Added all DAA in python

DAA/A5.py

@@ -0,0 +1,80 @@
+def solve_n_queens_with_first(n, first_pos, find_all=False):
+    """
+    Solve n-Queens given a pre-placed queen at first_pos (r, c), 0-indexed.
+    Returns:
+      - if find_all=False: one solution as a list of rows where board[r][c] = 1
+      - if find_all=True: list of all such solutions
+      If no solution: returns None (or empty list when find_all=True).
+    """
+    r0, c0 = first_pos
+    # validate first position
+    if not (0 <= r0 < n and 0 <= c0 < n):
+        raise ValueError("first_pos must be within board bounds (0..n-1).")
+
+    # Prepare trackers
+    cols = set([c0])
+    diag1 = set([r0 - c0])   # r - c
+    diag2 = set([r0 + c0])   # r + c
+    board = [-1] * n         # board[r] = c or -1
+    board[r0] = c0
+
+    solutions = []
+
+    def place(row):
+        # If row already has the placed queen, skip to next row
+        if row == n:
+            # a solution found; build matrix representation
+            mat = [[0]*n for _ in range(n)]
+            for rr in range(n):
+                c = board[rr]
+                if c != -1:
+                    mat[rr][c] = 1
+            if find_all:
+                solutions.append(mat)
+                return False  # continue searching
+            else:
+                solutions.append(mat)
+                return True   # stop search (found one)
+        if board[row] != -1:
+            # fixed queen row, just advance
+            return place(row+1)
+
+        for c in range(n):
+            if c in cols or (row - c) in diag1 or (row + c) in diag2:
+                continue
+            # choose
+            board[row] = c
+            cols.add(c); diag1.add(row - c); diag2.add(row + c)
+            stop = place(row + 1)
+            # unchoose
+            cols.remove(c); diag1.remove(row - c); diag2.remove(row + c)
+            board[row] = -1
+            if stop and not find_all:
+                return True
+        return False
+
+    # Start from row 0
+    place(0)
+
+    if find_all:
+        return solutions  # possibly empty list
+    else:
+        return solutions[0] if solutions else None
+
+
+# ---------- Example usage ----------
+if __name__ == "__main__":
+    # Example 1: n=8, first queen at row0,col0 (top-left)
+    n = 8
+    first = (0, 0)  # 0-indexed
+    sol = solve_n_queens_with_first(n, first, find_all=False)
+    if sol is None:
+        print("No solution found.")
+    else:
+        print("One solution matrix (1 = queen):")
+        for row in sol:
+            print(row)
+
+    # Example 2: get all solutions with first queen at (0, 3)
+    # all_sols = solve_n_queens_with_first(8, (0, 3), find_all=True)
+    # print(f"Found {len(all_sols)} solutions.")