hdu 1394 Minimum Inversion Number - 树状数组

Posted 2020-10-01 阿波罗2003

The inversion number of a given number sequence a1, a2, ..., an is the number of pairs (ai, aj) that satisfy i < j and ai > aj.  
For a given sequence of numbers a1, a2, ..., an, if we move the first m >= 0 numbers to the end of the seqence, we will obtain another sequence. There are totally n such sequences as the following:  
a1, a2, ..., an-1, an (where m = 0 - the initial seqence)  

a2, a3, ..., an, a1 (where m = 1) 

a3, a4, ..., an, a1, a2 (where m = 2)  

...  

an, a1, a2, ..., an-1 (where m = n-1)  
You are asked to write a program to find the minimum inversion number out of the above sequences. 

Input

The input consists of a number of test cases. Each case consists of two lines:

the first line contains a positive integer n (n <= 5000);

the next line contains a permutation of the n integers from 0 to n-1. 

Output

For each case, output the minimum inversion number on a single line. 

Sample Input

10
1 3 6 9 0 8 5 7 4 2

Sample Output

16

---

　　题目大意 求循环排列最小逆序对数。

　　老是刷cf，不做暑假作业估计会被教练鄙视，所以还是做做暑假作业。

　　先用各种方法算出原始序列的逆序对数。

　　显然你可直接算出把开头的一个数挪到序列后面增加的逆序对数。(后面有多少个比它大减去有多少个比它小)

　　于是这道题就水完了。

Code

  1 /**
  2  * hdu
  3  * Problem#1394
  4  * Accepted
  5  * Time: 62ms
  6  * Memory: 1680k
  7  */
  8 #include <iostream>
  9 #include <fstream>
 10 #include <sstream>
 11 #include <cstdio>
 12 #include <ctime>
 13 #include <cmath>
 14 #include <cctype>
 15 #include <cstring>
 16 #include <cstdlib>
 17 #include <algorithm>
 18 #include <map>
 19 #include <set>
 20 #include <list>
 21 #include <stack>
 22 #include <queue>
 23 #include <vector>
 24 #ifndef WIN32
 25 #define Auto "%lld"
 26 #else
 27 #define Auto "%I64d"
 28 #endif
 29 using namespace std;
 30 typedef bool boolean;
 31 const signed int inf = (signed)((1u << 31) - 1);
 32 const signed long long llf = (signed long long)((1ull << 61) - 1);
 33 const double eps = 1e-9;
 34 const int binary_limit = 256;
 35 #define smin(a, b) a = min(a, b)
 36 #define smax(a, b) a = max(a, b)
 37 #define max3(a, b, c) max(a, max(b, c))
 38 #define min3(a, b, c) min(a, min(b, c))
 39 template<typename T>
 40 inline boolean readInteger(T& u){
 41     char x;
 42     int aFlag = 1;
 43     while(!isdigit((x = getchar())) && x != ‘-‘ && x != -1);
 44     if(x == -1) {
 45         ungetc(x, stdin);    
 46         return false;
 47     }
 48     if(x == ‘-‘){
 49         x = getchar();
 50         aFlag = -1;
 51     }
 52     for(u = x - ‘0‘; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - ‘0‘);
 53     ungetc(x, stdin);
 54     u *= aFlag;
 55     return true;
 56 }
 57 
 58 #define lowbit(x) ((x) & (-x))
 59 
 60 typedef class IndexedTree {
 61     public:
 62         int* lis;
 63         int s;
 64         IndexedTree() {        }
 65         IndexedTree(int s):s(s) {
 66             lis    = new int[(s + 1)];
 67             memset(lis, 0, sizeof(int) * (s + 1));
 68         }
 69         
 70         inline void add(int idx, int val) {
 71             for(; idx <= s; idx += lowbit(idx))
 72                 lis[idx] += val;
 73         }
 74         
 75         inline int getSum(int idx) {
 76             int ret = 0;
 77             for(; idx; idx -= lowbit(idx))
 78                 ret += lis[idx];
 79             return ret;
 80         }
 81 }IndexedTree;
 82 
 83 int n;
 84 int* arr;
 85 inline boolean init() {
 86     if(!readInteger(n))    return false;
 87     arr = new int[(n + 1)];
 88     for(int i = 1; i <= n; i++)
 89         readInteger(arr[i]), arr[i] += 1;
 90     return true;
 91 }
 92 
 93 IndexedTree it;
 94 int ans, cmp;
 95 inline void solve() {
 96     ans = 10000000, cmp = 0;
 97     it = IndexedTree(n);
 98     for(int i = 1; i <= n; i++) {
 99         it.add(arr[i], 1);
100 //        cout << 1;
101         cmp += i - it.getSum(arr[i]);
102     }
103     ans = cmp;
104     for(int i = 1; i < n; i++) {
105         cmp -= arr[i] - 1, cmp += n - arr[i];
106         smin(ans, cmp);
107     }
108     printf("%d\n", ans);
109 }
110 
111 inline void clear() {
112     delete[] arr;
113     delete[] it.lis;
114 }
115 
116 int main() {
117     while(init()) {
118         solve();
119         clear();
120     }
121     return 0;
122 }