Python Program for Number of jump required of given length to reach a point of form (d, 0) from origin in 2D plane

Given three positive integers a, b and d. You are currently at origin (0, 0) on infinite 2D coordinate plane. You are allowed to jump on any point in the 2D plane at euclidean distance either equal to a or b from your current position. The task is to find the minimum number of jump required to reach (d, 0) from (0, 0).

Examples:

Input : a = 2, b = 3, d = 1 
Output : 2
First jump of length a = 2, (0, 0) -> (1/2, √15/2)
Second jump of length a = 2, (1/2, √15/2) -> (1, 0)
Thus, only two jump are required to reach 
(1, 0) from (0, 0).

Input : a = 3, b = 4, d = 11 
Output : 3
(0, 0) -> (4, 0) using length b = 4
(4, 0) -> (8, 0) using length b = 4
(8, 0) -> (11, 0) using length a = 3

# Python code to find the minimum number
# of jump required to reach
# (d, 0) from (0, 0)

def minJumps(a, b, d):

    temp = a
    a = min(a, b)
    b = max(temp, b)

    if (d >= b):
        return (d + b - 1) / b

    # if d is 0
    if (d == 0):
        return 0

    # if d is equal to a.
    if (d == a):
        return 1

    # else make triangle, and only 2
    # steps required.
    return 2

# main()
a = 3
b = 4
d = 11
print (int(minJumps(a, b, d)))

# Contributed by _omg

Output

3

Please refer complete article on Number of jump required of given length to reach a point of form (d, 0) from origin in 2D plane for more details!