Problem Description Dance Revolution is the pioneering series of the rhythm and dance genre in video games The core games involve placing your feet on certain tile according to the instruction on screen. Here you will have four tiles up, down, righ
To solve this problem, we need to determine the minimum number of moves required to follow a sequence of dance instructions using two legs which can start on any of the available tiles: up, down, left, and right.
### Problem Analysis
1. **Tiles**: We have four tiles, which we can denote as:
- `0`: up
- `1`: down
- `2`: left
- `3`: right
2. **Instructions**: We need to read a sequence of instructions where each instruction specifies a tile.
3. **Leg Positions**: Initially, we can place our two legs on any combination of the four tiles. The movements of the legs based on instructions can lead to a minimum number of moves if we start smartly.
### Solution Approach
1. **State Representation**: We can represent the positions of the legs with a tuple `(leg1, leg2)`.
2. **Dynamic Programming or BFS**:
- Use a BFS to explore all possible leg placements and count the moves needed to follow the instruction set.
- Keep track of any states (positions of legs) we've already visited to avoid re-processing.
3. **Initialization**: Start by considering all combinations where you can place your legs on any of the four positions.
That said, let's implement this in Python:
```python
from collections import deque
def min_moves_to_follow_instructions(n, instructions):
tiles = ['up', 'down', 'left', 'right']
tile_index = {tiles[i]: i for i in range(4)}
# Create a simplified list of instructions as indices
instruction_indices = [tile_index[instr] for instr in instructions]
# BFS setup
initial_positions = [(i, j) for i in range(4) for j in range(4)]
queue = deque(initial_positions)
visited = set()
for pos in initial_positions:
visited.add(pos)
moves = 0
# BFS process
while queue:
for _ in range(len(queue)):
leg1, leg2 = queue.popleft()
# If we've fully processed all instructions
if moves == n:
return moves
# Follow the nth instruction
current_instruction = instruction_indices[moves]
# Check if we are already on the required tile
if leg1 == current_instruction or leg2 == current_instruction:
# If we can follow the instruction without a move
next_positions = [(leg1, leg2)]
else:
# If we need to move one of the legs to the tile
next_positions = [(current_instruction, leg2), (leg1, current_instruction)]
for next_pos in next_positions:
if next_pos not in visited:
visited.add(next_pos)
queue.append(next_pos)
moves += 1
return moves
# Reading input
n = int(input())
instructions = [input().strip() for _ in range(n)]
# Getting minimum moves
result = min_moves_to_follow_instructions(n, instructions)
print(result)
```
### Explanation of Code
1. **Input Handling**: We read the number of instructions and the instructions themselves.
2. **Tile Mapping**: We map the strings `up`, `down`, `left`, and `right` to numerical indices for easier processing.
3. **BFS Logic**:
- Use a queue to traverse through all possible leg positions.
- For each leg position, we check whether we can satisfy the current instruction without moving or if we need to move one of the legs.
- We keep track of visited positions to avoid reprocessing them.
4. **Moves Count**: Each level of the BFS corresponds to a move; when we can no longer keep track of new positions, we return the count of moves.
This approach allows us to effectively find the minimum number of movements needed to complete the sequence of dance instructions while accommodating the constraint of starting leg positions.