Software Engineer

A ComplexNumber class contains two data members: one is the real part (R) and the other is imaginary (I) (both integers).

Implement the Complex numbers class that contains the following functions -

1. constructor

You need to create the appropriate constructor.

2. plus -

This function adds two given complex numbers and updates the first complex number.

e.g.

if C1 = 4 + i5 and C2 = 3 +i1
C1.plus(C2) results in: 
C1 = 7 + i6 and C2 = 3 + i1

3. multiply -

This function multiplies two given complex numbers and updates the first complex number.

e.g.

if C1 = 4 + i5 and C2 = 1 + i2
C1.multiply(C2) results in: 
C1 = -6 + i13 and C2 = 1 + i2

4. print -

This function prints the given complex number in the following format :

a + ib

Note: There is space before and after '+' (plus sign) and no space between 'i' (iota symbol) and b.

You are walking on a street of length ‘N’. You want to light up the street by installing street lights.

There are 'M' streetlights and the 'ith' streetlight can be installed at position 'Ci'.

You are also given the range of the streetlights 'R' which means that the 'ith' streetlight installed at position 'Ci' will enlighten street from 'Ci-R' to 'Ci+R'.

Output the minimum number of street lights required to light up the whole street or output -1 if it is impossible to light the whole street under the given conditions.

It is sufficient to enlighten the integer positions, it is not required to enlighten the area between two integer positions.

For example : 'N' = 8, 'M' = 2, 'C' = [1, 6], 'R' = 2. The answer for this case is 2 as we can enlighten streetlight at position 1 and streetlight at position 6. These two will enlighten the positions 1, 2, 3, 4, 5, 6, 7, 8.

Example:-

N=10, M=3
C = [2,4,7] ( The positions of the streetlights )
R = 3 ( The range of the street-lights)


The answer will be 2 as we can install the first street light at position 2 so it illuminates the street from positions from 1 to 5 and the third street light at 7 so it illuminates the street from positions from 4 to 10.