Fréchet distance

import math
import numpy as np

#Euclidean distance
def euc_dist(pt1, pt2):
    return math.sqrt((pt2[0]-pt1[0])*(pt2[0]-pt1[0])+(pt2[1]-pt1[1])*(pt2[1]-pt1[1]))

def _c(ca,i,j,P,Q):  
    if ca[i,j] > -1:  
        return ca[i,j]  
    elif i == 0 and j == 0:  
        ca[i,j] = euc_dist(P[0],Q[0])  
    elif i > 0 and j == 0:  
        ca[i,j] = max(_c(ca,i-1,0,P,Q),euc_dist(P[i],Q[0]))  
    elif i == 0 and j > 0:  
        ca[i,j] = max(_c(ca,0,j-1,P,Q),euc_dist(P[0],Q[j]))  
    elif i > 0 and j > 0:  
        ca[i,j] = max(min(_c(ca,i-1,j,P,Q),_c(ca,i-1,j-1,P,Q),_c(ca,i,j-1,P,Q)),euc_dist(P[i],Q[j]))  
    else:  
        ca[i,j] = float("inf")  
    return ca[i,j]

def frechet_distance(P,Q):  
    ca = np.ones((len(P),len(Q)))  
    ca = np.multiply(ca,-1)  
    return _c(ca,len(P)-1,len(Q)-1,P,Q)

Algorithm:Computing Discrete Frechet Distance