CH-2 with beam search

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diff --git a/challenge-062/sangeet-kar/python/ch-2a.py b/challenge-062/sangeet-kar/python/ch-2a.py
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+++ b/challenge-062/sangeet-kar/python/ch-2a.py
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+#!/usr/bin/env python
+
+import sys
+import heapq
+
+# 1. n_queens_3d finds the solution using beam search
+# 2. the higher the beam_width, the better is the solution. 
+# 3. with beam_width=1, it's very fast but the solution may not be optimal maximising the number of queens.
+# 4. with beam-width=-1, it searches the entire search space. Ensures best solution but slow as hell for high n
+# 5. I think one can find the best solution with beam-width 2-3 for n-values less than 8
+
+
+def n_queens_3d (n = 2, beam_width = 2):
+    solutions = []
+    place_queen ([(i, j, k) for i in range(n) for j in range(n) for k in range(n)], 
+                 [], 
+                 solutions, 
+                 beam_width=beam_width)
+    best = max(solutions, key=len)
+    print(f"queens: {len(best)}")
+    return indices_to_array( best, n)
+
+def place_queen (indices, queens, solutions, beam_width=2):
+    if not indices: 
+        solutions.append(queens)
+        return
+    if beam_width == -1:
+        best = ((index, [i for i in indices if is_available(index, i)]) for index in indices)
+    else:
+        best = heapq.nlargest(beam_width, 
+                              ((index, [i for i in indices if is_available(index, i)]) for index in indices), 
+                              key=lambda pair: len(pair[1]))
+    for pos, available in best:
+        place_queen (available, [*queens, pos], solutions, beam_width=beam_width)
+
+def is_available(ref, pos):
+    diff = {abs(i - j) for i, j in zip (ref, pos)}
+    return not ( len(diff) < 2 or (len(diff) == 2 and 0 in diff))
+
+def indices_to_array (indices, n):
+    array = [[[0 for _ in range(n)] for _ in range(n)] for _ in range(n)]
+    for i, j, k in indices:
+        array[i][j][k] = 1
+    return array
+
+n = int(sys.argv[1]) if len(sys.argv) > 1 else 2
+beam_width = int(sys.argv[2]) if len(sys.argv) > 2 else 2
+
+print(n_queens_3d (n, beam_width))
+