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61 lines
1.8 KiB
Markdown
61 lines
1.8 KiB
Markdown
---
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title: Lee's Algorithm
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---
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## Lee's Algorithm
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The Lee algorithm is one possible solution for maze routing problems. It always gives an optimal solution, if one exists, but is
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slow and requires large memory for dense layout.
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### Understanding how it works
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The algorithm is a `breadth-first` based algorithm that uses `queues` to store the steps. It usually uses the following steps:
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1. Choose a starting point and add it to the queue.
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2. Add the valid neighboring cells to the queue.
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3. Remove the position you are on from the queue and continue to the next element.
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4. Repeat steps 2 and 3 until the queue is empty.
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### Implementation
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C++ has the queue already implemented in the `<queue>` library, but if you are using something else you are welcome to implement
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your own version of queue.
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C++ code:
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```cpp
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int dl[] = {-1, 0, 1, 0}; // these arrays will help you travel in the 4 directions more easily
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int dc[] = {0, 1, 0, -1};
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queue<int> X, Y; // the queues used to get the positions in the matrix
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X.push(start_x); // initialize the queues with the start position
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Y.push(start_y);
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void lee()
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{
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int x, y, xx, yy;
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while(!X.empty()) // while there are still positions in the queue
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{
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x = X.front(); // set the current position
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y = Y.front();
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for(int i = 0; i < 4; i++)
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{
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xx = x + dl[i]; // travel in an adiacent cell from the current position
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yy = y + dc[i];
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if('position is valid') //here you should insert whatever conditions should apply for your position (xx, yy)
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{
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X.push(xx); // add the position to the queue
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Y.push(yy);
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mat[xx][yy] = -1; // you usually mark that you have been to this position in the matrix
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}
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}
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X.pop(); // eliminate the first position, as you have no more use for it
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Y.pop();
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}
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}
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```
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