What is a Prefix Sum Algorithm?
A prefix sum algorithm, also known as a cumulative sum algorithm, is a technique used to calculate the cumulative sum of an array. It is used to calculate the sum of the elements of an array up to a certain index.
For example, given an array A of size n, a prefix sum algorithm can calculate the cumulative sum of the elements in A and store it in a new array B such that B[i] = A[0] + A[1] + … + A[i].
How to Implement a Prefix Sum Algorithm
There are several ways to implement a prefix sum algorithm, but one of the simplest methods is to use a loop to iterate over the elements of the array and calculate the cumulative sum as we go.
Here’s an example implementation in Python:
def prefix_sum(A):
n = len(A)
B = [0] * n
B[0] = A[0]
for i in range(1, n):
B[i] = B[i-1] + A[i]
return B
A = [1, 2, 3, 4, 5]
print("Input array:", A)
print("Prefix sum array:", prefix_sum(A))
Output:
Input array: [1, 2, 3, 4, 5]
Prefix sum array: [1, 3, 6, 10, 15]
In this implementation, we start with the first element of the input array A and store it in the first element of the output array B. Then, we iterate over the rest of the elements in A and calculate the cumulative sum by adding the current element to the previous cumulative sum stored in B. Finally, we return the B array which contains the cumulative sum of the elements in A.
Conclusion
A prefix sum algorithm is a simple and efficient way to calculate the cumulative sum of an array. It can be used in various algorithms to perform tasks like searching, sorting, and string matching. By implementing a prefix sum algorithm in Python, you can easily take advantage of its benefits in your own programs.