Algorithm for Human Towering

Question

In Cracking the Coding Interview, Fourth Edition, there is such a problem:

A circus is designing a tower routine consisting of people standing atop

Answer 1

Tried solving this myself, did not meant to give 'ready made solution', but still giving , more to check my own understanding and if my code(Python) is ok and would work of all test cases. I tried for 3 cases and it seemed to work of correct answer.

#!/usr/bin/python
#This function takes a list of tuples. Tuple(n):(height,weight) of nth person
def htower_len(ht_wt):
    ht_sorted = sorted(ht_wt,reverse=True)
    wt_sorted = sorted(ht_wt,key=lambda ht_wt:ht_wt[1])
    max_len = 1 

    len1 = len(ht_sorted)
    i=0
    j=0
    while i < (len1-1):
        if(ht_sorted[i+1][1] < ht_sorted[0][1]):
            max_len = max_len+1
        i=i+1           

    print "maximum tower length :" ,max_len

###Called above function with below sample app code.
testcase =1 
print "Result of Test case ",testcase   
htower_len([(5,75),(6.7,83),(4,78),(5.2,90)])

testcase = testcase + 1
print "Result of Test case ",testcase   
htower_len([(65, 100),(70, 150),(56, 90),(75, 190),(60, 95),(68, 110)])

testcase = testcase + 1
print "Result of Test case ",testcase   

htower_len([(3,2),(5,9),(6,7),(7,8)])