在 Python 中计算欧几里得距离

Question

I am trying to calculate Euclidean distance in python using the following steps outlined as comments. It keeps on saying my calculation is wrong. I'm not sure why.

def euclidean_distance(vector1 , vector2):
    ## the sum_squares variable will contain the current value of the sum of squares of each i-th coordinate pair
    sum_squares = 0
    
    numberOfIterations = len(vector1)
    
    ## TODO: Complete loop below ## 
    
    # The number of times the loop will be executed is the length of the vectors.
    # 
    # At each loop iteration, you will:
    #  Step 1. index into each vector and find the difference between 
    #the ith element in vector2 and vector1 
    #  Step 2. square the difference
    #  Step 3. update the value of the 'sum_squares' variable by 
    #adding the result in Step 2 to 
    #          the existing value of sum_squares
    

    for i in range(numberOfIterations):
        
        # Inside this loop follow steps 1-3 to update the value of THE
        #'sum_squares' variable by adding the squared difference of the i'th coordinate pair to the sum.
        dist = ((vector2[0] - vector1[i]) **2 + (vector1[0] - vector2[i]) **2)
        sum_squares =  sum_squares + dist 
        

    ### TODO: Compute the Distance ###  
    
    # Compute the square root of the variable 'sum_squares' and assign 
    # that result to a new variable named 'distance'
    import math
    distance = math.sqrt(sum_squares)

    
    # return the Euclidean distance
    return distance

Answer 1

The problem is just with your code of calculating the distance.

#  Step 1. index into each vector and find the difference between 
#the ith element in vector2 and vector1 
#  Step 2. square the difference

Using these two steps, the correct line of code should be:

dist = (vector2[i] - vector1[i]) ** 2

This will square the distance between the i'th coordinate pair, and the next line will add it to the variable sum_squares

We can see that changing this line of code will give us the correct answer:

print(euclidean_distance([1,2],[2,3])) #1.414
print(euclidean_distance([1,2,3],[4,8,10])) #9.695

as:

sqrt( (2 - 1)^2 + (3 - 2)^2 ) = sqrt(2) = 1.414
sqrt( (4 - 1)^2 + (8 - 2)^2 + (10 - 3)^2 ) = sqrt(94) = 9.695

I hope this helped! Let me know if you need any further help or clarification :)

Answer 2

Iteration over the lists (vectors) is best achieved with zip() . Summation of the squares is best achieved with sum() . Therefore:

def euclidean_distance(vx, vy):
    return sum((y-x)**2 for x, y in zip(vx, vy)) ** 0.5

print(euclidean_distance([1,2,3,4],[4,8,10,12]))

Output:

12.569805089976535