Python – Suffix Product in list

We are given a list of numbers, and our task is to compute the suffix product for each position in the list. The suffix product at any index is the product of all elements to the right, including the element at that index. For example, given a = [2, 3, 4, 5], the suffix products would be [120, 60, 20, 5]. Let’s discuss different ways in which we can compute suffix product in list in Python.

Using a Right-to-Left Traversal

We can compute the suffix product efficiently in a single pass by iterating from right to left and maintaining a running product.

# Initializing list  
a = [2, 3, 4, 5]  

# Storing length  
n = len(a)  

# Initializing suffix product list  
suffix = [1] * n  

# Computing suffix products  
for i in range(n - 2, -1, -1):  
    suffix[i] = suffix[i + 1] * a[i + 1]  

print(suffix)

[60, 20, 5, 1]

Explanation:

• We initialize a suffix list with 1s.
• We iterate from the second-last element to the start, multiplying by the next element in the list.

Using Prefix and Suffix Arrays

We can also use two auxiliary lists to store prefix and suffix products separately, then combine them.

# Initializing list  
a = [2, 3, 4, 5]  
n = len(a)  

# Initializing prefix and suffix lists  
prefix = [1] * n  
suffix = [1] * n  

# Computing prefix products  
for i in range(1, n):  
    prefix[i] = prefix[i - 1] * a[i - 1]  

# Computing suffix products  
for i in range(n - 2, -1, -1):  
    suffix[i] = suffix[i + 1] * a[i + 1]  

# Getting final suffix product by multiplying prefix and suffix  
result = [prefix[i] * suffix[i] for i in range(n)]  

print(result) 

[60, 40, 30, 24]

Explanation:

• The prefix array stores the product of all elements before each index.
• The suffix array stores the product of all elements after each index.
• The final suffix product is obtained by multiplying corresponding values in both arrays.

Using NumPy for Efficient Computation

NumPy provides an efficient way to compute suffix products using cumulative product functions.

import numpy as np  

# Initializing list  
a = np.array([2, 3, 4, 5])  

# Computing suffix product using cumprod  
suffix = np.cumprod(a[::-1])[::-1]  

print(suffix) 

[120  60  20   5]

Explanation:

• a[::-1] reverses the list.
• np.cumprod() computes cumulative products.
• The result is reversed again to match the correct order.

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Article Tags :

• Python
• Python Programs
• Python list-programs

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• python