feat(cf/895): nonlazy prop soln

codeforces/1013/a.py

@@ -0,0 +1,47 @@
+def can_arrange_columns(x, m, n):
+    """
+    Determine if x columns can be arranged in m columns with non-adjacent batches 
+    where each batch is <= n columns.
+    
+    Args:
+    x (int): Total number of columns to arrange
+    m (int): Total available column slots
+    n (int): Maximum batch size
+    
+    Returns:
+    bool: True if arrangement is possible, False otherwise
+    
+    Time complexity: O(1)
+    Space complexity: O(1)
+    """
+    # If x is 0, it's always possible
+    if x == 0:
+        return True
+    
+    # Calculate the maximum number of batches that can be placed
+    # Each batch requires space for cols + an empty col (except potentially the last)
+    max_gaps = (m + 1) // (n + 1)
+    
+    # Maximum total columns that can be placed
+    max_columns = max_gaps * n
+    
+    # Check if we can fit all x columns
+    return x <= max_columns
+
+# Comprehensive test cases
+def test_column_arrangement():
+    # Test cases
+    test_cases = [
+        # x, m, n, expected_result
+        (3, 5, 2, True)
+    ]
+    
+    for x, m, n, expected in test_cases:
+        result = can_arrange_columns(x, m, n)
+        print(f"x={x}, m={m}, n={n}: {result} (Expected: {expected})")
+        assert result == expected, f"Failed for x={x}, m={m}, n={n}"
+    
+    print("All test cases passed!")
+
+# Run the tests
+test_column_arrangement()