2018/2/17 Daily One Learning tree array

Tree-like array

What is a tree-like array??

See

Where A[i] is a single element value, C[i] is a tree-like array.

It's not hard to find c[1]=a[1],c[2]=a[1]+a[2],c[3]=a[3]

where 1 = (01) 2, 2 = (10) 2,3= (11) 2

OK, we found C[i]=a[i-2<<k+1]+......+a[i] (k is the lowest bit in the I binary to the highest consecutive 0 numbers)

So, what is the way to quickly find out 2<<k?

Notice the binary (????) for a number of x. 100000 ... It is known that the number of 0 must be K. Then this 1 (and at the very end of 1) represents the decimal digit 2<<k.

Okay, so how do you find the 1 position??

Here we think of anti-code, bitwise take counter plus 1, pay attention to add one!!! Then there must be the original code at the end of the 1 corresponding binary location of the inverse code is also 1 (think, why?) ）

So 2<<k=x&-x, that's it. We resolved how to modify the C array.

So what does a tree-like array do?

Ask for the interval and!!

How can I ask?

For example, ask A[3]+......+a[6]

We use the prefix and the idea is to seek sum[6]-sum[2], then how to seek sum[x]?

Look at the code:

int sum (int  x) {int res=0;  while (x>0) res+=c[x],x-=x&-x; return Res;}

See while (x>0) res+=c[x],x-=x&-x; It is not difficult to find that sum is going from the current point to the left.

What if I want to make x+d?

Look at the code:

void Add (int x,int  d) {while (x<=n) c[x]+=d,x+=x&- x;}

See X+=x&-x, know is to go right.

Have you learned it?

2018/2/17 Daily One Learning tree array