# Editing Prefix sum array and difference array

**Warning:** You are not logged in. Your IP address will be publicly visible if you make any edits. If you **log in** or **create an account**, your edits will be attributed to your username, along with other benefits.

The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.

Latest revision | Your text | ||

Line 1: | Line 1: | ||

− | Given an [[array]] of numbers, we can construct a new array by replacing each element by the difference between itself and the previous element, except for the | + | Given an [[array]] of numbers, we can construct a new array by replacing each element by the difference between itself and the previous element, except for the last element, which we simply ignore. This is called the '''difference array''', because it contains the first differences of the original array. We will denote the difference array of array <math>A</math> by <math>D(A)</math>. For example, the difference array of <math>A = [9, 2, 6, 3, 1, 5, 0, 7]</math> is <math>D(A) = [2-9, 6-2, 3-6, 1-3, 5-1, 0-5, 7-0]</math>, or <math>[-7, 4, -3, -2, 4, -5, 7]</math>. |

We see that the difference array can be computed in [[linear time]] from the original array, and is shorter than the original array by one element. Here are implementations in C and Haskell. (Note that the Haskell implementation actually takes a list, but returns an array.) | We see that the difference array can be computed in [[linear time]] from the original array, and is shorter than the original array by one element. Here are implementations in C and Haskell. (Note that the Haskell implementation actually takes a list, but returns an array.) |