Reorder the Books
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 244 Accepted Submission(s): 168
dxy puts these books in a book stack with the order of their numbers increasing from top to bottom. dxy takes great care of these books and no one is allowed to touch them.
One day Evensgn visited dxy's home, because dxy was dating with his girlfriend, dxy let Evensgn stay at home himself. Evensgn was curious about this series of books.So he took a look at them. He found out there was a story about "Little E&Little Q". While losing himself in the story,he disrupted the order of the books.
Knowing that dxy would be back soon,Evensgn needed to get the books ordered again.But because the books were too heavy.The only thing Evensgn could do was to take out a book from the book stack and and put it at the stack top.
Give you the order of the disordered books.Could you calculate the minimum steps Evensgn would use to reorder the books? If you could solve the problem for him,he will give you a signed book "The Stories of SDOI 9: The Story of Little E" as a gift.
There is an positive integer T(T≤30) in the first line standing for the number of testcases.
For each testcase, there is an positive integer n in the first line standing for the number of books in this series.
Followed n positive integers separated by space standing for the order of the disordered books,the ith integer stands for the ith book's number(from top to bottom).
Hint:
For the first testcase:Moving in the order of book3,book2,book1 , (4,1,2,3)→(3,4,1,2)→(2,3,4,1)→(1,2,3,4),and this is the best way to reorder the books.
For the second testcase:It's already ordered so there is no operation needed.
dxy家收藏了一套书,这套书叫《SDOI故事集》,《SDOI故事集》有n(n≤19)本,每本书有一个编号,从1号到n号。 dxy把这些书按编号从小到大,从上往下摞成一摞。dxy对这套书极其重视,不允许任何人动这套书。 有一天Evensgn到dxy家玩,dxy因为和妹子有约会,就让Evensgn自己待在他家。Evensgn对这套书非常好奇,偷偷的看了一下,结果发现这里面竟然有当年小E和小Q的故事。Evensgn看得出神,结果把一摞书的顺序打乱了。 眼看着dxy就要回来了,Evensgn需要尽快把这摞书恢复到原先排好序的状态。由于每本书都非常重,所以Evensgn能做的操作只有把一本书从书堆中抽出来,然后把这本书放到书堆的顶部。 给你打乱的书的顺序,你能帮Evensgn算算最少需要几次上述的操作,他才能把这套书恢复顺序?假如你能算出来的话,Evensgn答应送给你一本他签名的书《SDOI故事集9:小E的故事》
把这题的模型简化一下,有一个1→n的排列形成的数列,我们要用最少的操作次数把这个数列排序,每次操作都是把一个数放到整个数列的最前面。 首先我们可以注意到每个数最多只会被操作一次。因为假如有一个数被往前拿了两次,显然第一次的操作是没有意义的。 然后能发现一定先操作大的数,再操作小的数。因为假如先把小的数放前面去了,再把大的数放前面去,小的数就又在大的数后面了,小的数必定还得再操作一次,然而操作两次是不划算的。
到这里,对于19的数据范围,我们有一个很暴力的做法,2n枚举要操作哪些数,这些操作按数的大小从大往小的顺序,模拟一下,然后检查一下最后的序列是否有序,复杂度O(n∗2n)。
我们很快又能发现,假如操作了大小等于k的数,那么所有小于k的数也都得操作了。所以我们不用2^n枚举,直接m从1开始从小到大枚举,表示要操作前m小的数,然后模拟,验证,这样复杂度为O(n2)。
不过其实m也是不用枚举的。 首先可以发现最大的数n是不用操作的(其他数操作好了,数"n"自然就在最后面了)。 于是我们先找到最大的数"n"的位置,从这个位置往前找,直到找到(n−1)。假如找到头也没找到(n−1),那么数"(n−1)"需要操作,而一旦操作了(n−1),根据前面结论,总共就需要(n−1)次操作了;假如找到了(n-1),那么数"(n−1)"也不需要操作(和数"n"不需要操作一个道理)。 同理,我们接着从(n−1)的位置往前找(n−2),再从(n−2)的位置往前找(n−3)...假如数k找不到了,那么就至少需要k次操作。这种做法的复杂度是O(n)的
我的思路:
其实这个题并不是很难,几行代码就搞定了,关键是怎么想,我是想将输入的序列从后往前找,最开始Max == m, 如果arr[i] == Max的话,Max--,反正肯定是1 - m之间的数。所以我们只需要从后往前找,知道找不到为止。。
上代码:
#include <iostream> #include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include <vector> #include <queue> #include <algorithm> #include <set> #include <map> using namespace std; #define MM(a) memset(a,0,sizeof(a)) typedef long long LL; typedef unsigned long long ULL; const int maxn = 2*1e5+5; const int mod = 1000000007; const double eps = 1e-7; const double pi = 3.1415926; bool cmp(int a, int b) { return a > b; } int arr[25]; int main() { int t, m; cin>>t; while(t--) { cin>>m; for(int i=1; i<=m; i++) cin>>arr[i]; int Max = m; for(int i=m; i>=1; i--) { if(arr[i] == Max) Max--; } cout<<Max<<endl; } return 0; }