public void findGreatestDiff(State state) //O(n^3)
{
int chosenX = 0; //city x to city y
int chosenY = 0;
double greatestDiff = double.NegativeInfinity; //initialize to -oo to find what the greatest
//difference is
List <PointF> points = new List <PointF>();
for (int i = 0; i < state.getMap().GetLength(0); i++) //rows, O(n)
{
for (int j = 0; j < state.getMap().GetLength(1); j++) //columns
{
if (state.getPoint(i, j) == 0) //if point is 0
{
points.Add(new PointF(i, j)); //store all 0's in a point array
}
}
}
for (int i = 0; i < points.Count; i++) //loop through 0's to find the greatest difference
{ //O(n^3) there will be atmost n points, because the entire
//matrix will be 0
int possibleMax = findExcludeMinusInclude(Convert.ToInt32(points[i].X), Convert.ToInt32(points[i].Y), state); //O(n^2)
if (possibleMax >= greatestDiff) //set the point to point values, if it is 0 is covered by =
{
chosenX = Convert.ToInt32(points[i].X);
chosenY = Convert.ToInt32(points[i].Y);
greatestDiff = possibleMax;
}
}
State include = makeInclude(chosenX, chosenY, state); //O(n^2)
if (BSSF > include.getLB()) //if include's lowerbound is better than the BSSF
{
include.setEdge(chosenX, chosenY); //set the edge in the dictionary
checkCycles(include, chosenX, chosenY); //O(n), make sure there are no potential cycles
queue.Add(include); //add to the queue to be popped off later
}
if (isDictionaryFilled(include)) //O(n), have all of the edges been filled? then the include.LB is better
{ //than the current BSSF, set the BSSF
BSSF = include.getLB();
bestState = include; //save the "bestState"
}
State exclude = makeExclude(chosenX, chosenY, state); //O(n^2)
if (BSSF > exclude.getLB()) //if exclude's lowerbound is than the BSSF, add it to the queue
{
queue.Add(exclude);
}
if (isDictionaryFilled(exclude)) //O(n), have all of the edges been filled?
{ // then exclude's lowerbound is better, set the BSSF to exclude.LB
BSSF = exclude.getLB();
bestState = exclude;
}
}
public State makeInclude(int x, int y, State state) //O(n^2)
{
State includeState = new State(copyMatrix(state.getMap()), state.getLB(), state.getEdges()); //O(n^2)
includeState.setPoint(y, x, double.PositiveInfinity); //set the "opposite point to infinity"
for (int j = 0; j < includeState.getMap().GetLength(1); j++) //set the row to infinity, O(n)
{
includeState.setPoint(x, j, double.PositiveInfinity);
}
for (int i = 0; i < includeState.getMap().GetLength(0); i++) //set the column to infinity, O(n)
{
includeState.setPoint(i, y, double.PositiveInfinity);
}
reduceMatrix(includeState); //O(n^2)
includeState.setEdges(state.getEdges()); //initialize includeState's dictionary of edges
return(includeState);
}
public State makeExclude(int x, int y, State state) //O(n^2)
{
State excludeState = new State(copyMatrix(state.getMap()), state.getLB(), state.getEdges()); //O(n^2)
excludeState.setPoint(x, y, double.PositiveInfinity); //make chosen point infinity
reduceMatrix(excludeState); //O(n^2)
excludeState.setEdges(state.getEdges()); //initialize excludeStates edges
return(excludeState);
}
public void reduceMatrix(State currentState) //O(n^2)
{
double lowerBound = currentState.getLB();
for (int i = 0; i < currentState.getMap().GetLength(0); i++) // reduce rows
{ //O(n^2)
double minimum = double.PositiveInfinity; //find the lowest value in that row to reduce
for (int j = 0; j < currentState.getMap().GetLength(1); j++)
{
if (currentState.getPoint(i, j) < minimum)
{
minimum = currentState.getPoint(i, j);
}
}
if (minimum == 0) //if there is already a 0 in that row, don't waste time looping through it
{
continue;
}
if (minimum != double.PositiveInfinity)
{
for (int j = 0; j < currentState.getMap().GetLength(1); j++)
{ //reduce the other entire row by that value
double reducedPoint = currentState.getPoint(i, j) - minimum;
currentState.setPoint(i, j, reducedPoint);
}
lowerBound += minimum; //add that lowest value to the lowerBound
}
}
for (int j = 0; j < currentState.getMap().GetLength(1); j++) //reduce columns
{ //O(n^2)
double minimum = double.PositiveInfinity;
for (int i = 0; i < currentState.getMap().GetLength(0); i++)
{
if (currentState.getPoint(i, j) < minimum)
{
minimum = currentState.getPoint(i, j); //find the lowest value in the column
}
}
if (minimum == 0) //if there is already a 0 in that column, don't waste time looping through it
{
continue;
}
if (minimum != double.PositiveInfinity)
{
for (int i = 0; i < currentState.getMap().GetLength(0); i++)
{//reduce the entire column by that value
double lowerPoint = currentState.getPoint(i, j) - minimum;
currentState.setPoint(i, j, lowerPoint);
}
lowerBound += minimum; //add that minimum value to the lowerBound
}
}
currentState.setLB(lowerBound); //set the lowerbound
}
//O(n^2)
public void reduceMatrix(State currentState)
{
double lowerBound = currentState.getLB();
for (int i = 0; i < currentState.getMap().GetLength(0); i++) // reduce rows
{//O(n^2)
double minimum = double.PositiveInfinity; //find the lowest value in that row to reduce
for (int j = 0; j < currentState.getMap().GetLength(1); j++)
{
if (currentState.getPoint(i, j) < minimum)
minimum = currentState.getPoint(i, j);
}
if (minimum == 0) //if there is already a 0 in that row, don't waste time looping through it
continue;
if (minimum != double.PositiveInfinity)
{
for (int j = 0; j < currentState.getMap().GetLength(1); j++)
{ //reduce the other entire row by that value
double reducedPoint = currentState.getPoint(i, j) - minimum;
currentState.setPoint(i, j, reducedPoint);
}
lowerBound += minimum; //add that lowest value to the lowerBound
}
}
for (int j = 0; j < currentState.getMap().GetLength(1); j++) //reduce columns
{//O(n^2)
double minimum = double.PositiveInfinity;
for (int i = 0; i < currentState.getMap().GetLength(0); i++)
{
if (currentState.getPoint(i, j) < minimum)
minimum = currentState.getPoint(i, j); //find the lowest value in the column
}
if (minimum == 0) //if there is already a 0 in that column, don't waste time looping through it
continue;
if (minimum != double.PositiveInfinity)
{
for (int i = 0; i < currentState.getMap().GetLength(0); i++)
{//reduce the entire column by that value
double lowerPoint = currentState.getPoint(i, j) - minimum;
currentState.setPoint(i, j, lowerPoint);
}
lowerBound += minimum; //add that minimum value to the lowerBound
}
}
currentState.setLB(lowerBound); //set the lowerbound
}
//O(n^2)
public State makeInclude(int x, int y, State state)
{
State includeState = new State(copyMatrix(state.getMap()), state.getLB(), state.getEdges()); //O(n^2)
includeState.setPoint(y, x, double.PositiveInfinity); //set the "opposite point to infinity"
for (int j = 0; j < includeState.getMap().GetLength(1); j++) //set the row to infinity, O(n)
{
includeState.setPoint(x, j, double.PositiveInfinity);
}
for (int i = 0; i < includeState.getMap().GetLength(0); i++) //set the column to infinity, O(n)
{
includeState.setPoint(i, y, double.PositiveInfinity);
}
reduceMatrix(includeState); //O(n^2)
includeState.setEdges(state.getEdges()); //initialize includeState's dictionary of edges
return includeState;
}
//O(n^2)
public State makeExclude(int x, int y, State state)
{
State excludeState = new State(copyMatrix(state.getMap()), state.getLB(), state.getEdges()); //O(n^2)
excludeState.setPoint(x, y, double.PositiveInfinity); //make chosen point infinity
reduceMatrix(excludeState); //O(n^2)
excludeState.setEdges(state.getEdges()); //initialize excludeStates edges
return excludeState;
}
//O(n^3)
public void findGreatestDiff(State state)
{
int chosenX = 0; //city x to city y
int chosenY = 0;
double greatestDiff = double.NegativeInfinity; //initialize to -oo to find what the greatest
//difference is
List<PointF> points = new List<PointF>();
for (int i = 0; i < state.getMap().GetLength(0); i++) //rows, O(n)
{
for (int j = 0; j < state.getMap().GetLength(1); j++) //columns
{
if (state.getPoint(i, j) == 0) //if point is 0
{
points.Add(new PointF(i, j)); //store all 0's in a point array
}
}
}
for (int i = 0; i < points.Count; i++) //loop through 0's to find the greatest difference
{//O(n^3) there will be atmost n points, because the entire
//matrix will be 0
int possibleMax = findExcludeMinusInclude(Convert.ToInt32(points[i].X), Convert.ToInt32(points[i].Y), state); //O(n^2)
if (possibleMax >= greatestDiff) //set the point to point values, if it is 0 is covered by =
{
chosenX = Convert.ToInt32(points[i].X);
chosenY = Convert.ToInt32(points[i].Y);
greatestDiff = possibleMax;
}
}
State include = makeInclude(chosenX, chosenY, state); //O(n^2)
if (BSSF > include.getLB()) //if include's lowerbound is better than the BSSF
{
include.setEdge(chosenX, chosenY); //set the edge in the dictionary
checkCycles(include, chosenX, chosenY); //O(n), make sure there are no potential cycles
queue.Add(include); //add to the queue to be popped off later
}
if (isDictionaryFilled(include))//O(n), have all of the edges been filled? then the include.LB is better
{ //than the current BSSF, set the BSSF
BSSF = include.getLB();
bestState = include; //save the "bestState"
}
State exclude = makeExclude(chosenX, chosenY, state);//O(n^2)
if (BSSF > exclude.getLB()) //if exclude's lowerbound is than the BSSF, add it to the queue
queue.Add(exclude);
if (isDictionaryFilled(exclude))//O(n), have all of the edges been filled?
{ // then exclude's lowerbound is better, set the BSSF to exclude.LB
BSSF = exclude.getLB();
bestState = exclude;
}
}