Destination Problem Solution || Exploring Point Transformations: Converting (sx, sy) to (tx, ty) || The Magic of Point Operations: From (sx, sy) to (tx, ty)

Destination

Given four integers sx, sy, tx, and ty, return true if it is possible to convert the point (sx, sy) to the point (tx, ty) through some operations, or false otherwise.

The allowed operation on some point (x, y) is to convert it to either (x, x + y) or (x + y, y).

Input Format:

the input line contains four integers separaed by space

Example 1:

Input: sx = 1, sy = 1, tx = 3, ty = 5

Output: true

Explanation:One series of moves that transforms the starting point to the target is:(1, 1) -> (1, 2) (1, 2) -> (3, 2)(3, 2) -> (3, 5)

Sample input E

1 1 2 2

Sample output

false

Program:

def target(sx, sy, tx, ty):

    if sx > tx or sy > ty:

        return False

    if sx == tx and sy == ty:

        return True

    return target(sx, sx + sy, tx, ty) or target(sx + sy, sy, tx, ty)

# Input

sx, sy, tx, ty = map(int, input().split())

# Output

print(str(target(sx, sy, tx, ty)).lower())

Explanation:

1.'def target(sx, sy, tx, ty):'

1)This is a function definition in Python named target.

2)It takes four integer arguments: sx, sy, tx, and ty, which represent the starting point             coordinates (sx, sy) and the target point coordinates (tx, ty).

2.'if sx > tx or sy > ty:'

1)This is the first conditional statement to check if the starting point (sx, sy) is already         beyond the target point (tx, ty) along the x-axis (sx > tx) or the y-axis (sy > ty). If this            condition is true, it means it is impossible to reach the target, and the function immediately returns False.

3.'if sx == tx and sy == ty:'

1)This is the second conditional statement to check if the starting point (sx, sy) is                 already the same as the target point (tx, ty). If this condition is true, it means we have          reached the target, and the function returns True.

4.'return target(sx, sx + sy, tx, ty) or target(sx + sy, sy, tx, ty)'

1)If the function hasn't returned yet, it means the starting point is not beyond the                     target, and they are not the same point. So, the function attempts to recursively call             itself with two different coordinates:

1)The first recursive call is (sx, sx + sy). This represents the operation (x, x + y).

2)The second recursive call is (sx + sy, sy). This represents the operation (x + y,                         y).

2)The function returns True if either of these recursive calls reaches the target. If both             recursive calls fail to reach the target, the function returns False.

5.'sx, sy, tx, ty = map(int, input().split())'

1)This line takes input from the user, which should be four space-separated integers             representing sx, sy, tx, and ty.

6.'print(str(can_reach_target(sx, sy, tx, ty)).lower())'

1)This line calls the can_reach_target function with the user-provided input values and         converts the output (True/False) to a string using str().

2)The lower() method is then used to convert the string to lowercase, resulting in                 "true" or "false" as the final output.

The code checks whether it is possible to reach the target point (tx, ty) from the starting point (sx, sy) by applying the allowed operations: (x, x + y) and (x + y, y). It returns the result as "true" or "false," which matches the expected output format.