Add motivation for data structure

jxu · web-flow · commit fa7282552de3 · 2022-07-11T00:50:35.000-04:00
diff --git a/src/data_structures/segment_tree.md b/src/data_structures/segment_tree.md
@@ -24,12 +24,11 @@ To start easy, we consider the simplest form of a Segment Tree.
 We want to answer sum queries efficiently. 
 The formal definition of our task is:
 We have an array $a[0 \dots n-1]$, and the Segment Tree must be able to find the sum of elements between the indices $l$ and $r$ (i.e. computing the sum $\sum_{i=l}^r a[i]$), and also handle changing values of the elements in the array (i.e. perform assignments of the form $a[i] = x$). 
-The Segment Tree should be able to process both queries in $O(\log n)$ time.
+If we computed each query naively, each query would take $O(n)$ time. The Segment Tree should be able to process both queries in $O(\log n)$ time.
 
 ### Structure of the Segment Tree
 
-So, what is a Segment Tree?
-
+We can take a divide-and-conquer approach when it comes to array segments. 
 We compute and store the sum of the elements of the whole array, i.e. the sum of the segment $a[0 \dots n-1]$. 
 We then split the array into two halves $a[0 \dots n/2]$ and $a[n/2+1 \dots n-1]$ and compute the sum of each halve and store them. 
 Each of these two halves in turn also split in half, their sums are computed and stored. 
