pivot(T[i..j]; l )
// permutes the elements in array T[i..j] and returns a value l such that , at the end, i   <=l <=j, T[k] <= p for all i <= k < l, T[l] = p, and T[k] > p for all l < k <= j, where p is the initial value of T[i]

p = T[i]
k = i; l = j + 1
repeat k = k + 1 until T[k] > p or k >= j
repeat l = l - 1 until T[l] <= p
while k < l do
  swap T[k] and T[l]
  repeat k = k + 1 until T[k] > p
  repeat l = l -1 until T[l] <= p
swap T[i] and T[l]

queens( k, col, diag45, diag135 )
// sol[1..k] is k-promising
// col = { sol[i] | 1 <= i <= k }
// diag45 = { sol[i] - i + 1 | 1 <= i <= k } 
// diag135 = { sol[i] + i - 1 | 1 <= i <= k }

if k = 8 then // an 8-promising vector is a solution  
                  write sol
else // explore (k+1)-promising vectors of sol
  for j = 1 to 8 do
    if j not-in col and j-k not-in diag45 and j+k not-in diag135
    then sol[k+1] = j // sol[1..k+1] is (k+1)-promising
            queens(k+1, col u {j}, diag45 u {j-k}, diag135 u {j+k}  )

queenLV( sol[1..8], success)
array ok[1..8]  //  available positions
col, diag45, diag135 = empty
for k = 0 to 7 do
// sol[1..k] is k-promising, place the (k+1) th queen
nb = 0  // count the number of possibilities
  for j = 1 to 8 do
    if j not-in col and j-k not-in diag45 and j+k not-in diag135
    then // column j is available for the (k+1) th queen
           nb = nb - 1
           ok[nb] = j
  if nb = 0 then return success = false
  j = ok[uniform(1..nb)]
  col = col u {j}
  diag45 = diag45 u { j - k }
  diag135 = diag135 u { j + k }
  sol[ k + 1] = j
return success = true

for j =1 to 8 do
  if