Hello! In this post, we will discuss solving algorithmic problems using Python. The topic is “DDR”. DDR stands for Dance Dance Revolution, which means that players must step in time with the music in the game. We will convert the patterns of such games into algorithmic problems and solve them.
Problem Description
We will solve the following problem:
Problem: In the DDR game, the player has a sequence for each step. This sequence represents directions: right, left, up, and down. Write a function to check if the given step sequence is valid. A valid step sequence must have an even length and cannot have the same direction appearing consecutively more than once. For example:
- Valid sequence: “UDLRUDLR”
- Invalid sequence: “UUDDLRR”
Problem Analysis
First, let’s analyze the problem. To check if the given conditions are satisfied, we need to verify the following two conditions:
- The length of the sequence must be even.
- The same direction must not appear consecutively more than once.
The directions can be mapped as follows:
- U: Up
- D: Down
- L: Left
- R: Right
Algorithm Design
Now, let’s design the algorithm. To check if the sequence is valid, we will follow these steps:
- Check the length of the input sequence.
- Iterate over each character in the sequence, remembering the previous character to compare with the current one.
- If a condition is not satisfied, return False; otherwise, return True if all conditions are satisfied.
Code Implementation
Now let’s write the code in Python. Below is the implementation based on the algorithm we designed:
def is_valid_ddr_sequence(sequence):
# 1. Check if the sequence length is even
if len(sequence) % 2 != 0:
return False
# 2. Store the previous character for checking consecutive directions
previous = ''
for direction in sequence:
# 3. If the current direction is the same as the previous, return False
if direction == previous:
return False
previous = direction # Update previous direction
return True # Return True if all conditions are satisfiedTest Cases
Let’s validate the function we wrote with various test cases. Here are some test cases:
print(is_valid_ddr_sequence("UDLRUDLR")) # True
print(is_valid_ddr_sequence("UUDDLRR")) # False
print(is_valid_ddr_sequence("UU")) # False
print(is_valid_ddr_sequence("UDLR")) # True
print(is_valid_ddr_sequence("UDLRRUDL")) # FalseResults Analysis
Now let’s analyze the test results:
is_valid_ddr_sequence("UDLRUDLR"): True – Valid sequenceis_valid_ddr_sequence("UUDDLRR"): False – “U” appears consecutively twiceis_valid_ddr_sequence("UU"): False – “U” appears consecutively twiceis_valid_ddr_sequence("UDLR"): True – Valid sequenceis_valid_ddr_sequence("UDLRRUDL"): False – “R” appears consecutively twice
Additional Considerations
In solving this problem, we should consider potential performance issues that may arise if the sequence is long. The current algorithm has a time complexity of O(n), providing sufficient efficiency. However, if the number of characters increases rapidly, we may consider optimizing the design for better structures.
Conclusion
In this post, we covered an algorithmic problem related to the DDR game. Implementing an algorithm through simple condition checks to determine validity will be very helpful for basic algorithm design. I hope to cultivate algorithmic thinking through various problems in the future. Thank you!