K.Bro Sorting(思维题)

K.Bro Sorting

Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 3072    Accepted Submission(s): 1390

Problem Description

Matt’s friend K.Bro is an ACMer.

Yesterday, K.Bro learnt an algorithm: Bubble sort. Bubble sort will compare each pair of adjacent items and swap them if they are in the wrong order. The process repeats until no swap is needed.

Today, K.Bro comes up with a new algorithm and names it K.Bro Sorting.

There are many rounds in K.Bro Sorting. For each round, K.Bro chooses a number, and keeps swapping it with its next number while the next number is less than it. For example, if the sequence is “1 4 3 2 5”, and K.Bro chooses “4”, he will get “1 3 2 4 5” after this round. K.Bro Sorting is similar to Bubble sort, but it’s a randomized algorithm because K.Bro will choose a random number at the beginning of each round. K.Bro wants to know that, for a given sequence, how many rounds are needed to sort this sequence in the best situation. In other words, you should answer the minimal number of rounds needed to sort the sequence into ascending order. To simplify the problem, K.Bro promises that the sequence is a permutation of 1, 2, . . . , N .

Input

The first line contains only one integer T (T ≤ 200), which indicates the number of test cases. For each test case, the first line contains an integer N (1 ≤ N ≤ 10⁶).

The second line contains N integers a_i (1 ≤ a_i ≤ N ), denoting the sequence K.Bro gives you.

The sum of N in all test cases would not exceed 3 × 10⁶.

Output

For each test case, output a single line “Case #x: y”, where x is the case number (starting from 1), y is the minimal number of rounds needed to sort the sequence.

Sample Input

2

5

5 4 3 2 1

5

5 1 2 3 4

Sample Output

Case #1: 4

Case #2: 1

Hint

In the second sample, we choose “5” so that after the first round, sequence becomes “1 2 3 4 5”, and the algorithm completes.

Source

2014ACM/ICPC亚洲区北京站-重现赛（感谢北师和上交）

//题意:N 个数，要排序，用一种特殊的方法排，可以任意选择一个数，将它与右边的比较，如果大于右边的，就向右移动，直到小于。这样算移动一次，问用这种方法排序，最少要几次将数字排好序。

题解:从后向前遍历，如果比后面某个数要大，则说明一定需要一次来移动

 #include <iostream>
 #include <stdio.h>
 #include <string.h>
 using namespace std;
 #define MX 1000005
 int n;
 int num[MX];

 int main()
 {
     int T;
     cin>>T;
     for (int cnt=;cnt<=T;cnt++)
     {
         scanf("%d",&n);
         for (int i=;i<=n;i++)
             scanf("%d",&num[i]);
         int ans =;
         int mmm = num[n];
         for (int i=n-;i>=;i--)
         {
             if (num[i]>mmm)
                 ans++;
             else
                 mmm = num[i];
         }
         printf("Case #%d: %d\n",cnt,ans);
     }
     return ;
 }