1394-Minimum Inversion Number
2024-09-27 00:12:39
Minimum Inversion Number
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 20162 Accepted Submission(s):
12110
Problem Description
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.
..., 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.
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.
single line.
Sample Input
10
1 3 6 9 0 8 5 7 4 2
1 3 6 9 0 8 5 7 4 2
Sample Output
16
Author
CHEN, Gaoli
逆序数的概念:在一个排列中,如果一对数的前后位置与大小顺序相反,即前面的数大于后面的数,那末它们就称为一个逆序。
一个排列中逆序的总数就称为这个排列的逆序数。
思路:先暴力求出开始时的逆序数,然后会有一个性质:每次把末尾的数掉到序列前面时,减少的逆序对数为n-1-a[i] ,增加的逆序对数为a[i] ,所以求出其他情况时的逆序数。
一个排列中逆序的总数就称为这个排列的逆序数。
思路:先暴力求出开始时的逆序数,然后会有一个性质:每次把末尾的数掉到序列前面时,减少的逆序对数为n-1-a[i] ,增加的逆序对数为a[i] ,所以求出其他情况时的逆序数。
#include<cstdio> int t[];
int n,ans,sum;
int main()
{
while (scanf("%d",&n)!=EOF)
{
sum = ;
for (int i=; i<=n; ++i)
scanf("%d",&t[i]);
for (int i=; i<n; ++i)
for (int j=i+; j<=n; ++j)
if (t[i]>t[j]) sum++;
ans = sum;
for (int i=n; i>=; --i)
{
sum -= n--t[i];
sum += t[i];
if (sum < ans) ans = sum;
}
printf("%d\n",ans);
}
return ;
}
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