Tree-like array "Template 1"

Title Description

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

1. Add a number to the X

2. Find out the amount of each number in a range and

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 row contains 3 integers for each row, indicating an operation, as follows:

Action 1: Format: 1 x k Meaning: Add x number plus K

Action 2: Format: 2 x y meaning: the and of each number in the output interval [x, y]

Output format:

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

input/Output sampleInput Sample

5 51 5 4 2 31 1 32 2 51 3-11 4 22 1 4

Output Sample

1416

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:

Therefore, the output results 14, 16

Explain:

Why use a tree-like array? Ask a few questions first:

1. Give a series, several operations, each operation of the required number plus a number (that is, the number modified)

We use an array, O (1) can do

2. Give a series of series, several operations, each operation to the requirements of the interval and to find out

This is also simple, using the prefix and finish preprocessing, O (1) can also be done

But what about both the modification and the prefix?

Also as described above, each time we modify the prefix and will be re-updated, multiple operations down, will be very time-consuming

So, a magical approach arises--a tree-like array

It is good at a lowbit operation, and then modifies the single point at the same time, in a magical way, quickly updated the interval and

Specific explanation of reference materials

Code

#include <stdio.h>Const intmx=500001;intA[MX],C[MX];intn,m;intLowbit (intx) {    returnx&-x;}voidAddintXinttx) {     for(inti=x;i<=n;i+=lowbit (i)) {C[i]+=TX; }}intAskintx) {    inttot=0;  for(inti=x;i;i-=lowbit (i)) tot+=C[i]; returntot; }intMain () {scanf ("%d%d",&n,&m);  for(intI=1; i<=n;++i) {scanf ("%d",&A[i]);    Add (I,a[i]); }             while(m--){        intKiss; scanf ("%d",&kiss); if(kiss==1){            intKis,jia; scanf ("%d%d",&kis,&Jia);        Add (Kis,jia); }        Else if(kiss==2){            intL,r; scanf ("%d%d",&l,&R); printf ("%d\n", ask (R)-ask (l1)); }    }    return 0;}

Tree-like array "Template 1"