HDOJ5122 K.Bro Sorting(树状数组 & 模拟)

K.Bro Sorting

Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 1101    Accepted Submission(s): 492

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

255 4 3 2 155 1 2 3 4

 

Sample Output

Case #1: 4Case #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.
 

 

定义了一种新的排序，如果一个数比右边的大，就一直向右边移动，问你最少需要移动多少次。

AC代码(树状数组)：

#include "iostream"#include "cstdio"#include "cstring"#include "algorithm"using namespace std;const int MAXN = 1e6 + 5;int a[MAXN], b[MAXN], n;int lowbit(int x){return x & (-x);}void add(int x, int v){while(x <= n) {b[x] += v;x += lowbit(x);}}int get_sum(int x){int sum = 0;while(x > 0) {sum += b[x];x -= lowbit(x);}return sum;}int main(int argc, char const *argv[]){int t;scanf("%d", &t);for(int cas = 1; cas <= t; ++cas) {memset(a, 0, sizeof(a));memset(b, 0, sizeof(b));scanf("%d", &n);for(int i = 1; i <= n; ++i)scanf("%d", &a[i]);int ans = 0;for(int i = n; i >= 1; --i) {add(a[i], 1);int cur = get_sum(a[i] - 1);if(cur > 0) ans++;}printf("Case #%d: %d\n", cas, ans);}return 0;}

AC代码(模拟)：

#include "iostream"#include "cstdio"#include "cstring"#include "algorithm"using namespace std;const int MAXN = 1e6 + 5;int a[MAXN], n;int main(int argc, char const *argv[]){int t;scanf("%d", &t);for(int cas = 1; cas <= t; ++cas) {memset(a, 0, sizeof(a));scanf("%d", &n);for(int i = 1; i <= n; ++i)scanf("%d", &a[i]);int ans = 0;for(int i = n - 1; i >= 1; --i)if(a[i] > a[i + 1]) {ans++;swap(a[i], a[i + 1]);}printf("Case #%d: %d\n", cas, ans);}return 0;}