Q:

Solution to Kickstart's Wiggle Walk

I'm trying to optimize my solution to Wiggle Walk for Kickstart's round 1C. 

Problem
Banny has just bought a new programmable robot. Eager to test his
  coding skills, he has placed the robot in a grid of squares with R
  rows (numbered 1 to R from north to south) and C columns (numbered 1
  to C from west to east). The square in row r and column c is denoted
  (r, c).
Initially the robot starts in the square (SR, SC). Banny will give the
  robot N instructions. Each instruction is one of N, S, E or W,
  instructing the robot to move one square north, south, east or west
  respectively.
If the robot moves into a square that it has been in before, the robot
  will continue moving in the same direction until it reaches a square
  that it has not been in before. Banny will never give the robot an
  instruction that will cause it to move out of the grid.
Can you help Banny determine which square the robot will finish in,
  after following the N instructions? 
Input
The first line of the input gives the number of test cases, T. T test
  cases follow. Each test case starts with a line containing the five
  integers N, R, C, SR and SC, the number of instructions, the number of
  rows, the number of columns, the robot's starting row and starting
  column, respectively.
Then, another line follows containing a single string of N characters;
  the i-th of these characters is the i-th instruction Banny gives the
  robot (one of N, S, E or W, as described above). 
Output
For each test case, output one line containing Case #x: r c, where x
  is the test case number (starting from 1), r is the row the robot
  finishes in and c is the column the robot finishes in. 
Limits
Memory limit: 1GB. 1 ≤ T ≤ 100. 1 ≤ R ≤ 5 × 104. 1 ≤ C ≤ 5 × 104. 1 ≤
  SR ≤ R. 1 ≤ SC ≤ C. The instructions will not cause the robot to move
  out of the grid. Test set 1 (Visible)
Time limit: 20 seconds. 1 ≤ N ≤ 100. Test set 2 (Hidden)
Time limit: 60 seconds. 1 ≤ N ≤ 5 × 104.

Here's my current solution:
def main():
    T = int(input())  # the number of test cases

    for case in range(1, T+1):
        N, R, C, r, c = map(int, input().split())
        instructions = input()  # string of N, S, E or W
        seen = {(r, c)}

        for i in instructions:
            if i == 'N':
                r -= 1
                while (r, c) in seen:
                    r -= 1
            elif i == 'S':
                r += 1
                while (r, c) in seen:
                    r += 1
            elif i == 'E':
                c += 1
                while (r, c) in seen:
                    c += 1
            else:  # 'W'
                c -= 1
                while (r, c) in seen:
                    c -= 1
            seen.add((r, c))

        print('Case #{}: {} {}'.format(case, r, c))

main()

How can I represent visited areas in the grid so that getting the destination cell for each instruction would be faster?

A:

A simple dictionary will do once you get the idea ;)
def get_neighbor(r, c, i, neighbors):
    if (r, c, i) in neighbors:
        return neighbors[(r, c, i)]

    if i == 'N':
        return (r - 1, c)
    elif i == 'S':
        return (r + 1, c)
    elif i == 'E':
        return (r, c + 1)
    else:  # 'W'
        return (r, c - 1)

def link_neighbors(r, c, neighbors):
    north = get_neighbor(r, c, 'N', neighbors)
    south = get_neighbor(r, c, 'S', neighbors)
    east = get_neighbor(r, c, 'E', neighbors)
    west = get_neighbor(r, c, 'W', neighbors)

    neighbors[(*north, 'S')] = south
    neighbors[(*south, 'N')] = north
    neighbors[(*east, 'W')] = west
    neighbors[(*west, 'E')] = east

def main():
    T = int(input())  # the number of test cases

    for case in range(1, T+1):
        N, R, C, r, c = map(int, input().split())
        instructions = input()  # string of N, S, E or W
        neighbors = {}

        for i in instructions:
            link_neighbors(r, c, neighbors)
            r, c = get_neighbor(r, c, i, neighbors)  # new position

        print('Case #{}: {} {}'.format(case, r, c))

main()

