. ``Show me your messages."
Fine, the first message iss1=‘‘c" and the second one is s2=‘‘ff" .
Thei -th message is si=si−2+si−1 afterwards. Let me give you some examples.
s3=‘‘cff" , s4=‘‘ffcff" and s5=‘‘cffffcff" .
``I found thei -th message's utterly charming," Jesus said.
``Look at the fifth message".s5=‘‘cffffcff" and two ‘‘cff" appear in it.
The distance between the first‘‘cff" and the second one we said, is 5 .
``You are right, my friend," Jesus said. ``Love is patient, love is kind.
It does not envy, it does not boast, it is not proud. It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs.
Love does not delight in evil but rejoices with the truth.
It always protects, always trusts, always hopes, always perseveres."
Listen - look at him in the eye. I will find you, and count the sum of distance between each two different‘‘cff" as substrings of the message.
``But Jesus is here!" the priest intoned. ``Show me your messages."
Fine, the first message is
The
``I found the
``Look at the fifth message".
The distance between the first
``You are right, my friend," Jesus said. ``Love is patient, love is kind.
It does not envy, it does not boast, it is not proud. It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs.
Love does not delight in evil but rejoices with the truth.
It always protects, always trusts, always hopes, always perseveres."
Listen - look at him in the eye. I will find you, and count the sum of distance between each two different
Input
An integer T (1≤T≤100) , indicating there are T test cases.
FollowingT lines, each line contain an integer n (3≤n≤201314) , as the identifier of message.
Following
Output
The output contains exactly T lines.
Each line contains an integer equaling to:
∑i<j:sn[i..i+2]=sn[j..j+2]=‘‘cff"(j−i) mod 530600414,
wheresn as a string corresponding to the n -th message.
Each line contains an integer equaling to:
where
Sample Input
956781131205199312199401201314
Sample Output
Case #1: 5Case #2: 16Case #3: 88Case #4: 352Case #5: 318505405Case #6: 391786781Case #7: 133875314Case #8: 83347132Case #9: 16520782
题意:给你两个初始串s1 = cff, s2 = ffcff。已知s[i] = s[i-2] + s[i-1]即串s[i-2] 后面接上串s[i-1],问你第N个串中所有字符c之间的距离之和。
一开始没看这道题,看了之后发现很简单。。。
思路:对每个串,我们用结构体Node保留四个信息——
串长度len,串中字符c的个数num,串中所有字符c的位置之和sum,串中所有字符c之间的距离之和ans。
我们可以得到公式
一、node[i].len = node[i-1].len + node[i-2].len;
二、node[i].num = node[i-1].num + node[i-2].num;
三、node[i].sum = node[i-1].sum + node[i-2].sum + node[i-2].len*node[i-1].num。
四、node[i].ans = node[i-1].ans + node[i-2].ans+(node[i-2].len*node[i-2].num-node[i-2].sum)*node[i-1].num+node[i-1].sum*node[i-2].num;
注意取余的操作,要不测试数据都过不了。
AC代码:
#include <cstdio>#include <cstring>#define MAXN 201314+1#define MOD 530600414#define LL long longstruct Node{ LL len, num, sum, ans;};Node node[MAXN];void getNode(){ node[3].len = 3, node[3].num = 1; node[3].sum = 1, node[3].ans = 0; node[4].len = 5, node[4].num = 1; node[4].sum = 3, node[4].ans = 0; for(int i = 5; i < MAXN; i++) { node[i].len = (node[i-1].len + node[i-2].len)%MOD; node[i].num = (node[i-1].num + node[i-2].num)%MOD; node[i].sum = (node[i-1].sum + node[i-2].sum+(node[i-2].len*node[i-1].num)%MOD)%MOD; node[i].ans = (node[i-1].ans + node[i-2].ans+(((node[i-2].len*node[i-2].num-node[i-2].sum)%MOD)*node[i-1].num)%MOD+(node[i-1].sum*node[i-2].num)%MOD)%MOD; }}int main(){ getNode(); int t, N, k = 1; scanf("%d", &t); while(t--) { scanf("%d", &N); printf("Case #%d: %lld\n", k++, node[N].ans); } return 0;}
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