Calculate Path Height Change Sum

Background

During a hike, you need to calculate the total sum of height changes along a path.

Problem Description

We have an array of heights, representing the altitude along a walking trail. Given start/end indexes into the array, return the sum of the changes for a walk beginning at the start index and ending at the end index, however increases in height count double. For example, with the heights $\{5, 3, 6, 7, 2\}$ and $start=2$, $end=4$ yields a sum of $1 imes 2 + 5 = 7$. The start and end index will both be valid indexes into the array with $start \le end$.

Input Format

The input is given from standard input in the following format.

heights: An integer array representing altitudes along the path. start: An integer, the starting index. end: An integer, the ending index.

Output Format

Output an integer to standard output in the following format.

sum: An integer, the calculated total sum of height changes.

Sample

[5 3 6 7 2] 2 4

7

[5 3 6 7 2] 0 1

2

[5 3 6 7 2] 0 4

15

Sample Explanation

For the first sample [5 3 6 7 2] 2 4:

• heights[2] = 6, heights[3] = 7, heights[4] = 2.
• From index $2$ to $3$: height increases from $6$ to $7$, change is $7 - 6 = 1$. Since it's an increase, it counts as $1 imes 2 = 2$.
• From index $3$ to $4$: height decreases from $7$ to $2$, change is $|2 - 7| = 5$. Since it's a decrease, it counts as $5$.
• Total sum is $2 + 5 = 7$.

Constraints

Time limit: 1s, Memory limit: 1024KiB.