An interview question from MicroStrategy

去年校招时的一道面试题，觉得蛮有意思，贴出来。

Question:

Spy start at a, during an interval he moves |b| to right when b >=0; moves |b| to left when b <0; I can ask the spy if he is in position x, if he is then I win.

Answer:

Here is how I analyze this problem:

1) First assume a = 0; then b could be 0, 1, 2….

i. |b| = 0 , I can guess 0 at first interval just caught the spy;

ii. |b| = 1 , then b could be 1 or -1, so I can guess 1 at first interval ; if not caught the spy, guess -2 at second interval and I will catch the spy;

iii. |b| = 2 , then b could be 2 or -2, so I can guess 2 at first interval ; if not caught the spy, guess -4 at second interval and I will catch the spy;

iv. ……

To sum it up ,I will take this list to catch the spy with n intervals,n start at 1:

0*1, 1*2, (-1)*3, (2)*4, (-2)*5, 3*6, (-3)*7, 4*8, (-4)*9 …… ((n/2)(-1)^n)*n;

2) But |a| can have many values not only zero ,when a=0,this is one-dimensional problem. We can regard (a, b) as a point in a Plane coordinate system .

　　

This make the (a,b) in many squares, and we find the spy’s location from the most inside square to outside, and in every square we start at the point(|a|,0) as the red point showed in the picture. The same to the first problem is the time interval increases in Linear growth. And we can use the point’s value to calculate the location referenced to the point ,and can get the spy.

For example
1) (0,0): 0 + 0*1(this is the number of intervals);

2) (1,0): 1+ 0*2; (1,1): 1+ 1*3; (0,1): 0+ 1*4; (-1,1): -1+ 1*5……

3) As the picture shows;