nulldata

DP Analytics, a well-known analytics company came up with an interestingly logical written interview test.

Question:

2xx2 = 4
2xx3 = 16
2xx4 = 65536 = 2^16
3xx2 = 27
3xx3 = 7625597484987 = 3^27
4x3 = 64
2xxx3 = 65536
2xxx3 = 2xxx4

In general,
MxxN = M^M^M^....^M for N times
MxxxN = MxxMxxMxx.....xxM (N times)
and so on

Let the symbol 'x' be represented by a computer function 'T'. The inputs to 
'T' function are(left number, number of x, right number). so,

T(2,2,2)=4
T(2,2,3)=16
T(2,4,3)=T(2,3,4)

 
def T(m,t,n):
 
    if t == 1:
        result = m ** n
        return result
    n = n + (t-2)  
    result = m    
    while(n>1):
        result = m ** result
        n = n-1
    return result
 
print T(3,2,3)
print T(2,2,3)
print T(4,1,3)
 

Understanding: For t=2, N-1 is the number of times M must be raised to the power of itself (eg: when N is 2, then M ^ M and when N is 3, then M ^ M ^ M) We built a logic that is only valid for xx hence if the number of x is greater than two then it is brought down to 2 and N is incremented by the same count, and when x is one, M ^ N is the actual result. Happy Coding!