What is a Cumulative Array and How is it Defined?

Understanding Cumulative Array

Cumulative Array Definition: An array is said to be cumulative if each element from the second element onwards is equal to the sum of all the preceding elements, including itself.

Let's take the example of the array {1, 1, 2, 4, 8}. The first element is 1, which is only compared to itself. The second element is also 1, which is the sum of the first element and itself. The third element is 2, which is the sum of the first two elements (1 + 1). The fourth element is 4, which is the sum of the first three elements (1 + 1 + 2). Finally, the fifth element is 8, which is the sum of all preceding elements (1 + 1 + 2 + 4).

This pattern of each element being the sum of all preceding elements continues for each element in a cumulative array. This concept is important in various mathematical and computational problems where the cumulative nature of elements plays a crucial role in calculations and analysis.