2016 Update

Task/Zig-zag-matrix/Python/zig-zag-matrix-5.py

@@ -0,0 +1,65 @@
+from __future__ import print_function
+
+import math
+
+
+def zigzag( dimension):
+    ''' generate the zigzag indexes for a square array
+        Exploiting the fact that an array is symmetrical around its
+        centre
+    '''
+    NUMBER_INDEXES = dimension ** 2
+    HALFWAY = NUMBER_INDEXES // 2
+    KERNEL_ODD = dimension & 1
+
+    xy = [0 for _ in range(NUMBER_INDEXES)]
+    # start at 0,0
+    ix = 0
+    iy = 0
+    # 'fake' that we are going up and right
+    direction = 1
+    # the first index is always 0, so start with the second
+    # until halfway
+    for i in range(1, HALFWAY + KERNEL_ODD):
+        if direction > 0:
+            # going up and right
+            if iy == 0:
+                # are at top
+                ix += 1
+                direction = -1
+            else:
+                ix += 1
+                iy -= 1
+        else:
+            # going down and left
+            if ix == 0:
+                # are at left
+                iy += 1
+                direction = 1
+            else:
+                ix -= 1
+                iy += 1
+        # update the index position
+        xy[iy * dimension + ix] = i
+
+    # have first half, but they are scattered over the list
+    # so find the zeros to replace
+    for i in range(1, NUMBER_INDEXES):
+        if xy[i] == 0 :
+            xy[i] = NUMBER_INDEXES - 1 - xy[NUMBER_INDEXES - 1 - i]
+
+    return xy
+
+
+def main(dim):
+    zz = zigzag(dim)
+    print( 'zigzag of {}:'.format(dim))
+    width = int(math.ceil(math.log10(dim**2)))
+    for j in range(dim):
+        for i in range(dim):
+            print('{:{width}}'.format(zz[j * dim + i], width=width), end=' ')
+        print()
+
+
+if __name__ == '__main__':
+    main(5)