UVA679 Dropping Balls [두 갈래 나무 결점 번호]

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, either false 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 the false 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 Ith ball being dropped. You may assume the value of I will 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: 
\begin{displaymath}2\le D\le 20,\mbox{ and } 1\le I\le 524288.\end{displaymath} Input  Contains l+2 lines. Line 1 I the number of test cases  Line 2 $D_1\I_1$ test case #1, two decimal numbers that are separatedby one blank  ...   Line k+1 $D_k\I_k$ test case #k  Line l+1 $D_l\I_l$ 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  5 4 2 3 4 10 1 2 2 8 128
-1
Sample Output  12 7 512 3 255 Miguel Revilla 
2000-08-14
제목 대의: 깊이가 D인 완전한 두 갈래 나무를 주고 노드 번호는 위에서 아래로 왼쪽에서 오른쪽으로 하나, 둘, 셋, 넷...
결점 1 위에 있는 작은 공이 한 결점에 떨어지면 그 점의 스위치가 바뀐다.켜야 한다면
왼쪽으로 가라, 그렇지 않으면 오른쪽으로 가라, 너에게 I개의 공을 주고, 마지막 공이 마지막으로 떨어질 수 있는 잎 번호를 물어라.
사고방식: 매 결점에서 첫 번째 작은 공은 왼쪽 나무에 떨어지고 짝수 작은 공은 오른쪽 나무에 떨어진다.
마지막 작은 공에 대해 직접 판단하면 된다.만약 I가 이 결점 홀수라면, 그것은 왼쪽으로 가는 첫 번째 (I+1)/2개의 작은 공이다.
짝수라면 오른쪽으로 가는 I/2개의 작은 공이다.

#include<stdio.h>
#include<string.h>

int main()
{
    int D,I,N;
    while(~scanf("%d",&N) && N!=-1)
    {
        while(N--)
        {
            int k = 1;
            scanf("%d%d",&D,&I);
            for(int i = 1; i < D; i++)
            {
                if(I&1)
                {
                    k <<= 1;
                    I = (I+1)>>1;
                }
                else
                {
                    k = (k<<1|1);
                    I >>= 1;
                }
            }
            printf("%d
",k);
        }
    }

    return 0;
}