Luogu P3368 "template" Tree array 2 [interval modification-single point query]

P3368 "template" Tree array 2 title description

Title, you need to perform the following two operations, known as a sequence:

1. Add x to each number of intervals

2. Find out the number of a

Input/output format Input Format:

The first line contains two integers n, M, respectively, indicating the number of numbers and the total number of operations.

The second line contains n space-delimited integers, where the I number represents the initial value of item I of a sequence.

The next M line contains 2 or 4 integers, representing an operation, as follows:

Action 1: Format: 1 x y k meaning: Add K to each number in the interval [x, y]

Action 2: Format: 2 x Meaning: output x number of values

output Format:

The output contains several line integers, which is the result of all Operation 2.

Input/Output sample Input Sample # #:

5 51 5 4 2 31 2 4 22 31 1 5-11 3 5 72 4

Sample # # of output:

610

Description

Time limit: 1000ms,128m

Data size:

For 30% data: n<=8,m<=10

For 70% data: n<=10000,m<=10000

For 100% data: n<=500000,m<=500000

Sample Description:

So the output is 6, 10

Solution

We define $c[i]$ to mean that $a[i]-a[i-1]$ is the distance between $a[i]$ and $a[i-1]$.
and rules $c[1]=a[1]$.
Then it's obvious.
$a [i-1]+c[i]=a[i]$
Let's put C in the tree-shaped array E.
# # Note E is a tree-like array!!!

Inquire

And then we can draw
$query (x) =\sum^{i<=x}_{i=1}c[i]$
$ =c[1]+c[2]+...+c[x-1]+c[x]$
$ = (A[1]) + (a[2]-a[1]) +...+ (a[x-1]-a[x-2]) + (A[x]-a[x-1]) $
$ =a[1]-a[1]+a[2]+...-a[x-2]+a[x-1]-a[x-1]+a[x]$
$ =a[x]$

Initial insert

Just start by inserting $c[i]$ (that is, $now-last$) into a tree-like array.

Modify

Because after giving $a[x]+z$
The distance between the $a [x]$ and $a[x-1]$ increased by Z, so we had to add $z$ to $a[x]-a[x-1]$ (ie $c[x]$)
Because after giving $a[y]+z$
The distance between the $a [y]$ and $a[y+1]$ decreased by Z, so we had to add $-z$ to $a[y]-a[y+1]$ (ie $c[y+1]$)
The middle $x<i<y$ don't have to deal with it?
Of course, because $c[i]$ save only $a[i] and a[i-1]$ distance Ah!

Codes

1  ProgramNo;2 var3 4 N,m,i,now,last,c,x,y,z:longint;5E:Array[1..500000] ofLongint;6 7 functionlowbit (apple:longint): Longint;8 begin9Lowbit:=apple and-Apple;Ten End; One  A procedureAdd (x,a:longint); - begin -      whileX<=n Do the      begin -e[x]:=e[x]+A; -x:=x+lowbit (x); -      End; + End; -  + functionquery (x:longint): Longint; A begin atquery:=0; -      whileX>0  Do -     begin -query:=query+E[x]; -x:=x-lowbit (x); -     End; in End; -  to begin +Assign (input,'1.in'); Assign (output,'1.out'); - reset (input); rewrite (output); the  * readln (n,m); $      fori:=1  toN DoPanax Notoginseng     begin - read (now); theAdd (i,now-Last ); +last:=Now ; A     End; the  +      fori:=1  toM Do -     begin $ read (c,x); $         ifC=1  Then -           begin - readln (y,z); the Add (x,z); -Add (y+1,-z);Wuyi           End the         Elsewriteln (query (x)); -     End; Wu  - close (input); Close (output); About End.

Luogu P3368 "template" Tree array 2 [interval modification-single point query]