Kata

We have the following function of two variables x, y (values of x, y are in determined ranges of values):

The function above is studied for x, y, positive integers, and x ≠ y.

⌊ ⌋ - represents the function floor and | | the absolute value.

In the image below there is 3D graph that may show some features of the function:

xmin = 0, xmax = 10 ; ymin = 0, ymax = 10 and zmax (the same value of hMax) near 250.

The function has extremely high values for wider ranges of x and y.

We need a function max_val_f(), that accepts four arguments:

(1) range1: m ≤ x ≤ n -----> [m, n] (The values of x belong to the interval range1)

(2) range2: p ≤ y ≤ q -----> [p, q] (The values of y belong to the interval range2)

(3) hMax: f(x, y) ≤ hMax (The values of f(x, y) selected should be bellow or equal hMax)

(4) the length for the wanted array for the output

The function should output the largest values of f(x, y) less or equal than hMax, in increasing order (the amount of highest values coincides with the entry (4))

To explain graphicaly the features of our asked function:

max_val_f([m, n], [p, q], hMax, k) -------> [f(x1, y1), f(x2, y2), ....f(xk, yk)] # 

f(x1, y1) < f(x2, y2) < ....< f(xk, yk) ≤ hMax 

Let's see some cases:

range1 = [1, 10]
range2 = [1, 10]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [81.0, 125.0, 243.0, 256.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [361.0, 400.0, 441.0, 484.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 1000
k = 5
max_val_f(range1, range2, hMax, k) -----> [784.0, 841.0, 900.0, 961.0, 1000.0]

range1 = [1, 10]
range2 = [1, 10]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [81.0, 125.0, 243.0, 256.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [361.0, 400.0, 441.0, 484.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 1000
k = 5
max_val_f(range1, range2, hMax, k) -----> [784.0, 841.0, 900.0, 961.0, 1000.0]

range1 = (1, 10)
range2 = (1, 10)
hMax = 500
k = 4
maxValF range1 range2 hMax k -----> [81.0, 125.0, 243.0, 256.0]

range1 = (1, 50)
range2 = (1, 50)
hMax = 500
k = 4
maxValF range1 range2 hMax k -----> [361.0, 400.0, 441.0, 484.0]

range1 = (1, 50)
range2 = (1, 50)
hMax = 1000
k = 5
maxValF range1 range2 hMax k -----> [784.0, 841.0, 900.0, 961.0, 1000.0]

range1 = [1, 10]
range2 = [1, 10]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [81.0, 125.0, 243.0, 256.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 500
k = 4
max_val_f(range1, range2, hMax, k) -----> [361.0, 400.0, 441.0, 484.0]

range1 = [1, 50]
range2 = [1, 50]
hMax = 1000
k = 5
max_val_f(range1, range2, hMax, k) -----> [784.0, 841.0, 900.0, 961.0, 1000.0]

Enjoy it and happy coding!