Voici la méthode de J.F. Sebastians traduite en C# :
private Vector2 MaxRectSize(int[] histogram) {
Vector2 maxSize = Vector2.zero;
int maxArea = 0;
Stack<Vector2> stack = new Stack<Vector2>();
int x = 0;
for (x = 0; x < histogram.Length; x++) {
int start = x;
int height = histogram[x];
while (true) {
if (stack.Count == 0 || height > stack.Peek().y) {
stack.Push(new Vector2(start, height));
} else if(height < stack.Peek().y) {
int tempArea = (int)(stack.Peek().y * (x - stack.Peek().x));
if(tempArea > maxArea) {
maxSize = new Vector2(stack.Peek().y, (x - stack.Peek().x));
maxArea = tempArea;
}
Vector2 popped = stack.Pop();
start = (int)popped.x;
continue;
}
break;
}
}
foreach (Vector2 data in stack) {
int tempArea = (int)(data.y * (x - data.x));
if(tempArea > maxArea) {
maxSize = new Vector2(data.y, (x - data.x));
maxArea = tempArea;
}
}
return maxSize;
}
public Vector2 GetMaximumFreeSpace() {
// STEP 1:
// build a seed histogram using the first row of grid points
// example: [true, true, false, true] = [1,1,0,1]
int[] hist = new int[gridSizeY];
for (int y = 0; y < gridSizeY; y++) {
if(!invalidPoints[0, y]) {
hist[y] = 1;
}
}
// STEP 2:
// get a starting max area from the seed histogram we created above.
// using the example from above, this value would be [1, 1], as the only valid area is a single point.
// another example for [0,0,0,1,0,0] would be [1, 3], because the largest area of contiguous free space is 3.
// Note that at this step, the heigh fo the found rectangle will always be 1 because we are operating on
// a single row of data.
Vector2 maxSize = MaxRectSize(hist);
int maxArea = (int)(maxSize.x * maxSize.y);
// STEP 3:
// build histograms for each additional row, re-testing for new possible max rectangluar areas
for (int x = 1; x < gridSizeX; x++) {
// build a new histogram for this row. the values of this row are
// 0 if the current grid point is occupied; otherwise, it is 1 + the value
// of the previously found historgram value for the previous position.
// What this does is effectly keep track of the height of continous avilable spaces.
// EXAMPLE:
// Given the following grid data (where 1 means occupied, and 0 means free; for clairty):
// INPUT: OUTPUT:
// 1.) [0,0,1,0] = [1,1,0,1]
// 2.) [0,0,1,0] = [2,2,0,2]
// 3.) [1,1,0,1] = [0,0,1,0]
//
// As such, you'll notice position 1,0 (row 1, column 0) is 2, because this is the height of contiguous
// free space.
for (int y = 0; y < gridSizeY; y++) {
if(!invalidPoints[x, y]) {
hist[y] = 1 + hist[y];
} else {
hist[y] = 0;
}
}
// find the maximum size of the current histogram. If it happens to be larger
// that the currently recorded max size, then it is the new max size.
Vector2 maxSizeTemp = MaxRectSize(hist);
int tempArea = (int)(maxSizeTemp.x * maxSizeTemp.y);
if (tempArea > maxArea) {
maxSize = maxSizeTemp;
maxArea = tempArea;
}
}
// at this point, we know the max size
return maxSize;
}
Quelques points à noter à ce sujet :
- Cette version est destinée à être utilisée avec l'API de Unity. Vous pouvez facilement la rendre plus générique en remplaçant les instances de Vector2 par KeyValuePair. Vector2 n'est utilisé que comme un moyen pratique de stocker deux valeurs.
- invalidPoints[] est un tableau de bool, où true signifie que le point de grille est "en service", et false signifie qu'il ne l'est pas.
1 votes
Veuillez envisager de changer la réponse acceptée par la réponse de J.F. Sebastian, qui est maintenant correcte et dont la complexité est optimale.
1 votes
Veuillez vérifier les questions très similaires (je dirais même dupliquées) : stackoverflow.com/questions/7770945/ , stackoverflow.com/a/7353193/684229 . La solution est
O(n).0 votes
J'essaie de faire la même chose avec un rectangle orienté dans n'importe quelle direction. Voir la question : stackoverflow.com/questions/22604043/
0 votes
@TMS C'est en fait l'inverse. Ces questions sont des doublons de celle-ci.