hdu 5122 K.Bro Sorting(单调栈)

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 ai (1 ≤ ai ≤ 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

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

solution：
根据题意，我们要找移动最少的回合数可以使得这个序列升序，那么我们可以维护一个单调上升的栈，即单调栈，退栈的次数和就是答案

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <map>
#include <set>
#include <queue>
#include <cmath>
#include <stack>
#include <vector>
#define CLR0(a) (memset(a,0,sizeof(a)))
#define CLR1(a) (memset(a,-1,sizeof(a)))
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
stack<int> S;
int main()
{
int T; cin >> T;
int ca = 1;
while (T--)
{
int n; scanf("%d", &n);
while (!S.empty())S.pop();
int x, ans = 0;
for (int i = 0; i < n; i++)
{
scanf("%d", &x);
while (!S.empty() && S.top()>x) { S.pop(); ans++; }
S.push(x);
}
printf("Case #%d: %d\n", ca++, ans);
}
return 0;
}