// 990. Satisfiability of Equality Equations
// This solution is super easy and mathmatically brilliant with the usage of Union-Find
public bool EquationsPossible(string[] equations)
{
var uf = new UnionFind(26);
foreach (var eq in equations)
{
if (eq.Substring(1, 2) == "==")
{
uf.Union(eq[0] - 'a', eq[3] - 'a');
}
}
foreach (var eq in equations)
{
if (eq.Substring(1, 2) == "!=")
{
if (uf.Connected(eq[0] - 'a', eq[3] - 'a'))
{
return(false);
}
}
}
return(true);
}
// 130. Surrounded Regions
// This solution with Union-find, very hard-core algorithm
public void Solve(char[][] board)
{
var m = board.Length;
var n = board[0].Length;
var totalLength = m * n;
var uf = new UnionFind(totalLength + 1); // one extra cell for initial connectivity
// input perimeter cells
for (int i = 0; i < n; i++)
{
if (board[0][i] == 'O')
{
uf.Union(i, totalLength);
}
if (board[m - 1][i] == 'O')
{
uf.Union((m - 1) * n + i, totalLength);
}
}
for (int j = 0; j < m; j++)
{
if (board[j][0] == 'O')
{
uf.Union(j * n, totalLength);
}
if (board[j][n - 1] == 'O')
{
uf.Union(j * n + n - 1, totalLength);
}
}
for (int x = 0; x < m; x++)
{
for (int y = 0; y < n; y++)
{
if (board[x][y] != 'O')
{
continue;
}
if (x - 1 >= 0 && board[x - 1][y] == 'O')
{
uf.Union(x * n + y, (x - 1) * n + y);
}
if (x + 1 < m && board[x + 1][y] == 'O')
{
uf.Union(x * n + y, (x + 1) * n + y);
}
if (y - 1 >= 0 && board[x][y - 1] == 'O')
{
uf.Union(x * n + y, x * n + y - 1);
}
if (y + 1 < n && board[x][y + 1] == 'O')
{
uf.Union(x * n + y, x * n + y + 1);
}
}
}
for (int x = 1; x < m - 1; x++)
{
for (int y = 1; y < n - 1; y++)
{
if (board[x][y] == 'O' && !uf.Connected(x * n + y, totalLength))
{
board[x][y] = 'X';
}
}
}
}