2013
12-09

# Inversion

Let { A1,A2,…,An } be a permutation of the set{ 1,2,…, n}. If i < j and Ai > Aj then the pair (Ai,Aj) is called an "inversion" of the permutation. For example, the permutation {3, 1, 4, 2} has three inversions: (3,1), (3,2) and (4,2).
The inversion table B1,B2,…,Bn of the permutation { A1,A2,…,An } is obtained by letting Bj be the number of elements to the left of j that are greater than j. (In other words, Bj is the number of inversions whose second component is j.) For example, the permutation:
{ 5,9,1,8,2,6,4,7,3 }
has the inversion table
2 3 6 4 0 2 2 1 0
since there are 2 numbers, 5 and 9, to the left of 1; 3 numbers, 5, 9 and 8, to the left of 2; etc.
Perhaps the most important fact about inversions is Marshall Hall’s observation that an inversion table uniquely determines the corresponding permutation. So your task is to convert a permutation to its inversion table, or vise versa, to convert from an inversion table to the corresponding permutation.

The input consists of several test cases. Each test case contains two lines.
The first line contains a single integer N ( 1 <= N <= 50) which indicates the number of elements in the permutation/invertion table.
The second line begins with a single charactor either ‘P’, meaning that the next N integers form a permutation, or ‘I’, meaning that the next N integers form an inversion table.

For each case of the input output a line of intergers, seperated by a single space (no space at the end of the line). If the input is a permutation, your output will be the corresponding inversion table; if the input is an inversion table, your output will be the corresponding permutation.

9
P 5 9 1 8 2 6 4 7 3
9
I 2 3 6 4 0 2 2 1 0
0

2 3 6 4 0 2 2 1 0
5 9 1 8 2 6 4 7 3

1. for(int i=1; i<=m; i++){
for(int j=1; j<=n; j++){
dp = dp [j-1] + 1;
if(s1.charAt(i-1) == s3.charAt(i+j-1))
dp = dp[i-1] + 1;
if(s2.charAt(j-1) == s3.charAt(i+j-1))
dp = Math.max(dp [j - 1] + 1, dp );
}
}
这里的代码似乎有点问题？ dp(i)(j) = dp(i)(j-1) + 1;这个例子System.out.println(ils.isInterleave("aa","dbbca", "aadbbcb"));返回的应该是false

2. 学算法中的数据结构学到一定程度会乐此不疲的，比如其中的2－3树，类似的红黑树，我甚至可以自己写个逻辑文件系统结构来。

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