Created
September 18, 2019 06:33
-
-
Save anilpai/dd00a9671c062390c848952eaddbbe1e to your computer and use it in GitHub Desktop.
Currency Arbitrage using Bellman Ford Algorithm
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
from typing import Tuple, List | |
from math import log | |
rates = [ | |
[1, 0.23, 0.25, 16.43, 18.21, 4.94], | |
[4.34, 1, 1.11, 71.40, 79.09, 21.44], | |
[3.93, 0.90, 1, 64.52, 71.48, 19.37], | |
[0.061, 0.014, 0.015, 1, 1.11, 0.30], | |
[0.055, 0.013, 0.014, 0.90, 1, 0.27], | |
[0.20, 0.047, 0.052, 3.33, 3.69, 1], | |
] | |
currencies = ('PLN', 'EUR', 'USD', 'RUB', 'INR', 'MXN') | |
def negate_logarithm_convertor(graph: Tuple[Tuple[float]]) -> List[List[float]]: | |
''' log of each rate in graph and negate it''' | |
result = [[-log(edge) for edge in row] for row in graph] | |
return result | |
def arbitrage(currency_tuple: tuple, rates_matrix: Tuple[Tuple[float, ...]]): | |
''' Calculates arbitrage situations and prints out the details of this calculations''' | |
trans_graph = negate_logarithm_convertor(rates_matrix) | |
# Pick any source vertex -- we can run Bellman-Ford from any vertex and get the right result | |
source = 0 | |
n = len(trans_graph) | |
min_dist = [float('inf')] * n | |
pre = [-1] * n | |
min_dist[source] = source | |
# 'Relax edges |V-1| times' | |
for _ in range(n-1): | |
for source_curr in range(n): | |
for dest_curr in range(n): | |
if min_dist[dest_curr] > min_dist[source_curr] + trans_graph[source_curr][dest_curr]: | |
min_dist[dest_curr] = min_dist[source_curr] + trans_graph[source_curr][dest_curr] | |
pre[dest_curr] = source_curr | |
# if we can still relax edges, then we have a negative cycle | |
for source_curr in range(n): | |
for dest_curr in range(n): | |
if min_dist[dest_curr] > min_dist[source_curr] + trans_graph[source_curr][dest_curr]: | |
# negative cycle exists, and use the predecessor chain to print the cycle | |
print_cycle = [dest_curr, source_curr] | |
# Start from the source and go backwards until you see the source vertex again or any vertex that already exists in print_cycle array | |
while pre[source_curr] not in print_cycle: | |
print_cycle.append(pre[source_curr]) | |
source_curr = pre[source_curr] | |
print_cycle.append(pre[source_curr]) | |
print("Arbitrage Opportunity: \n") | |
print(" --> ".join([currencies[p] for p in print_cycle[::-1]])) | |
if __name__ == "__main__": | |
arbitrage(currencies, rates) | |
# Time Complexity: O(N^3) | |
# Space Complexity: O(N^2) |
manipulating source_curr in code is skipping few edges for negative cycle check.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
This results in seemingly impossible trips:
In everything except the first trip the starting and ending currencies are different. Can you please explain why this is happening?
Thanks