UVa679（Dropping Balls）（二叉树的编号）

  Dropping Balls 

A number of K balls are dropped one by one from the root of a fully binary tree structure FBT. Each time the ball being dropped first visits a non-terminal node. It then keeps moving down, either follows the path of the left subtree, or follows the path of the right subtree, until it stops at one of the leaf nodes of FBT. To determine a ball's moving direction a flag is set up in every non-terminal node with two values, eitherfalse or true. Initially, all of the flags are false. When visiting a non-terminal node if the flag's current value at this node is false, then the ball will first switch this flag's value, i.e., from thefalse to the true, and then follow the left subtree of this node to keep moving down. Otherwise, it will also switch this flag's value, i.e., from the true to the false, but will follow the right subtree of this node to keep moving down. Furthermore, all nodes of FBT are sequentially numbered, starting at 1 with nodes on depth 1, and then those on depth 2, and so on. Nodes on any depth are numbered from left to right.

For example, Fig. 1 represents a fully binary tree of maximum depth 4 with the node numbers 1, 2, 3, ..., 15. Since all of the flags are initially set to be false, the first ball being dropped will switch flag's values at node 1, node 2, and node 4 before it finally stops at position 8. The second ball being dropped will switch flag's values at node 1, node 3, and node 6, and stop at position 12. Obviously, the third ball being dropped will switch flag's values at node 1, node 2, and node 5 before it stops at position 10.

Fig. 1: An example of FBT with the maximum depth 4 and sequential node numbers.

Now consider a number of test cases where two values will be given for each test. The first value is D, the maximum depth of FBT, and the second one is I, the I^th ball being dropped. You may assume the value of Iwill not exceed the total number of leaf nodes for the given FBT.

Please write a program to determine the stop position P for each test case.

For each test cases the range of two parameters D and I is as below: 

Input 

Contains l+2 lines.

Line 1  I the number of test cases Line 2  test case #1, two decimal numbers that are separatedby one blank ...   Line k+1 test case #k Line l+1 test case #l Line l+2 -1  a constant -1 representing the end of the input file

Output 

Contains l lines.

Line 1  the stop position P for the test case #1 ...  Line k the stop position P for the test case #k ...  Line l the stop position P for the test case #l

Sample Input 

54 23 410 12 28 128-1

Sample Output 

1275123255

题意：有一个编号为1，2，3,...2^D-1的二叉树，D为最大深度。且所有叶子的深度都相同，也就是满二叉树。在结点1处放一个小球，

它会下落，每个内结点上都有一个开关，初始状态都为关闭，每次有小球落到开关上时，该开关状态就会改变。如果小球到达1个结点

时，该结点的开关关闭，则往左走，否则往右走，直到走到叶子结点。输出给定n个小球中第n个小球最终所在的叶子编号。

对于一个结点k，其左子结点，右子结点的编号分别是2k，2k+1.

如果使用题目中给的编号I，当I是奇数时，它是往左走的第（I+1）/2个小球，当I

是偶数时，它是往右走的第I/2个小球。可以直接模拟最后一个小球的路线。。。

#include<stdio.h> int main() { int test,m,n,k; while(scanf("%d",&test)&&test!=-1) { while(test--) { scanf("%d%d",&m,&n); k=1; for(int i=0;i<m-1;i++) { if(n%2) { k*=2,n=(n+1)/2;}else{k=2*k+1;n/=2;} }printf("%d\n",k); } } }