Taxi me algunos números

9

Los números de taxis u OEIS A011541 son los números mínimos que pueden representarse como n sumas diferentes de dos enteros en cubos positivos, para n sucesivas .

Deberá imprimir el número n del taxi. Esto debería funcionar para cualquier n en teoría.

Sin embargo, como solo se han descubierto 6 números de taxis hasta ahora, no habrá un n por encima de 6. Los números son 2, 1729, 87539319, 6963472309248, 48988659276962496, 24153319581254312065344.

No está permitido codificar estas variables, porque su programa debe funcionar para cualquier n arbitraria en teoría.

code-golf math number sequence Morgan Thrapp
fuente
¿Requiere esto que admitamos números de longitud arbitraria? Si sólo podemos manejar valores de hasta 2 ^ 32-1 pero el programa sería trabajar para valores mayores si sólo se les permitió, es que está bien?
Engineer Toast
Claro, eso está bien conmigo. Mientras el algoritmo mismo funcione para cualquier número, eres bueno.
Morgan Thrapp

Respuestas:

5

Haskell, 60 bytes

f n=[k|k<-[0..],n<=sum[1|x<-[1..k],y<-[1..x],x^3+y^3==k]]!!0

Muy claro. Cuenta cuántas maneras kse puede escribir un número como una suma de dos cubos. Filtra por k's tal que este número es al menos n, y toma el primero.

Un método de igual longitud con until:

f n=until(\k->n<=sum[1|x<-[1..k],y<-[1..x],x^3+y^3==k])(+1)0
xnor
fuente
Su programa produce el número más pequeño que es una suma de dos cubos en n formas diferentes. El problema pide encontrar el enésimo número, que es una suma de dos cubos de dos maneras diferentes.
Itai Bar-Natan
1
@ ItaiBar-Natan Me parece que la especificación está pidiendo el menor número que sea la suma de dos cubos en n formas diferentes.
xnor
Vaya, acabo de releer el problema y creo que tienes razón. Supongo que lo leí mal.
Itai Bar-Natan
6

Taxi, 4758 bytes

¿Qué mejor lenguaje para calcular los números de taxis que uno que simule taxis?
Esto es una broma. Hay muchos idiomas mejores. ¿Qué pasó con los últimos dos días de mi vida?

Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 1 l 2 r.Pickup a passenger going to Bird's Bench.Pickup a passenger going to Cyclone.Go to Zoom Zoom:n.Go to Cyclone:w.Pickup a passenger going to Rob's Rest.Pickup a passenger going to Cyclone.Go to Bird's Bench:n 1 r 2 r 1 l.Go to Rob's Rest:n.Go to Cyclone:s 1 l 1 l 2 l.[a]Pickup a passenger going to Firemouth Grill.Pickup a passenger going to The Underground.Go to Zoom Zoom:n.Go to Firemouth Grill:w 3 l 2 l 1 r.Go to The Underground:e 1 l.Switch to plan "b" if no one is waiting.Pickup a passenger going to Cyclone.Go to Cyclone:n 3 l 2 l.Switch to plan "a".[b]Go to Firemouth Grill:s 1 r.[c]Pickup a passenger going to Cyclone.Go to Cyclone:w 1 l 1 r 2 r.Pickup a passenger going to Cyclone.Go to Zoom Zoom:n.Go to Cyclone:w.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to Trunkers.Go to Trunkers:s 1 r 2 l.Go to Firemouth Grill:e 1 l 1 r.Switch to plan "e" if no one is waiting.Switch to plan "c".[e]Go to Trunkers:w 1 l 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:w 2 r.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 1 r.[f]Go to Trunkers:s 1 l.Switch to plan "g" if no one is waiting.Pickup a passenger going to Sunny Skies Park.Go to Cyclone:w 2 r.Pickup a passenger going to Cyclone.Go to Zoom Zoom:n.Go to Cyclone:w.Go to Sunny Skies Park:n 1 r.Switch to plan "f".[g]Go to Cyclone:w 2 r.Switch to plan "h" if no one is waiting.Pickup a passenger going to Firemouth Grill.Go to Zoom Zoom:n.Go to Firemouth Grill:w 3 l 2 l 1 r.Go to Trunkers:w 1 l 1 r.Switch to plan "g".[h]Go to Sunny Skies Park:n 1 r.Switch to plan "i" if no one is waiting.Pickup a passenger going to Cyclone.Go to Firemouth Grill:s 1 l 1 l 1 r.Pickup a passenger going to Addition Alley.Go to Cyclone:w 1 l 1 r 2 r.Pickup a passenger going to Addition Alley.Pickup a passenger going to Trunkers.Go to Zoom Zoom:n.Go to Trunkers:w 3 l.Go to Addition Alley:w 2 r 2 r 1 r.Pickup a passenger going to Narrow Path Park.Go to Narrow Path Park:n 1 r 1 l 1 r.Go to Cyclone:w 1 l 1 r 2 l.Switch to plan "h".[i]Go to Trunkers:s 1 l.Pickup a passenger going to Knots Landing.Go to Knots Landing:e 1 r 2 l 5 r.Go to Trunkers:w 1 l 3 r 1 l.Switch to plan "j" if no one is waiting.Go to Firemouth Grill:e 1 l 1 r.Switch to plan "e".[j]0 is waiting at Starchild Numerology.Go to Starchild Numerology:w 1 l 2 l.Pickup a passenger going to Addition Alley.[k]Go to Rob's Rest:w 1 r 2 l 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:s 1 l 1 l 2 l.Pickup a passenger going to Rob's Rest.Pickup a passenger going to Equal's Corner.Go to Zoom Zoom:n.Go to Rob's Rest:w 2 l 2 r 1 r.Go to Narrow Path Park:s 1 l 1 l 1 r 1 r 2 l 5 l.Switch to plan "o" if no one is waiting.Pickup a passenger going to Equal's Corner.Go to Equal's Corner:w 1 l 1 r 2 l 1 l.Switch to plan "l" if no one is waiting.Pickup a passenger going to Knots Landing.1 is waiting at Starchild Numerology.Switch to plan "m".[l]0 is waiting at Starchild Numerology.[m]Go to Starchild Numerology:n 1 r.Pickup a passenger going to Addition Alley.Go to Addition Alley:w 1 r 3 r 1 r 1 r.Pickup a passenger going to Addition Alley.Go to Knots Landing:n 1 r 2 r 1 l.Go to Starchild Numerology:w 1 l 3 r 1 l 1 l 2 l.Switch to plan "k".[o]0 is waiting at Starchild Numerology.Go to Starchild Numerology:w 1 l 1 r 2 l 1 l 3 l.Pickup a passenger going to Equal's Corner.Go to Equal's Corner:w 1 l.Go to Addition Alley:n 4 r 1 r 1 r.Pickup a passenger going to Equal's Corner.Go to Bird's Bench:n 1 l 1 l 1 l 2 r 1 l.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 r 1 l 2 l.Pickup a passenger going to Bird's Bench.Pickup a passenger going to Equal's Corner.Go to Bird's Bench:n 1 r 2 r 1 l.Go to Equal's Corner:n 1 r 1 r.Switch to plan "p" if no one is waiting.Go to Starchild Numerology:n 1 r.Go to Rob's Rest:w 1 r 2 l 1 r.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 l 1 r 1 r 1 r.Pickup a passenger going to Post Office.Go to Post Office:n 1 l 1 r.Switch to plan "z".[p]1 is waiting at Starchild Numerology.Go to Starchild Numerology:n 1 r.Pickup a passenger going to Addition Alley.Go to Rob's Rest:w 1 r 2 l 1 r.Pickup a passenger going to Addition Alley.Go to Addition Alley:s 1 l 1 l 2 r 1 r 1 r.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 1 l.Pickup a passenger going to Rob's Rest.Pickup a passenger going to Cyclone.Go to Rob's Rest:n 1 r 2 r 1 r.Go to Cyclone:s 1 l 1 l 2 l.Switch to plan "a".[z]

Pruébalo en línea!
¡Pruébelo en línea pero con comentarios y saltos de línea!
Nota: TIO puede manejar una entrada de 1but 2y superior que causa un problema de tiempo de espera. Escribí un pequeño fragmento para imprimir el valor que se verificaba en cada iteración y solo llegó hasta que 137se agotó el tiempo de espera. Si alguien que sabe lo que está haciendo podría ejecutarlo a través de un intérprete (los enlaces de la página de inicio a una versión de C ++ ) para verificar valores más altos, lo agradecería. Puede tardar mucho tiempo en ejecutarse.

Ungolfed con comentarios:

[ FIND THE NTH TAXI CAB NUMBER ]
[ https://en.wikipedia.org/wiki/Taxicab_number ]
[ Inspired by https://codegolf.stackexchange.com/q/73827/38183 ]

[ A taxi cab number T(n) is the smallest number that can be made from the sum  ]
[ of two positive cubes in n different ways. For example, T(1) = 2 because     ]
[ 2 = 1^3 + 1^3. That is the only way to make 2 by summing positive cubes. No  ]
[ solution exists for 1 so 2 is T(1). T(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3.   ]
[ This program takes n as input and finds T(n). The (bad) psuedocode is:       ]
[                                                                              ]
[    S = STDIN;  // Use Bird's Bench                                           ]
[    T = STDIN;  // Use Rob's Rest. Saves bytes and T(n) > n is always true.   ]
[    while (true) {                                                            ]
[       // Fill an array (Firemouth Grill) with the numbers 1 through T        ]
[       // This will make it much easier to compute the cubes because a taxi   ]
[       // can only carry three passengers at a time.                          ]
[       for (i = T; i > 0; i--) { A.push(i) }                                  ]
[       // Fill an array (Trunkers) with the cubes of all integers 1 through T ]
[       for (i = T; i > 0; i--) { B.push(i ^ 3) }                              ]
[       // Fill an array (Sunny Skies Park) with each possible sum of cubes    ]
[       while (B(0) != null) {                                                 ]
[          // Make copies of the next value to add to each remaining value     ]
[          C.push(B(0));                                                       ]
[          while (B(0) != null) {                                              ]
[             C.push(C(0));                                                    ]
[             D.push(B(0));                                                    ]
[             B.shift();                                                       ]
[          }                                                                   ]
[          // Store each possible sum with this cube                           ]
[          while (C(0) != null) {                                              ]
[             E.push(C(0) + D(0));                                             ]
[             B.push(D(0));                                                    ]
[             C.shift;                                                         ]
[             D.shift;                                                         ]
[          }                                                                   ]
[       }                                                                      ]
[       // Check each possible sum to see if it equals T                       ]
[       N = 0;                                                                 ]
[       while (D(0) != null) {                                                 ]
[          if (D(0) = T) { N++ }                                               ]
[          D.shift();                                                          ]
[       }                                                                      ]
[       // If we found the desired number of sums, ouput and break             ]
[       // Otherwise, go to the next T and keep going                          ]
[       if (N = S) {                                                           ]
[          print(T);                                                           ]
[          break;                                                              ]
[       } else {                                                               ]
[          T++;                                                                ]
[       }                                                                      ]
[    }                                                                         ]
[                                                                              ]



[ S = STDIN;  // Use Bird's Bench                                         ]
[ T = STDIN;  // Use Rob's Rest. Saves bytes and T(n) > n is always true. ]
Go to Post Office: west 1st left 1st right 1st left.
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery: south 1st left 1st right.
Pickup a passenger going to Cyclone.
Go to Cyclone: north 1st left 1st left 2nd right.
Pickup a passenger going to Bird's Bench.
Pickup a passenger going to Cyclone.
Go to Zoom Zoom: north.
Go to Cyclone: west.
Pickup a passenger going to Rob's Rest.
Pickup a passenger going to Cyclone.
Go to Bird's Bench: north 1st right 2nd right 1st left.
Go to Rob's Rest: north.


[ // Fill an array (Firemouth Grill) with the numbers 1 through T      ]
[ // This will make it much easier to compute the cubes because a taxi ]
[ //  can only carry three passengers at a time.                       ]
[ for (i = T; i > 0; i--) { A.push(i) }                                ]
Go to Cyclone: south 1st left 1st left 2nd left.
[a]
Pickup a passenger going to Firemouth Grill.
Pickup a passenger going to The Underground.
Go to Zoom Zoom: north.
Go to Firemouth Grill: west 3rd left 2nd left 1st right.
Go to The Underground: east 1st left.
Switch to plan "b" if no one is waiting.
Pickup a passenger going to Cyclone.
Go to Cyclone: north 3rd left 2nd left.
Switch to plan "a".


[b]
[ // Fill an array (Trunkers) with the cubes of all integers 1 through T ]
[ for (i = T; i > 0; i--) { B.push(i ^ 3); }                             ]
Go to Firemouth Grill: south 1st right.
[c]
Pickup a passenger going to Cyclone.
Go to Cyclone: west 1st left 1st right 2nd right.
Pickup a passenger going to Cyclone.
Go to Zoom Zoom: north.
Go to Cyclone: west.
Pickup a passenger going to Multiplication Station.
Pickup a passenger going to Multiplication Station.
Pickup a passenger going to Multiplication Station.
Go to Multiplication Station: south 1st left 2nd right 4th left.
Pickup a passenger going to Trunkers.
Go to Trunkers: south 1st right 2nd left.
Go to Firemouth Grill: east 1st left 1st right.
Switch to plan "e" if no one is waiting.
Switch to plan "c".


[e]
[ // Fill an array with each possible sum of cubes                ]
[ while (B(0) != null) {                                          ]
[ // Make copies of the next value to add to each remaining value ]
[ C.push(B(0));                                                   ]
[ while (B(0) != null) {                                          ]
[    C.push(C(0));                                                ]
[    D.push(B(0));                                                ]
[    B.shift();                                                   ]
[ }                                                               ]
[ Setup Cyclone with a copy of the first value ]
Go to Trunkers: west 1st left 1st right.
Pickup a passenger going to Cyclone.
Go to Cyclone: west 2nd right.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park: north 1st right.

[f]
[ Move any remaining values to Sunny Skies Park, duplicating Cyclone each time ]
Go to Trunkers: south 1st left.
Switch to plan "g" if no one is waiting.
Pickup a passenger going to Sunny Skies Park.
Go to Cyclone: west 2nd right.
Pickup a passenger going to Cyclone.
Go to Zoom Zoom: north.
Go to Cyclone: west.
Go to Sunny Skies Park: north 1st right.
Switch to plan "f".

[g]
[ // Store each possible sum with this cube ]
[ while (C(0) != null) {                    ]
[    E.push(C(0) + D(0));                   ]
[    B.push(D(0));                          ]
[    C.shift;                               ]
[    D.shift;                               ]
[ }                                         ]
[ Move everything at Cyclone to Firemouth Grill ]
Go to Cyclone: west 2nd right.
Switch to plan "h" if no one is waiting.
Pickup a passenger going to Firemouth Grill.
Go to Zoom Zoom: north.
Go to Firemouth Grill: west 3rd left 2nd left 1st right.
Go to Trunkers: west 1st left 1st right.
Switch to plan "g".

[h]
[ Copy Sunny Skies Park to Trunkers and add it to Firemouth Grill ]
Go to Sunny Skies Park: north 1st right.
Switch to plan "i" if no one is waiting.
Pickup a passenger going to Cyclone.
Go to Firemouth Grill: south 1st left 1st left 1st right.
Pickup a passenger going to Addition Alley.
Go to Cyclone: west 1st left 1st right 2nd right.
Pickup a passenger going to Addition Alley.
Pickup a passenger going to Trunkers.
Go to Zoom Zoom: north.
Go to Trunkers: west 3rd left.
Go to Addition Alley: west 2nd right 2nd right 1st right.
Pickup a passenger going to Narrow Path Park.
Go to Narrow Path Park: north 1st right 1st left 1st right.
Go to Cyclone: west 1st left 1st right 2nd left.
Switch to plan "h".

[i]
[ } // End of 'while (B(0) != null)' up near plan "e" ]
Go to Trunkers: south 1st left.
Pickup a passenger going to Knots Landing.
Go to Knots Landing: east 1st right 2nd left 5th right.
Go to Trunkers: west 1st left 3rd right 1st left.
Switch to plan "j" if no one is waiting.
Go to Firemouth Grill: east 1st left 1st right.
Switch to plan "e".


[j]
[ // Check each possible sum to see if it equals T ]
[ N = 0;                                           ]
[ while (D(0) != null) {                           ]
[    if (D(0) = T) { N++; }                        ]
[    D.shift();                                    ]
[ }                                                ]
[ Set N = 0 ]
0 is waiting at Starchild Numerology.
Go to Starchild Numerology: west 1st left 2nd left.
Pickup a passenger going to Addition Alley.

[k]
[ Pickup T ]
Go to Rob's Rest: west 1st right 2nd left 1st right.
Pickup a passenger going to Cyclone.
Go to Cyclone: south 1st left 1st left 2nd left.
Pickup a passenger going to Rob's Rest.
Pickup a passenger going to Equal's Corner.
Go to Zoom Zoom: north.
Go to Rob's Rest: west 2nd left 2nd right 1st right.
Go to Narrow Path Park: south 1st left 1st left 1st right 1st right 2nd left 5th left.
Switch to plan "o" if no one is waiting.

[ Check the next value against T ]
Pickup a passenger going to Equal's Corner.
Go to Equal's Corner: west 1st left 1st right 2nd left 1st left.
Switch to plan "l" if no one is waiting.

[ It's a match so N = N + 1 ]
Pickup a passenger going to Knots Landing.
1 is waiting at Starchild Numerology.
Switch to plan "m".

[l]
[ It's not a match so N = N + 0 ]
0 is waiting at Starchild Numerology.

[m]
Go to Starchild Numerology: north 1st right.
Pickup a passenger going to Addition Alley.
Go to Addition Alley: west 1st right 3rd right 1st right 1st right.
Pickup a passenger going to Addition Alley.
Go to Knots Landing: north 1st right 2nd right 1st left.
Go to Starchild Numerology: west 1st left 3rd right 1st left 1st left 2nd left.
Switch to plan "k".


[o]
[ // If we found the desired number of sums, ouput and break ]
[ // Otherwise, go to the next T and keep going              ]
[ if (N = S) {                                               ]
[    print(T);                                               ]
[    break;                                                  ]
[ } else {                                                   ]
[    T++;                                                    ]
[ }                                                          ]
[ T is still going to Equal's Corner so just get rid of it ]
0 is waiting at Starchild Numerology.
Go to Starchild Numerology: west 1st left 1st right 2nd left 1st left 3rd left.
Pickup a passenger going to Equal's Corner.
Go to Equal's Corner: west 1st left.

[ N is still going to Addition Alley so redirect it to Equal's Corner ]
Go to Addition Alley: north 4th right 1st right 1st right.
Pickup a passenger going to Equal's Corner.

[ Compare N = S ]
Go to Bird's Bench: north 1st left 1st left 1st left 2nd right 1st left.
Pickup a passenger going to Cyclone.
Go to Cyclone: north 1st right 1st left 2nd left.
Pickup a passenger going to Bird's Bench.
Pickup a passenger going to Equal's Corner.
Go to Bird's Bench: north 1st right 2nd right 1st left.
Go to Equal's Corner: north 1st right 1st right.
Switch to plan "p" if no one is waiting.

[ It's a match! The value we want is T, waiting at Rob's Rest. ]
[Go to Rob's Rest:n 3 l 1 r.]
Go to Starchild Numerology: north 1st right.
Go to Rob's Rest: west 1st right 2nd left 1st right.
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery: south 1st left 1st left 1st right 1st right 1st right.
Pickup a passenger going to Post Office.
Go to Post Office: north 1st left 1st right.
Switch to plan "z".

[p]
[ It's not a match. T = T + 1 and start over. ]
1 is waiting at Starchild Numerology.
Go to Starchild Numerology: north 1st right.
Pickup a passenger going to Addition Alley.
Go to Rob's Rest: west 1st right 2nd left 1st right.
Pickup a passenger going to Addition Alley.
Go to Addition Alley: south 1st left 1st left 2nd right 1st right 1st right.
Pickup a passenger going to Cyclone.
Go to Cyclone: north 1st left 1st left.
Pickup a passenger going to Rob's Rest.
Pickup a passenger going to Cyclone.
Go to Rob's Rest: north 1st right 2nd right 1st right.
Go to Cyclone: south 1st left 1st left 2nd left.
Switch to plan "a".

[z]
[ Terminate program with 10 less bytes than going back to the Taxi Garage ]
Tostadas de ingeniero
fuente
Me encanta lo loco de un idioma que es Taxi.
Morgan Thrapp
@MorganThrapp No me había encontrado con esto antes, pero rápidamente se convirtió en un problema que puedes almacenar un máximo de 6 matrices enteras y eso es solo porque Trunkersy Rounders Pubjugar muy bien con los enteros. Si está almacenando decimales, solo obtiene 4 matrices. Además, Firemouth Grillrecoge los números en orden aleatorio, así que eso está fuera si necesita mantener el orden. Realmente, solo obtienes 2 colas y 1 pila. Buena suerte.
Engineer Toast
Me quejaría de los votos positivos que se otorgan a las presentaciones en idiomas divertidos, pero de todos modos esto realmente merece un voto positivo.
Esolanging Fruit