HDU 1166 enemy deployment (tree array entry)

Tree array introduction:

The requirements for query and modification are similar. The complexity of logn can be achieved by using a tree array.

The array c Represented by the red rectangle is a tree array. here, C [I] indicates the sum of a [I-2 ^ k + 1] to a [I], and K indicates the number of 0 at the end of I in binary, or the smallest index when I is expressed by the power of 2.

The so-called K is also the height of the node in the tree.

Modify the I-th element. To maintain the meaning of array C, you need to modify all the ancestors of C [I] and C [I, instead of the node of the C [I] ancestor, modifications to the I-th element will not change. The ancestor has a total of "tree height-C [I] node height"

The difference between the [p, q] elements and can be calculated as [1, q], [1, p. Then the question is how to query the elements and values of a range [1, p], that is, evaluate s [p]. For the sum of the First N values of a series, you only need to find all the largest Subtrees before N and add the C values of the root nodes.
The key to implementing a tree array is to calculate the number K at the end of a binary number P (the smallest index when expressed by the power of 2 ). 2 ^ K is the distance between the pointer sliding when it is modified (and Statistics). We define this value as the lowbit of P.
More specifically, the lowbit of the positive integer p is the result of extracting the last 1 in the binary p.
For example, the lowbit of 23 (10111) is 1 (00001), and The lowbit of 20 (10100) is 4 (00100 ).

Lowbit (p) = P & (P ^ (p-1 ))

According to the signed integer complement rules, we can find that (P ^ (p-1) is exactly equal to-P, that is, the lowbit formula can be more concise:
Lowbit (p) = P &-P

Void plus (int x, int num) {While (x <= N) {C [x] + = num; x + = lowbit (x );}} int sum (int x) {int S = 0; while (x) {S + = C [X]; X-= lowbit (x);} return s ;} // enemy deployment # include <cstdio> # include <algorithm> # include <queue> # include <stack> using namespace STD; int t; int N; int A [500010]; int lowbit (int x) {return X & (-x);} void Update (int x, int num) {While (x <= N) {A [x] = A [x] + num; X = x + lowbit (x) ;}} int query (int x) {int ans = 0; while (x> 0) {ans + = A [X]; X-= lowbit (x);} return ans;} int main () {// freopen ("D: \ out.txt "," W ", stdout); int I, j, k; char STR [100], TMP [10]; scanf (" % d ", & T); k = 1; while (t --) {scanf ("% d", & N); memset (A, 0, sizeof ()); for (I = 1; I <= N; I ++) {scanf ("% d", & J); Update (I, j );} printf ("case % d: \ n", K ++); While (1) {scanf ("% s", STR ); if (STR [0] = 'E') break; scanf ("% d", & I, & J ); if (STR [0] = 'A') Update (I, j); If (STR [0] = 's') Update (I,-j ); // you can use the-number... if (STR [0] = 'q') printf ("% d \ n", query (j)-query (I-1); // note that this is a I-1, because tree arrays are closed intervals} return 0 ;}

HDU 1166 enemy deployment (tree array entry)