MO Team algorithm [country training team] small Z Socks

Topic Link Windam https://www.luogu.org/problemnew/show/P1494

Probably say what you understand.

The formula for calculating the probability first∑c ( 2,f (i ) )  /  c (2< Span id= "mathjax-span-89" class= "Mo" >,r l+ 1)    f (i) is the number of socks for each color in the interval

The last formula to be introduced is ∑f (i) *f (i)-(R? L+1)/C(2,r? ) L+1) (I don't know how to push it.) given by others);

The mere violence does not say O (n*n*n);

The Next and O (n*n);

Mo team is O (n*sqrt (n));

O (n*n) algorithm has two kinds of one is [l,r] interval with a small skill from the beginning to the end of the ans=10;

See the first 1 of us + 0; See the second 1 of US +1;-0; 31st; +3;-1;

every time ans1=ans1-sum[a[j]]* (sum[a[j]]-1);   sum[a[j]]++;   ans1=ans1+sum[a[j]]* (sum[a[j]]-1); The team also has this technique .

The second is the interval transfer from [A, b] to [P, Q] a-〉p b-q; Slightly smaller than O (n*n) According to the pre-order;

MO Team Algorithm

Each interval transfer can transfer n number

Mo team divides (1-n) into sqrt blocks each shift in each block up to sqrt (n) +n so finally sqrt (n) * (N+SQRT (n));

#include <bits/stdc++.h>#defineint long Longusing namespacestd;Const intmaxn=5e4+Ten;intN,m,unit,ans;intCOL[MAXN],BE[MAXN],SUM[MAXN];structMo {intL,r,id,a,b;} Q[MAXN];intSintx) {returnx*x;}BOOLCMP (Mo A,mo b) {returnbe[a.l]==be[b.l]?a.r<b.r:a.l<B.L;}BOOLCMP (Mo A,mo b) {returna.id<b.id;}voidRevise (intXintadd) {ans-=S (Sum[col[x]]); SUM[COL[X]]+=add; Ans+=S (Sum[col[x]]);} int32_t Main () {CIN>>n>>m; unit=sqrt (n);  for(intI=1; i<=n;i++) cin>>col[i],be[i]=i/unit+1;  for(intI=1; i<=m;i++) cin>>q[i].l>>q[i].r,q[i].id=i; Sort (q+1, q+m+1, CMP); intL=1; intR=0;  for(intI=1; i<=m;i++)    {       //cout<<q[i].l<< "" <<q[i].r<<endl;         while(L&LT;Q[I].L) Revise (l,-1), l++;  while(L&GT;Q[I].L) Revise (l1,1), l--;  while(R&LT;Q[I].R) Revise (r+1,1), r++;  while(R&GT;Q[I].R) Revise (r,-1), r--; if(Q[I].L==Q[I].R) {Q[i]. A=0; Q[i]. b=1;Continue;} Q[i]. A=ans-(q[i].r-q[i].l+1); Q[i]. B= (q[i].r-q[i].l+1) * (q[i].r-Q[I].L); intC=__GCD (Q[i]. A,q[i]. B); Q[i]. A=q[i]. A/C; Q[i]. B=q[i]. b/C; } sort (Q+1, q+m+1, CMP);  for(intI=1; i<=m;i++) printf ("%lld/%lld\n", Q[i]. A,q[i].    B); return 0;}

MO Team algorithm [country training team] small Z Socks