Data commit

Task/Taxicab-numbers/Python/taxicab-numbers-1.py

@@ -0,0 +1,17 @@
+from collections import defaultdict
+from itertools import product
+from pprint import pprint as pp
+
+cube2n = {x**3:x for x in range(1, 1201)}
+sum2cubes = defaultdict(set)
+for c1, c2 in product(cube2n, cube2n):
+	if c1 >= c2: sum2cubes[c1 + c2].add((cube2n[c1], cube2n[c2]))
+	
+taxied = sorted((k, v) for k,v in sum2cubes.items() if len(v) >= 2)
+
+#pp(len(taxied))  # 2068
+for t in enumerate(taxied[:25], 1):
+    pp(t)
+print('...')
+for t in enumerate(taxied[2000-1:2000+6], 2000):
+    pp(t)

Task/Taxicab-numbers/Python/taxicab-numbers-2.py

@@ -0,0 +1,20 @@
+cubes, crev = [x**3 for x in range(1,1200)], {}
+# for cube root lookup
+for x,x3 in enumerate(cubes): crev[x3] = x + 1
+
+sums = sorted(x+y for x in cubes for y in cubes if y < x)
+
+idx = 0
+for i in range(1, len(sums)-1):
+    if sums[i-1] != sums[i] and sums[i] == sums[i+1]:
+        idx += 1
+        if idx > 25 and idx < 2000 or idx > 2006: continue
+
+        n,p = sums[i],[]
+        for x in cubes:
+            if n-x < x: break
+            if n-x in crev:
+                p.append((crev[x], crev[n-x]))
+        print "%4d: %10d"%(idx,n),
+        for x in p: print " = %4d^3 + %4d^3"%x,
+        print

Task/Taxicab-numbers/Python/taxicab-numbers-3.py

@@ -0,0 +1,30 @@
+from heapq import heappush, heappop
+
+def cubesum():
+    h,n = [],1
+    while True:
+        while not h or h[0][0] > n**3: # could also pre-calculate cubes
+            heappush(h, (n**3 + 1, n, 1))
+            n += 1
+
+        (s, x, y) = heappop(h)
+        yield((s, x, y))
+        y += 1
+        if y < x:    # should be y <= x?
+            heappush(h, (x**3 + y**3, x, y))
+
+def taxis():
+    out = [(0,0,0)]
+    for s in cubesum():
+        if s[0] == out[-1][0]:
+            out.append(s)
+        else:
+            if len(out) > 1: yield(out)
+            out = [s]
+
+n = 0
+for x in taxis():
+    n += 1
+    if n >= 2006: break
+    if n <= 25 or n >= 2000:
+        print(n, x)