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.
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.
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
【题意】给出n个数,求其在第一个数到最后一个的过程中,最小的逆序数是多少
【思路】建立一颗空树,在插入每个数的时候,统计这个数前面有多少数大于他,当a[i]由第一个变为最后一个时,要加上a[i]后面大于a[i]的数的个数,有n-1-a[i]个,要减去a[i]后面小于a[i]的数的个数,有a[i]个(注意i是从0开始的)
#include<iostream> #include<string.h> #include<stdio.h> using namespace std; const int N=5005; struct node { int l,r; int num; }tree[N*4]; void build(int k,int l,int r)//建空树 { int mid=(l+r)/2; tree[k].l=l; tree[k].r=r; tree[k].num=0; if(l==r) return ; build(k*2,l,mid); build(k*2+1,mid+1,r); } void updata(int k,int c)//插入 { if(tree[k].l==c&&tree[k].r==c) { tree[k].num=1; return ; } int mid=(tree[k].l+tree[k].r)/2; if(c<=mid) updata(k*2,c); else updata(k*2+1,c); tree[k].num=tree[k*2].num+tree[k*2+1].num; } int get_sum(int k,int c,int n)//统计 { if(c<=tree[k].l&&tree[k].r<=n) return tree[k].num; else { int mid=(tree[k].l+tree[k].r)/2; int sum1=0,sum2=0; if(c<=mid) sum1=get_sum(k*2,c,n); if(n>mid) sum2=get_sum(k*2+1,c,n); return sum1+sum2; } } int main() { int n; while(scanf("%d",&n)>0) { int a[N]; build(1,0,n-1); int ans=0; for(int i=0;i<n;i++) { scanf("%d",&a[i]); ans+=get_sum(1,a[i]+1,n-1);
//每输入一个数时,检验一下先他输入的并比他大的数的个数,对于前面比他大的数来说,他是他们的逆序数 updata(1,a[i]); } int minx=ans; for(int i=0;i<n;i++) { ans=ans+n-2*a[i]-1; //当a[i]由第一个变为最后一个时,要加上a[i]后面大于a[i]的数的个数,有n-1-a[i]个,要 if(ans<minx) //减去a[i]后面小于a[i]的数的个数,有a[i]个(注意i是从0开始的) minx=ans; } printf("%d ",minx); } return 0; }
#include<iostream> #include<stdio.h> #include<string.h> #include<algorithm> using namespace std; const int N=100000+10; int a[N],b[N],c[N],ans[N]; int n,cnt,sum; int lowbit(int x) { return x&(-x); } int query(int x) { int res=0; x++; while(x<=n) { res+=c[x]; x+=lowbit(x); } return res; } void update(int x) { while(x)//对在他前且比他小的数,逆序数加1; { c[x]++; x-=lowbit(x); } } int main() { while(~scanf("%d",&n)) { memset(a,0,sizeof(a)); memset(c,0,sizeof(c)); int sum=0; for(int i=1;i<=n;i++) { scanf("%d",&a[i]); update(a[i]+1); sum+=query(a[i]+1); } int tmp=0,s=sum; for(int i=1;i<=n;i++) { tmp=sum-a[i]+(n-a[i]-1); sum=tmp; if(tmp<s) s=tmp; } printf("%d ",s); } return 0; }