Codewars Test Tasks

#######################Sum of Intervals########################## Write a function called sumIntervals/sum_intervals() that accepts an array of intervals, and returns the sum of all the interval lengths. Overlapping intervals should only be counted once.

Intervals Intervals are represented by a pair of integers in the form of an array. The first value of the interval will always be less than the second value. Interval example: [1, 5] is an interval from 1 to 5. The length of this interval is 4.

Overlapping Intervals List containing overlapping intervals:

[ [1,4],

[7, 10],

[3, 5] ]

The sum of the lengths of these intervals is 7. Since [1, 4] and [3, 5] overlap, we can treat the interval as [1, 5], which has a length of 4.

Examples:

sumIntervals( [

[1,2],

[6, 10],

[11, 15]

] ); // => 9

sumIntervals( [

[1,4],

[7, 10],

[3, 5]

] ); // => 7

sumIntervals( [

[1,5],

[10, 20],

[1, 6],

[16, 19],

[5, 11]

] ); // => 19

####################### Playing with digits ########################################## Some numbers have funny properties. For example:

89 --> 8¹ + 9² = 89 * 1

695 --> 6² + 9³ + 5⁴= 1390 = 695 * 2

46288 --> 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51

Given a positive integer n written as abcd... (a, b, c, d... being digits) and a positive integer p

we want to find a positive integer k, if it exists, such as the sum of the digits of n taken to the successive powers of p is equal to k * n. In other words:

Is there an integer k such as : (a ^ p + b ^ (p+1) + c ^(p+2) + d ^ (p+3) + ...) = n * k

If it is the case we will return k, if not return -1.

Note: n and p will always be given as strictly positive integers.

digPow(89, 1) should return 1 since 8¹ + 9² = 89 = 89 * 1

digPow(92, 1) should return -1 since there is no k such as 9¹ + 2² equals 92 * k

digPow(695, 2) should return 2 since 6² + 9³ + 5⁴= 1390 = 695 * 2

digPow(46288, 3) should return 51 since 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51