線段樹之
求逆序數的方法: 1.直接暴力求解 2.線段樹求解 需要知道HASH(離散化)。//192和132逆序數是一樣的,所以可以對映到一樣的情況。 求逆序數的思路:遍歷每一個數字,如果這個數字前面有比它大的數字,那麼比它大的數字的個數即比他大的區間的sum值,例如a=5,它的逆序數即6-10的sum值。 例題:
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 本題思路:因為這個序列的數字是從0~n-1並且是沒有重複的數字,所以也就不需要離散化了,就遍歷輸入的序列即可,因為後面的序列的逆序數是ans-a[0]+n-a[n]-1;因為最前面的數字到了最後面,那麼假如n=10,a[0]=3,那麼在後面比它小的數字只有0、1、2,所以它到了最後面逆序數-3,而比它大的有3、4、5、6、7、8、9所以又多了6,之後以此類推。
//有問題。。。。 #include <cstdio> #include <iostream> #include <string.h> #define MAXSIZE 5005 using namespace std; int N; int number[MAXSIZE]; int mini[MAXSIZE]; int C; struct node{ int l,r; int sum; }tr[MAXSIZE<<2]; void build(int m,int l,int r); void pushup(int m); void update(int m,int index,int val);//單點更新 int query(int m,int l,int r);//區間查詢 int main(){ int cnt; while(~scanf("%d",&N)){ memset(tr,0,sizeof(tr)); C=0; cnt=0;//求這個點的逆序數 build(1,0,N-1);//建樹過程 for(int i=0;i<N;i++){ scanf("%d",&number[i]); update(1,number[i],1); if(number[i]+1<=N-1){//需要考慮是否越界 cnt+=query(1,number[i]+1,N-1); } } mini[C++]=cnt;//計算每個序列的逆序數 for(int i=0;i<N-1;i++){//意思是把number[i]移到序列最後面 mini[C]=mini[C-1]-number[i]+N-number[i]-1; C++; } int Min =100000000; for(int i=0;i<C;i++){ if(mini[i]<Min)Min = mini[i]; } printf("%d\n",Min); } return 0; } void pushup(int m){ tr[m].sum = tr[m<<1].sum+ tr[m<<1|1].sum; } void build(int m,int l,int r){ tr[m].l=l; tr[m].r=r; if(l==r){ tr[m].sum=0; return; } int mid = (l+r)>>1; build(m<<1,l,mid); build(m<<1|1,mid+1,r); pushup(m); } void update(int m,int index,int val){ if(tr[m].l==index&&tr[m].r==index){ tr[m].sum+=val; return; } int mid = (tr[m].r+tr[m].l)>>1; if(index>mid)update(m<<1|1,index,val); else if(index<=mid)update(m<<1,index,val); pushup(m); } int query(int m,int l, int r){ if(tr[m],l==l&&tr[m].r==r){ return tr[m].sum; } int mid =(tr[m].r+tr[m].l)>>1; int temp; if(r<=mid)temp = query(m<<1,l,r); else if(l>mid)temp = query(m<<1|1,l,r); else temp = query(m<<1,l,mid)+query(m<<1|1,mid+1,r); return temp; }