Python solution for google code jam 2013 Round 1C - Problem B - Pogo: http://code.google.com/codejam/contest/2437488/dashboard#s=p1

Pogo.py

"""
    Used to solve google code jam 2013 Round 1C - Problem B - Pogo
    Owner: Jamie Xu - [email protected]
"""
import math
def Pogo():
    in_f = open('A-large.in', 'r')
    out_f = open('output.txt', 'w')
    num_of_case = int(in_f.readline().rstrip('\n'))
    for i in range(1, num_of_case+1):
        solve_case(in_f, out_f, i)
        
def solve_case(in_f, out_f, case_index):
    print "start handling case #{}".format(case_index)
    case_info = in_f.readline().rstrip('\n').split(" ")
    x, y = map(int, case_info)
    x_agg_steps, x_pas_steps, x_current_length = get_steps(math.fabs(x), 1)
    y_agg_steps, y_pas_steps, y_current_length = get_steps(math.fabs(y), x_current_length + 1)
    str = "E" * x_agg_steps + "N" * y_agg_steps + "WE" * x_pas_steps + "SN" * y_pas_steps
    # handle the negative case
    if x < 0:
        str = str.replace("E", "T").replace("W", "E").replace("T", "W")
    if y < 0:
        str = str.replace("S", "T").replace("N", "S").replace("T", "N")
    out_f.write("Case #{}: {}\n".format(case_index, str))

def get_steps(goal, step_length=1):
    """
        agg_steps goes toward the goal directly, with one more units than last step.
        pas_steps goes toward the goal by one unit at a time by using two steps as a combination, for example "SN" goes to N one unit.
    """
    init_length = step_length
    init_goal = goal
    if step_length == 1:
        agg_steps = int(math.sqrt(2*goal+0.25) - 0.5)
        pas_steps = int(goal - ((1+agg_steps)*agg_steps)/2)
        current_length = agg_steps
    else:
        agg_steps = 0
        while goal >= step_length:
            agg_steps = agg_steps + 1
            goal = goal - step_length
            step_length = step_length + 1
        pas_steps = int(init_goal - (init_length + step_length - 1) * agg_steps / 2)
        current_length = step_length - 1
    return (agg_steps, pas_steps, current_length)

if __name__ == '__main__':    
    Pogo()