Ultraviolet A 679 dropping bils

Dropping bils

A numberKBils 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, eitherFalseOrTrue. Initially, all of the flags areFalse. When visiting a non-terminal node if the flag's current value at this node isFalse, Then the ball will first switch this flag's value, I. e., fromFalseToTrue, And then follow the left subtree of this node to keep moving down. Otherwise, it will also switch this flag's value, I. e., fromTrueToFalse, 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 beFalse, 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. obviusly, 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 isD, The maximum depth of FBT, and the second one isI,IThBall being dropped. You may assume the valueIWill not exceed the total number of leaf nodes for the given FBT.

Please write a program to determine the stop positionPFor each test case.

For each test cases the range of Two ParametersDAndIIs 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

I. A small ball falls down the odd number in a binary tree to the left when it reaches a node. Otherwise, I want to find the serial number of the last ball falling to the node at the bottom layer.

For the I-th ball at the root node, If I is an odd number, it is the (I + 1) to the left) /2 balls. If I is an even number, it is the nth ball to the right./2 balls.

For a node K, the number of its left subnode is 2 * K, and the number of the right subnode is 2 * k + 1. The result is obtained after I is updated to the bottom layer.

#include<cstdio>int main(){    int cas, ans, d, i;    while (scanf ("%d", &cas), cas + 1)    {        while (cas--)        {            ans = 1;            scanf ("%d%d", &d, &i);            while (--d)            {                if (i % 2)                    ans = ans * 2, i = (i + 1) / 2;                else                    ans = ans * 2 + 1, i = i / 2;            }            printf ("%d\n", ans);        }    }    return 0;}