T MaxLoading(T w[], T c, int n)
{// Return value of best loading.
// Use FIFO branch and bound.
// initialize for level 1 start
LinkedQueue<T> Q; // live-node queue
Q.Add(-1); // end-of-level marker
int i = 1; // level of E-node
T Ew = 0, // weight of E-node
bestw = 0; // best weight so far
// search subset space tree
while (true) {
// check left child of E-node
if (Ew + w[i] <= c) // x[i] = 1
AddLiveNode(Q, Ew + w[i], bestw, i, n);
// right child is always feasible
AddLiveNode(Q, Ew, bestw, i, n); // x[i] = 0
Q.Delete(Ew); // get next E-node
if (Ew == -1) { // end of level
if (Q.IsEmpty()) return bestw;
Q.Add(-1); // end-of-level marker
Q.Delete(Ew); // get next E-node
i++;} // level number of Ew
}
}
bool FindPath(Position start, Position finish,
int& PathLen, Position * &path)
{// Find a path from start to finish.
// Return true if successful, false if impossible.
// Throw NoMem exception if inadequate space.
if ((start.row == finish.row) &&
(start.col == finish.col))
{PathLen = 0; return true;} // start = finish
// initialize wall of blocks around grid
for (int i = 0; i <= m+1; i++) {
grid[0][i] = grid[m+1][i] = 1; // bottom & top
grid[i][0] = grid[i][m+1] = 1; // left & right
}
// initialize offsets
Position offset[4];
offset[0].row = 0; offset[0].col = 1; // right
offset[1].row = 1; offset[1].col = 0; // down
offset[2].row = 0; offset[2].col = -1; // left
offset[3].row = -1; offset[3].col = 0; // up
int NumOfNbrs = 4; // neighbors of a grid position
Position here, nbr;
here.row = start.row;
here.col = start.col;
grid[start.row][start.col] = 2; // block
// label reachable grid positions
LinkedQueue<Position> Q;
do {// label neighbors of here
for (int i = 0; i < NumOfNbrs; i++) {
nbr.row = here.row + offset[i].row;
nbr.col = here.col + offset[i].col;
if (grid[nbr.row][nbr.col] == 0) {
// unlabeled nbr, label it
grid[nbr.row][nbr.col]
= grid[here.row][here.col] + 1;
if ((nbr.row == finish.row) &&
(nbr.col == finish.col)) break; // done
Q.Add(nbr);} // end of if
} // end of for
// have we reached finish?
if ((nbr.row == finish.row) &&
(nbr.col == finish.col)) break; // done
// finish not reached, can we move to a nbr?
if (Q.IsEmpty()) return false; // no path
Q.Delete(here); // get next position
} while(true);
// construct path
PathLen = grid[finish.row][finish.col] - 2;
path = new Position [PathLen];
// trace backwards from finish
here = finish;
for (int j = PathLen-1; j >= 0; j--) {
path[j] = here;
// find predecessor position
for (int i = 0; i < NumOfNbrs; i++) {
nbr.row = here.row + offset[i].row;
nbr.col = here.col + offset[i].col;
if (grid[nbr.row][nbr.col] == j+2) break;
}
here = nbr; // move to predecessor
}
return true;
}
