Problem Description
This time, Chef has given you an array A containing N elements.
He had also asked you to answer M of his questions. Each question sounds like: "How many inversions will the array A contain, if we swap the elements at the i-th and the j-th positions?".
The inversion is such a pair of integers (i, j) that i < j and Ai > Aj.
Input
The first line contains two integers N and M - the number of integers in the array A and the number of questions respectively.
The second line contains N space-separated integers - A1, A2, ..., AN, respectively.
Each of next M lines describes a question by two integers i and j - the 1-based indices of the numbers we'd like to swap in this question.
Output
Output M lines. Output the answer to the i-th question of the i-th line.
Constraints
1 ≤ N, M ≤ 2 * 105
1 ≤ i, j ≤ N
1 ≤ Ai ≤ 109
Mind that we don't actually swap the elements, we only answer "what if" questions, so the array doesn't change after the question.
Example
Input:
6 3
1 4 3 3 2 5
1 1
1 3
2 5
Output:
5
6
0
Explanation
Inversions for the first case: (2, 3), (2, 4), (2, 5), (3, 5), (4, 5).
Inversions for the second case: (1, 3), (1, 5), (2, 3), (2, 4), (2,5), (4, 5).
In the third case the array looks like 1 2 3 3 4 5 and there are no inversions.
题解
tyvj《逆序对加强版》的加强版。同样的我们也考虑离线的做法。在那道题中,我们可以得到“修改一个点之后的逆序对”,这道题其实相当于同时改两个点。但要知道,每次交换算答案时要分情况讨论:当a[x]==a[y]和当a[x]!=a[y]时答案的计算是不一样的.
#include<cstdio> #include<cstring> #include<cstdlib> #include<iostream> #include<cmath> #include<algorithm> #define ll long long #define MAXN 200002 using namespace std; int n,m,a[MAXN],ha[MAXN],hs[MAXN],maxs,zz; struct qus{int l,r;} b[MAXN]; int lastl[MAXN],prel[MAXN],lastr[MAXN],prer[MAXN]; ll v[MAXN],cgl[MAXN],cgr[MAXN],tot,tr[MAXN]; void init() { scanf("%d%d",&n,&m); int i; for(i=1;i<=n;i++) {scanf("%d",&a[i]); ha[i]=a[i]; } sort(ha+1,ha+n+1); for(i=1;i<=n;i++) {if(ha[i]!=ha[i-1]) hs[++zz]=ha[i]; } for(i=1;i<=m;i++) {scanf("%d%d",&b[i].l,&b[i].r); prel[i]=lastl[b[i].l]; lastl[b[i].l]=i; prer[i]=lastr[b[i].r]; lastr[b[i].r]=i; } } int getw(int x) { int s=1,t=zz,mid; while(s<=t) {mid=(s+t)>>1; if(hs[mid]<x) s=mid+1; else t=mid-1; } return s; } int lowbit(int x) {return x&(-x);} ll find(int x) { ll sum=0; for(;x>0;x-=lowbit(x)) sum+=tr[x]; return sum; } void insert(int x) {for(;x<=zz;x+=lowbit(x)) tr[x]++;} void work() { int i,j,k,x,y; maxs=zz; for(i=1;i<=n;i++) {j=lastl[i]; k=lastr[i]; x=getw(a[i]); v[i]+=find(maxs)-find(x); tot+=v[i]; while(j) {y=getw(a[b[j].r]); cgl[j]+=find(maxs)-find(y); j=prel[j]; } while(k) {y=getw(a[b[k].l]); cgr[k]+=find(maxs)-find(y); k=prer[k]; } insert(x); } memset(tr,0,sizeof(tr)); for(i=n;i>0;i--) {j=lastl[i]; k=lastr[i]; x=getw(a[i]); v[i]+=find(x-1); while(k) {y=getw(a[b[k].l]); cgr[k]+=find(y-1); k=prer[k]; } while(j) {y=getw(a[b[j].r]); cgl[j]+=find(y-1); j=prel[j]; } insert(x); } for(i=1;i<=m;i++) {x=b[i].l; y=b[i].r; if(a[x]==a[y]) printf("%lld\n",tot); else printf("%lld\n",tot-v[x]-v[y]+cgl[i]+cgr[i]+1); } } int main() { init(); work(); return 0; }