Prefix sum Imagine a collection of items, like numbers, where the order of the items matters. The prefix sum operation works by calculating the sum of all e...
Prefix sum
Imagine a collection of items, like numbers, where the order of the items matters. The prefix sum operation works by calculating the sum of all elements in the collection starting from the first element.
Example:
Let's say we have the following collection: 1, 2, 3, 4, 5
The prefix sum would be:
1 + 2 + 3 + 4 + 5 = 15
Scan
In contrast to prefix sum, the scan operation works by iterating through the collection and adding each element to a running total.
Example:
Let's say we have the same collection and we want to calculate the sum using a scan operation.
The scan operation would be:
1 + 2 + 3 + 4 + 5 = 15
Difference between Prefix Sum and Scan
Prefix sum only considers elements from the start of the collection, while the scan operation considers all elements in the collection.
Applications of Prefix Sum and Scan
Prefix sum and scan operations are used in various algorithms, including:
Dynamic programming: To efficiently compute the sum of a subarray.
Sorting algorithms: To sort elements in ascending order by calculating their prefix sums.
Linear search: To find a specific element in a sorted collection by calculating the prefix sum of the collection.
Summary
Prefix sum is a technique for calculating the sum of a subcollection of elements, while scan is a technique for iterating through a collection and calculating the sum of each element