Considere una lista aleatoria de los enteros 1 a N. Desea ordenarla usando solo las siguientes acciones:

1. Intercambie el primer y el último elemento de la lista. (S)
2. Destaque el primer elemento y añádalo al final de la lista. (PAGS)

Esto siempre es posible porque cualquier lista se puede ordenar con suficientes intercambios de elementos adyacentes. Usando S y P puede intercambiar cualquier elemento adyacente llamando a P hasta que los dos elementos en cuestión sean el primero y el último elemento de la lista, luego llamando a S para intercambiarlos, luego llamando a P nuevamente hasta que estén en los índices originales (ahora intercambiados )

Sin embargo, en términos del número de operaciones S y P, es poco probable que este método sea óptimo para la mayoría de las listas.

Reto

Escriba un programa o función que tome una permutación de los números del 1 al N (N> 1). Se puede dar como una lista o cadena o lo que sea conveniente. Debería generar una secuencia de S y P que ordenaría la permutación cuando se aplica de izquierda a derecha. Esta secuencia no tiene que ser óptimamente corta, pero más corta es la mejor (ver Puntuación).

Ejemplo

Si la entrada fue [2, 1, 3]la salida podría ser SPporque

• S aplicado a lo [2, 1, 3]hace [3, 1, 2],
• y P aplicado a lo [3, 1, 2]hace [1, 2, 3], que se ordena.

Verificador

Este fragmento de pila se puede usar para verificar que una secuencia realmente ordena la lista. La lista debe tener corchetes y estar separada por comas. La secuencia SP es solo una cadena de S'sy P' s.

<style>*{font-family:monospace}</style><script>function swap(list) {var tmp = list[0];list[0] = list[list.length - 1];list[list.length - 1] = tmp;}function pop(list) {list.push(list.shift())}function check() {var result = 'Sorted sucessfully.';var details = '';try {var list = eval(document.getElementById('list').value);var seq = document.getElementById('seq').value;details += 'Sequence: ' + seq + '<br>Steps:<br>' + list + ' <-- original';for(var i = 0; i < seq.length; i++) {if (seq.charAt(i) == 'S')swap(list);else if (seq.charAt(i) == 'P')pop(list);details += ' (' + i + ')<br>' + list;}details += ' <-- final (' + i + ')';for(var i = 1; i < list.length; i++) {if (list[i-1] > list[i]) {result = 'Sorting failed!';break;}}} catch(e) {result = 'Error: ' + e;}document.getElementById('result').innerHTML = result;document.getElementById('details').innerHTML = details;}</script><p>List<br><input id='list'type='text'size='60'value='[2, 1, 3]'></p><p>SP Sequence<br><textarea id='seq'rows='1'cols='60'>SP</textarea><br></p><button type='button'onclick='check()'>Check</button><p id='result'></p><p id='details'></p>

Tanteo

Su algoritmo debe producir secuencias SP correctas, pero posiblemente subóptimas, para N = 2 a 256. Para cualquier permutación en este rango, debe ejecutarse en menos de 5 minutos en una computadora moderna decente .

Su puntaje es el número total de operaciones S y P que su algoritmo necesita para ordenar las 30 listas proporcionadas a continuación. El puntaje más bajo gana.

No puede codificar su programa para que se ajuste a estos datos. Si parece necesario, puedo agregar más datos de prueba para determinar el ganador.

1. Length 3
[2, 1, 3]
2. Length 7
[2, 7, 5, 3, 4, 6, 1]
3. Length 41
[7, 12, 17, 2, 14, 15, 33, 20, 37, 18, 9, 25, 41, 26, 39, 29, 16, 5, 23, 24, 35, 38, 32, 6, 11, 21, 27, 8, 40, 3, 10, 36, 13, 30, 31, 28, 1, 4, 19, 22, 34]
4. Length 52
[19, 49, 34, 26, 38, 3, 14, 37, 21, 39, 46, 29, 18, 6, 15, 25, 28, 47, 22, 41, 32, 51, 50, 5, 45, 4, 30, 44, 10, 43, 20, 17, 13, 36, 48, 27, 35, 24, 8, 12, 40, 2, 1, 16, 7, 31, 23, 33, 42, 52, 9, 11]
5. Length 65
[12, 53, 4, 5, 17, 32, 58, 54, 18, 43, 21, 26, 51, 45, 9, 2, 35, 28, 40, 61, 57, 27, 62, 39, 24, 59, 36, 25, 20, 33, 63, 56, 64, 47, 38, 7, 13, 34, 16, 30, 49, 22, 37, 3, 48, 11, 52, 1, 29, 42, 50, 23, 6, 8, 60, 65, 46, 10, 41, 31, 44, 15, 14, 19, 55]
6. Length 69
[58, 15, 63, 18, 24, 59, 26, 37, 44, 67, 14, 52, 2, 31, 68, 54, 32, 17, 55, 50, 42, 56, 65, 29, 13, 41, 7, 45, 53, 35, 21, 39, 61, 23, 49, 12, 60, 46, 27, 57, 28, 40, 10, 69, 1, 6, 19, 62, 8, 30, 64, 34, 3, 43, 38, 20, 25, 33, 66, 47, 4, 36, 16, 11, 5, 22, 51, 48, 9]
7. Length 75
[14, 69, 1, 43, 32, 42, 59, 37, 70, 63, 57, 60, 56, 73, 67, 6, 11, 36, 31, 22, 40, 7, 21, 35, 50, 64, 28, 41, 18, 17, 75, 54, 51, 19, 68, 33, 45, 61, 66, 52, 49, 65, 4, 72, 23, 34, 9, 15, 38, 16, 3, 71, 29, 30, 48, 53, 10, 8, 13, 47, 20, 55, 74, 27, 25, 62, 46, 24, 44, 39, 2, 26, 58, 12, 5]
8. Length 80
[3, 65, 44, 14, 19, 6, 11, 29, 79, 35, 42, 16, 68, 7, 62, 30, 38, 46, 15, 9, 75, 5, 52, 32, 22, 70, 64, 13, 21, 47, 10, 4, 55, 40, 45, 56, 77, 27, 23, 72, 17, 71, 53, 20, 18, 25, 73, 59, 36, 34, 37, 57, 1, 69, 24, 58, 33, 76, 2, 12, 49, 61, 78, 67, 66, 63, 50, 80, 28, 48, 26, 51, 41, 60, 31, 54, 39, 8, 74, 43]
9. Length 103
[40, 62, 53, 6, 32, 85, 8, 83, 33, 29, 87, 93, 22, 37, 80, 12, 74, 69, 64, 9, 18, 98, 17, 45, 60, 38, 10, 103, 19, 5, 54, 15, 90, 100, 79, 91, 46, 82, 43, 31, 51, 96, 30, 70, 76, 16, 55, 77, 11, 65, 58, 75, 61, 3, 28, 24, 101, 20, 41, 72, 86, 56, 35, 50, 78, 27, 67, 95, 44, 68, 48, 26, 39, 97, 21, 49, 102, 73, 63, 7, 71, 52, 1, 88, 34, 42, 14, 47, 36, 99, 4, 13, 94, 89, 59, 92, 57, 25, 23, 66, 81, 2, 84]
10. Length 108
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108]
11. Length 109
[48, 89, 25, 64, 8, 69, 81, 98, 107, 61, 106, 63, 59, 50, 83, 24, 86, 68, 100, 104, 56, 88, 46, 62, 94, 4, 47, 33, 19, 1, 77, 102, 9, 30, 44, 26, 16, 80, 67, 75, 70, 96, 108, 45, 79, 51, 12, 38, 73, 37, 65, 31, 60, 22, 28, 3, 43, 71, 105, 91, 93, 101, 13, 97, 29, 72, 82, 87, 27, 5, 17, 10, 34, 84, 53, 15, 78, 41, 85, 6, 14, 57, 76, 7, 23, 99, 32, 95, 49, 2, 21, 109, 74, 39, 11, 103, 18, 90, 35, 40, 58, 20, 55, 52, 36, 54, 42, 92, 66]
12. Length 151
[61, 7, 8, 79, 78, 4, 48, 13, 14, 117, 12, 96, 130, 118, 63, 110, 72, 57, 86, 126, 62, 10, 29, 102, 99, 28, 56, 135, 11, 151, 141, 97, 45, 109, 38, 150, 40, 149, 52, 140, 106, 80, 66, 134, 125, 137, 31, 85, 68, 94, 36, 26, 95, 92, 49, 25, 120, 148, 33, 73, 41, 100, 58, 127, 60, 122, 133, 9, 19, 81, 59, 55, 103, 146, 42, 21, 128, 75, 101, 82, 50, 142, 131, 76, 20, 69, 139, 83, 16, 64, 17, 124, 90, 138, 37, 1, 34, 43, 129, 77, 23, 35, 144, 121, 113, 115, 114, 67, 98, 70, 145, 104, 71, 5, 119, 6, 18, 88, 116, 111, 132, 39, 89, 24, 15, 107, 27, 65, 30, 47, 143, 93, 53, 108, 2, 74, 123, 44, 51, 54, 87, 147, 84, 3, 112, 46, 32, 91, 136, 22, 105]
13. Length 173
[93, 14, 141, 125, 64, 30, 24, 85, 44, 68, 91, 22, 103, 155, 117, 114, 123, 51, 131, 72, 67, 61, 5, 41, 10, 20, 129, 86, 154, 108, 161, 2, 82, 153, 96, 50, 136, 121, 128, 126, 120, 111, 89, 113, 104, 84, 18, 109, 42, 83, 162, 124, 173, 116, 12, 54, 52, 39, 122, 49, 46, 1, 130, 71, 152, 73, 56, 34, 149, 75, 133, 8, 74, 45, 88, 23, 7, 60, 115, 134, 53, 119, 106, 81, 112, 31, 35, 172, 159, 38, 59, 69, 142, 146, 110, 170, 160, 166, 43, 58, 4, 107, 78, 156, 47, 33, 145, 63, 163, 27, 70, 77, 36, 16, 100, 26, 19, 151, 57, 32, 15, 13, 40, 169, 98, 132, 135, 62, 66, 90, 102, 171, 99, 148, 80, 144, 147, 168, 94, 143, 17, 3, 140, 97, 11, 65, 55, 92, 95, 127, 167, 150, 87, 118, 28, 137, 9, 29, 105, 157, 25, 165, 158, 21, 164, 101, 79, 76, 6, 138, 48, 37, 139]
14. Length 177
[68, 117, 61, 159, 110, 148, 3, 20, 169, 145, 136, 1, 120, 109, 21, 58, 52, 97, 65, 168, 34, 134, 111, 176, 13, 156, 172, 53, 55, 124, 177, 88, 92, 23, 72, 26, 104, 121, 133, 73, 39, 140, 25, 71, 119, 158, 146, 128, 18, 94, 113, 45, 60, 96, 30, 5, 116, 153, 90, 115, 67, 80, 112, 154, 9, 17, 10, 33, 81, 38, 95, 118, 35, 160, 151, 150, 76, 77, 14, 147, 173, 135, 162, 114, 27, 100, 167, 74, 69, 165, 108, 79, 91, 48, 105, 125, 129, 75, 93, 11, 12, 64, 24, 170, 142, 98, 44, 37, 43, 78, 16, 28, 166, 155, 138, 164, 122, 163, 107, 130, 86, 56, 2, 161, 63, 126, 131, 144, 82, 106, 103, 32, 132, 54, 41, 171, 70, 85, 19, 143, 137, 87, 84, 66, 99, 102, 15, 49, 123, 175, 89, 51, 141, 62, 50, 36, 152, 47, 42, 8, 7, 46, 29, 22, 149, 139, 4, 40, 83, 6, 59, 57, 174, 31, 127, 101, 157]
15. Length 192
[82, 130, 189, 21, 169, 147, 160, 66, 133, 153, 143, 116, 49, 13, 63, 61, 94, 164, 35, 112, 141, 62, 87, 171, 19, 3, 93, 83, 149, 64, 34, 170, 129, 182, 101, 77, 14, 91, 145, 23, 32, 92, 187, 54, 184, 120, 109, 159, 27, 44, 60, 103, 134, 52, 122, 33, 78, 88, 108, 45, 15, 79, 137, 80, 161, 69, 6, 139, 110, 67, 43, 190, 152, 59, 173, 125, 168, 37, 151, 132, 1, 178, 20, 114, 119, 144, 25, 146, 42, 136, 162, 123, 31, 107, 131, 127, 51, 105, 2, 65, 28, 102, 76, 24, 135, 174, 9, 111, 98, 39, 74, 142, 70, 121, 154, 38, 113, 75, 40, 86, 100, 106, 181, 117, 95, 85, 138, 41, 167, 172, 4, 186, 17, 16, 104, 71, 81, 73, 57, 8, 140, 118, 158, 12, 148, 53, 29, 185, 18, 150, 22, 188, 72, 128, 84, 96, 47, 192, 126, 56, 163, 50, 157, 165, 97, 166, 180, 7, 46, 30, 191, 124, 5, 48, 175, 68, 36, 89, 177, 11, 176, 183, 99, 90, 55, 26, 10, 58, 115, 155, 179, 156]
16. Length 201
[23, 8, 58, 24, 19, 87, 98, 187, 17, 130, 116, 141, 129, 166, 29, 191, 81, 105, 137, 171, 39, 67, 46, 150, 102, 26, 163, 183, 170, 72, 160, 43, 9, 197, 189, 173, 196, 68, 100, 16, 93, 175, 74, 28, 133, 122, 27, 79, 107, 162, 62, 192, 108, 104, 97, 12, 60, 155, 161, 82, 167, 158, 149, 30, 124, 22, 168, 115, 134, 94, 34, 184, 127, 121, 177, 112, 142, 95, 164, 41, 59, 55, 143, 85, 176, 3, 156, 148, 153, 42, 180, 145, 78, 147, 119, 109, 139, 178, 61, 181, 136, 157, 91, 84, 47, 71, 70, 118, 18, 63, 80, 56, 123, 194, 117, 195, 152, 66, 48, 11, 99, 201, 128, 151, 138, 64, 21, 131, 159, 103, 75, 49, 169, 113, 53, 114, 69, 54, 165, 38, 101, 76, 200, 199, 140, 125, 193, 88, 32, 51, 126, 14, 13, 77, 52, 50, 198, 172, 5, 92, 96, 15, 106, 182, 31, 83, 120, 57, 135, 65, 7, 154, 20, 25, 45, 1, 6, 73, 40, 174, 132, 10, 111, 186, 190, 4, 36, 188, 185, 146, 44, 110, 179, 2, 90, 86, 35, 37, 33, 89, 144]
17. Length 201
[97, 146, 168, 5, 56, 147, 189, 92, 154, 13, 185, 109, 45, 126, 17, 10, 53, 98, 88, 41, 163, 99, 157, 35, 125, 34, 173, 171, 138, 104, 149, 172, 60, 183, 36, 65, 32, 180, 87, 167, 59, 84, 188, 11, 69, 57, 174, 61, 66, 7, 8, 111, 91, 58, 128, 94, 141, 139, 31, 78, 156, 70, 16, 162, 26, 33, 106, 175, 103, 21, 164, 110, 159, 80, 200, 82, 123, 144, 44, 148, 4, 55, 179, 184, 186, 124, 63, 107, 54, 112, 137, 165, 121, 25, 132, 196, 90, 89, 71, 160, 95, 117, 197, 37, 108, 39, 115, 12, 52, 119, 120, 79, 29, 49, 93, 22, 122, 161, 76, 38, 72, 169, 85, 178, 77, 105, 190, 100, 9, 86, 177, 194, 2, 136, 114, 51, 68, 19, 47, 195, 113, 193, 67, 96, 182, 170, 50, 83, 143, 166, 3, 192, 24, 127, 140, 176, 134, 158, 116, 199, 1, 135, 118, 145, 14, 15, 155, 48, 42, 73, 46, 102, 191, 28, 201, 181, 75, 133, 153, 6, 131, 130, 81, 20, 198, 64, 142, 150, 27, 101, 18, 30, 40, 23, 129, 43, 62, 187, 152, 151, 74]
18. Length 205
[161, 197, 177, 118, 94, 112, 13, 190, 200, 166, 127, 80, 115, 204, 186, 60, 50, 97, 175, 32, 26, 65, 16, 4, 55, 120, 143, 187, 121, 29, 18, 82, 17, 21, 144, 20, 88, 195, 99, 67, 203, 23, 176, 126, 137, 77, 70, 30, 103, 182, 113, 119, 36, 47, 90, 98, 54, 3, 49, 105, 57, 135, 153, 142, 174, 155, 158, 11, 157, 22, 171, 110, 28, 196, 129, 163, 79, 63, 38, 145, 140, 2, 128, 180, 106, 59, 25, 184, 81, 164, 95, 39, 68, 78, 178, 156, 72, 51, 202, 66, 48, 101, 71, 108, 130, 5, 107, 147, 199, 12, 27, 150, 167, 91, 64, 170, 191, 151, 149, 168, 34, 125, 188, 181, 139, 58, 75, 189, 124, 152, 183, 7, 111, 89, 84, 52, 141, 83, 69, 62, 73, 43, 123, 14, 179, 162, 114, 138, 117, 159, 74, 85, 10, 96, 86, 31, 132, 1, 104, 109, 45, 165, 148, 172, 154, 92, 173, 40, 19, 56, 37, 205, 44, 193, 122, 185, 93, 133, 53, 9, 169, 6, 61, 136, 46, 76, 33, 15, 116, 198, 160, 194, 131, 41, 42, 35, 146, 134, 192, 8, 87, 201, 100, 24, 102]
19. Length 211
[200, 36, 204, 198, 190, 161, 57, 108, 180, 203, 135, 48, 134, 47, 158, 10, 41, 11, 23, 127, 167, 121, 109, 211, 201, 1, 42, 40, 86, 104, 147, 139, 145, 101, 144, 166, 176, 92, 118, 54, 182, 30, 58, 123, 124, 67, 125, 154, 187, 168, 103, 17, 72, 98, 12, 184, 59, 87, 174, 93, 45, 116, 73, 69, 74, 80, 56, 14, 34, 85, 38, 185, 165, 110, 164, 151, 43, 192, 62, 4, 140, 170, 197, 111, 173, 141, 65, 77, 70, 136, 206, 83, 100, 148, 25, 183, 209, 189, 150, 33, 46, 16, 64, 114, 71, 102, 91, 39, 177, 196, 169, 128, 129, 44, 75, 188, 146, 26, 84, 138, 162, 194, 105, 37, 35, 88, 156, 130, 193, 19, 179, 82, 106, 181, 153, 28, 53, 21, 195, 66, 159, 115, 113, 112, 191, 172, 63, 143, 178, 94, 160, 186, 31, 29, 90, 68, 205, 155, 119, 117, 157, 107, 60, 79, 171, 149, 6, 24, 27, 50, 51, 126, 15, 133, 2, 131, 7, 49, 207, 163, 18, 120, 199, 61, 52, 32, 208, 20, 210, 13, 78, 55, 137, 202, 152, 8, 81, 76, 9, 97, 22, 99, 132, 95, 122, 89, 175, 5, 3, 96, 142]
20. Length 226
[204, 79, 88, 98, 197, 32, 40, 117, 153, 167, 29, 74, 170, 115, 127, 210, 22, 109, 65, 47, 41, 132, 110, 158, 192, 99, 96, 224, 190, 143, 33, 225, 195, 19, 70, 73, 54, 161, 75, 179, 181, 207, 26, 221, 66, 130, 152, 131, 30, 35, 155, 69, 68, 38, 129, 95, 116, 214, 7, 186, 62, 27, 212, 125, 216, 86, 148, 164, 141, 4, 140, 222, 16, 46, 12, 215, 78, 219, 211, 134, 118, 171, 121, 52, 123, 56, 220, 15, 25, 100, 137, 163, 51, 91, 10, 83, 55, 187, 182, 201, 149, 160, 8, 14, 218, 77, 3, 184, 114, 43, 122, 135, 142, 104, 120, 198, 45, 108, 85, 189, 151, 175, 136, 165, 226, 97, 124, 200, 60, 172, 20, 67, 1, 174, 87, 102, 119, 188, 223, 199, 103, 89, 49, 213, 57, 9, 101, 112, 36, 176, 194, 92, 145, 180, 168, 111, 94, 178, 39, 166, 193, 17, 2, 154, 58, 156, 217, 13, 80, 202, 206, 169, 107, 177, 144, 205, 139, 93, 34, 64, 106, 150, 146, 126, 185, 208, 63, 203, 105, 18, 191, 53, 183, 209, 6, 23, 84, 5, 61, 59, 162, 128, 37, 50, 28, 159, 173, 196, 24, 31, 72, 138, 82, 48, 133, 147, 42, 113, 81, 90, 71, 21, 11, 157, 76, 44]
21. Length 227
[197, 52, 91, 42, 29, 113, 82, 68, 147, 225, 80, 167, 117, 142, 140, 216, 65, 195, 97, 61, 133, 209, 214, 58, 152, 71, 56, 182, 201, 163, 227, 186, 63, 171, 207, 102, 161, 136, 224, 146, 92, 175, 45, 217, 6, 99, 20, 119, 210, 93, 77, 211, 21, 70, 90, 96, 115, 100, 183, 173, 69, 98, 172, 75, 111, 203, 19, 129, 35, 155, 74, 37, 23, 51, 192, 212, 33, 64, 59, 194, 112, 135, 1, 184, 5, 166, 185, 84, 199, 138, 144, 86, 128, 26, 190, 73, 179, 27, 118, 223, 46, 95, 159, 153, 226, 25, 180, 132, 189, 60, 32, 208, 123, 89, 87, 22, 181, 143, 47, 18, 198, 219, 156, 148, 193, 122, 110, 28, 106, 39, 30, 103, 4, 176, 114, 3, 131, 107, 204, 218, 141, 169, 16, 206, 36, 188, 174, 54, 94, 50, 205, 104, 170, 160, 72, 165, 78, 24, 222, 8, 108, 81, 76, 15, 13, 126, 79, 7, 105, 125, 162, 83, 41, 145, 139, 66, 127, 38, 12, 187, 130, 221, 48, 164, 191, 157, 88, 168, 196, 10, 9, 53, 124, 150, 31, 116, 49, 34, 200, 134, 220, 121, 2, 62, 149, 158, 101, 17, 202, 11, 109, 85, 55, 67, 120, 43, 154, 44, 215, 177, 178, 40, 57, 14, 213, 151, 137]
22. Length 230
[69, 204, 215, 61, 97, 149, 9, 11, 137, 71, 37, 219, 92, 115, 156, 159, 200, 222, 3, 89, 172, 177, 203, 45, 54, 82, 147, 176, 168, 6, 26, 81, 25, 132, 212, 70, 228, 122, 225, 141, 100, 12, 124, 30, 146, 73, 19, 49, 52, 62, 217, 166, 191, 102, 163, 50, 181, 7, 134, 58, 76, 199, 179, 169, 197, 108, 174, 22, 186, 171, 114, 103, 173, 68, 65, 4, 13, 117, 64, 10, 126, 77, 206, 133, 121, 60, 40, 38, 59, 178, 224, 211, 187, 80, 220, 140, 8, 34, 130, 41, 95, 105, 227, 66, 210, 180, 192, 106, 209, 107, 157, 188, 170, 101, 131, 87, 14, 165, 78, 182, 136, 193, 190, 20, 67, 125, 36, 5, 145, 218, 99, 138, 154, 16, 29, 152, 194, 53, 148, 93, 202, 229, 198, 109, 43, 214, 150, 51, 128, 216, 1, 83, 196, 135, 74, 119, 75, 42, 142, 72, 226, 185, 116, 162, 63, 2, 112, 33, 184, 158, 15, 213, 144, 223, 98, 57, 160, 143, 90, 44, 205, 35, 21, 48, 151, 85, 123, 32, 47, 39, 189, 161, 56, 207, 84, 94, 230, 46, 164, 113, 175, 18, 195, 110, 127, 96, 129, 88, 17, 153, 104, 91, 86, 31, 118, 111, 120, 201, 28, 221, 23, 139, 24, 27, 167, 208, 183, 155, 79, 55]
23. Length 238
[202, 18, 122, 135, 11, 57, 103, 35, 86, 2, 84, 232, 208, 186, 54, 77, 145, 101, 105, 137, 210, 234, 207, 93, 55, 63, 230, 66, 160, 10, 223, 36, 34, 216, 104, 174, 121, 25, 166, 75, 167, 176, 61, 32, 118, 89, 68, 5, 14, 27, 204, 99, 149, 88, 91, 222, 37, 144, 108, 78, 128, 131, 190, 17, 65, 168, 225, 165, 41, 49, 38, 72, 43, 147, 158, 74, 130, 7, 82, 64, 97, 69, 100, 22, 152, 85, 48, 33, 218, 47, 228, 113, 40, 185, 219, 112, 180, 120, 4, 213, 179, 194, 51, 96, 221, 44, 238, 31, 117, 114, 229, 81, 164, 193, 236, 26, 59, 30, 151, 12, 115, 170, 24, 70, 227, 159, 133, 52, 134, 203, 15, 197, 155, 83, 50, 111, 195, 139, 109, 127, 188, 87, 62, 157, 226, 142, 98, 76, 211, 138, 58, 140, 198, 220, 16, 46, 183, 107, 106, 29, 163, 173, 209, 217, 215, 1, 177, 233, 199, 110, 172, 23, 212, 79, 94, 102, 39, 20, 178, 150, 175, 119, 8, 13, 42, 156, 201, 73, 200, 124, 53, 161, 92, 123, 224, 143, 196, 28, 9, 6, 80, 56, 148, 125, 214, 60, 171, 153, 231, 181, 205, 19, 95, 206, 154, 132, 169, 116, 3, 126, 187, 162, 191, 67, 136, 45, 192, 189, 235, 129, 21, 141, 237, 184, 90, 146, 182, 71]
24. Length 241
[2, 33, 49, 83, 207, 204, 13, 57, 115, 86, 102, 219, 232, 44, 177, 197, 171, 227, 191, 10, 25, 162, 62, 11, 76, 214, 163, 201, 130, 91, 233, 194, 112, 179, 66, 139, 183, 116, 196, 193, 150, 211, 30, 144, 209, 97, 174, 3, 68, 38, 120, 165, 56, 64, 87, 15, 79, 131, 206, 96, 188, 7, 99, 195, 129, 8, 186, 78, 212, 125, 161, 230, 225, 239, 47, 107, 53, 218, 164, 106, 198, 215, 181, 226, 6, 175, 167, 236, 67, 80, 210, 128, 155, 40, 63, 74, 113, 89, 18, 190, 124, 221, 59, 149, 103, 42, 156, 157, 200, 168, 34, 77, 65, 146, 5, 187, 222, 231, 140, 141, 172, 234, 100, 94, 132, 237, 24, 216, 152, 22, 51, 69, 35, 43, 105, 23, 61, 1, 72, 135, 104, 9, 12, 21, 46, 192, 159, 205, 158, 109, 28, 98, 50, 122, 111, 71, 166, 229, 37, 114, 173, 134, 136, 81, 121, 185, 118, 223, 20, 14, 108, 82, 178, 54, 26, 153, 36, 39, 117, 147, 95, 90, 16, 17, 170, 119, 199, 19, 84, 213, 88, 93, 151, 4, 101, 142, 110, 184, 55, 138, 75, 133, 148, 145, 45, 70, 217, 143, 224, 241, 31, 240, 182, 52, 238, 126, 85, 154, 137, 160, 27, 180, 60, 29, 32, 169, 235, 123, 176, 48, 220, 203, 228, 127, 41, 58, 73, 92, 189, 202, 208]
25. Length 241
[105, 160, 132, 32, 10, 117, 76, 2, 190, 108, 178, 51, 71, 237, 232, 47, 14, 124, 100, 31, 169, 196, 8, 184, 21, 151, 223, 86, 42, 127, 55, 58, 229, 4, 219, 46, 238, 179, 24, 194, 203, 122, 66, 15, 81, 146, 172, 106, 129, 135, 216, 120, 92, 231, 144, 195, 181, 162, 69, 45, 137, 136, 9, 30, 5, 188, 91, 49, 147, 233, 198, 17, 241, 163, 36, 18, 183, 59, 16, 29, 116, 182, 41, 48, 23, 39, 154, 210, 68, 167, 95, 213, 79, 225, 37, 157, 109, 143, 78, 142, 173, 155, 200, 110, 20, 73, 141, 168, 156, 126, 150, 201, 114, 1, 230, 211, 217, 131, 140, 204, 209, 149, 103, 199, 165, 175, 35, 107, 74, 63, 193, 239, 218, 234, 197, 224, 174, 121, 60, 88, 22, 171, 133, 207, 152, 34, 43, 228, 125, 115, 101, 7, 12, 220, 82, 153, 134, 52, 130, 70, 72, 44, 177, 89, 65, 98, 94, 53, 208, 227, 161, 3, 123, 236, 221, 87, 102, 50, 90, 180, 185, 186, 67, 77, 26, 212, 27, 222, 6, 145, 11, 13, 84, 25, 164, 64, 85, 139, 214, 189, 61, 96, 191, 128, 93, 138, 148, 19, 119, 202, 75, 176, 159, 56, 104, 206, 40, 187, 215, 62, 166, 240, 112, 226, 170, 83, 97, 57, 99, 38, 28, 113, 205, 158, 235, 111, 54, 192, 118, 80, 33]
26. Length 244
[89, 13, 154, 161, 235, 225, 92, 188, 215, 194, 54, 58, 128, 21, 165, 85, 144, 205, 142, 77, 109, 24, 83, 69, 72, 7, 224, 240, 191, 204, 183, 203, 68, 70, 63, 95, 206, 170, 153, 180, 45, 178, 35, 27, 190, 132, 222, 41, 40, 156, 97, 20, 217, 177, 167, 65, 23, 136, 216, 234, 38, 201, 236, 164, 82, 241, 10, 141, 148, 229, 5, 125, 113, 159, 193, 187, 130, 179, 52, 108, 86, 196, 174, 123, 56, 116, 227, 30, 239, 98, 186, 67, 135, 118, 163, 43, 32, 50, 231, 226, 232, 172, 200, 99, 6, 143, 39, 93, 107, 34, 129, 157, 100, 127, 15, 84, 81, 73, 121, 220, 44, 8, 57, 105, 91, 171, 162, 211, 244, 104, 112, 238, 212, 133, 71, 192, 145, 160, 87, 181, 60, 184, 119, 4, 55, 96, 53, 12, 213, 124, 94, 22, 42, 3, 48, 131, 117, 140, 138, 228, 219, 155, 59, 29, 202, 169, 114, 101, 47, 233, 176, 139, 207, 33, 79, 16, 51, 66, 75, 90, 198, 168, 166, 31, 151, 49, 208, 150, 111, 14, 25, 197, 17, 76, 80, 78, 9, 173, 26, 137, 19, 120, 199, 106, 152, 88, 147, 36, 158, 28, 243, 221, 110, 74, 175, 237, 61, 2, 62, 214, 189, 134, 195, 218, 18, 102, 46, 103, 11, 122, 146, 185, 182, 209, 1, 149, 115, 64, 37, 126, 230, 223, 242, 210]
27. Length 246
[28, 186, 214, 18, 220, 73, 20, 88, 234, 187, 27, 102, 22, 129, 10, 228, 196, 56, 47, 2, 16, 67, 124, 137, 177, 179, 223, 147, 188, 23, 103, 109, 149, 60, 229, 99, 222, 90, 49, 80, 158, 93, 171, 71, 175, 143, 19, 212, 40, 226, 219, 120, 146, 66, 167, 232, 94, 174, 237, 9, 173, 70, 122, 241, 58, 82, 191, 211, 180, 104, 53, 36, 83, 37, 131, 25, 162, 32, 210, 144, 145, 69, 135, 63, 154, 165, 46, 57, 50, 74, 128, 140, 112, 118, 125, 231, 221, 233, 95, 200, 153, 6, 166, 98, 208, 91, 89, 141, 4, 26, 134, 86, 8, 30, 157, 156, 224, 201, 243, 7, 161, 1, 84, 115, 44, 230, 78, 79, 5, 17, 194, 148, 152, 121, 193, 107, 240, 181, 29, 43, 65, 164, 45, 110, 64, 195, 216, 127, 59, 197, 178, 151, 139, 85, 75, 11, 204, 184, 77, 54, 51, 205, 108, 142, 130, 138, 238, 87, 38, 101, 96, 31, 215, 244, 242, 172, 213, 136, 97, 35, 39, 76, 42, 245, 123, 227, 24, 168, 33, 159, 217, 239, 55, 176, 68, 207, 106, 132, 15, 116, 61, 198, 62, 182, 225, 202, 105, 150, 183, 81, 170, 13, 41, 199, 3, 185, 235, 14, 155, 21, 126, 119, 169, 72, 12, 236, 48, 209, 190, 113, 218, 100, 52, 111, 189, 92, 192, 114, 117, 160, 133, 203, 163, 34, 206, 246]
28. Length 250
[119, 57, 59, 181, 212, 120, 236, 121, 99, 247, 138, 187, 175, 108, 107, 197, 123, 101, 141, 77, 201, 3, 52, 60, 56, 240, 157, 39, 42, 199, 23, 18, 136, 74, 137, 143, 229, 170, 20, 160, 206, 219, 191, 185, 46, 223, 150, 190, 116, 96, 198, 221, 220, 159, 238, 48, 176, 113, 168, 33, 44, 142, 67, 244, 13, 218, 122, 246, 214, 234, 237, 27, 165, 24, 153, 90, 84, 154, 235, 196, 80, 111, 102, 231, 228, 135, 16, 148, 26, 45, 10, 71, 156, 224, 183, 232, 72, 94, 132, 54, 58, 248, 144, 213, 139, 129, 245, 115, 25, 164, 87, 19, 193, 81, 32, 78, 91, 167, 171, 40, 92, 226, 109, 69, 86, 38, 61, 5, 14, 118, 145, 103, 53, 93, 172, 178, 225, 68, 163, 210, 179, 192, 208, 169, 17, 12, 50, 233, 6, 55, 243, 158, 88, 188, 242, 36, 173, 126, 155, 184, 216, 149, 47, 76, 200, 1, 112, 28, 161, 174, 41, 73, 222, 66, 37, 63, 64, 124, 89, 205, 9, 186, 202, 70, 203, 127, 105, 250, 182, 79, 43, 133, 8, 241, 114, 128, 51, 83, 98, 49, 209, 7, 95, 151, 162, 189, 180, 75, 195, 62, 207, 21, 104, 30, 117, 110, 140, 29, 227, 249, 82, 152, 11, 34, 85, 106, 217, 211, 2, 35, 215, 4, 230, 134, 31, 194, 97, 22, 125, 130, 100, 239, 131, 166, 65, 15, 146, 177, 204, 147]
29. Length 253
[46, 245, 174, 180, 85, 29, 141, 70, 252, 119, 214, 225, 86, 91, 41, 67, 219, 118, 127, 243, 2, 71, 157, 114, 55, 92, 5, 200, 199, 139, 191, 235, 153, 102, 206, 171, 117, 58, 223, 249, 11, 211, 202, 175, 156, 133, 57, 163, 47, 65, 213, 247, 189, 111, 177, 49, 124, 154, 164, 145, 80, 15, 232, 142, 39, 69, 201, 185, 229, 215, 170, 42, 3, 248, 169, 136, 149, 218, 237, 90, 135, 7, 242, 246, 23, 186, 31, 4, 167, 207, 173, 132, 195, 196, 78, 212, 22, 35, 194, 54, 184, 183, 222, 230, 88, 43, 144, 151, 34, 97, 6, 109, 37, 147, 72, 158, 134, 33, 51, 238, 165, 162, 9, 63, 166, 113, 137, 198, 50, 121, 106, 224, 19, 104, 95, 129, 193, 79, 192, 122, 30, 12, 234, 168, 76, 103, 73, 66, 188, 178, 172, 176, 250, 182, 110, 231, 155, 26, 197, 10, 152, 98, 131, 25, 36, 81, 138, 150, 227, 24, 112, 120, 204, 75, 8, 179, 94, 17, 140, 32, 77, 61, 233, 38, 205, 93, 99, 27, 208, 56, 216, 48, 241, 20, 130, 240, 115, 83, 60, 108, 28, 13, 89, 128, 160, 82, 40, 126, 16, 253, 21, 251, 228, 59, 159, 64, 203, 236, 52, 18, 181, 105, 107, 239, 220, 44, 74, 125, 209, 84, 226, 217, 210, 190, 101, 100, 68, 116, 161, 148, 244, 221, 96, 45, 123, 187, 62, 87, 53, 1, 146, 143, 14]
30. Length 256
[159, 248, 75, 43, 111, 38, 4, 17, 155, 87, 81, 208, 53, 230, 65, 11, 108, 228, 146, 212, 137, 225, 144, 189, 86, 105, 84, 128, 97, 50, 223, 15, 83, 169, 217, 47, 88, 236, 114, 181, 115, 177, 102, 250, 246, 104, 80, 45, 240, 14, 196, 52, 247, 41, 198, 32, 182, 206, 226, 101, 70, 94, 113, 49, 254, 59, 42, 154, 77, 253, 112, 215, 99, 25, 134, 92, 95, 150, 64, 178, 118, 79, 130, 63, 129, 131, 57, 218, 85, 204, 3, 163, 158, 186, 10, 199, 24, 125, 251, 51, 74, 160, 207, 120, 233, 30, 19, 9, 56, 167, 58, 117, 164, 54, 220, 229, 234, 203, 211, 103, 205, 69, 39, 5, 31, 191, 106, 180, 116, 245, 21, 222, 91, 235, 8, 2, 214, 29, 238, 176, 135, 61, 227, 202, 122, 252, 231, 89, 187, 37, 149, 96, 190, 172, 73, 18, 71, 1, 179, 46, 156, 201, 165, 256, 151, 27, 242, 188, 126, 124, 244, 100, 107, 143, 170, 72, 255, 40, 67, 192, 185, 219, 20, 157, 98, 237, 136, 168, 141, 224, 232, 44, 139, 132, 22, 60, 109, 90, 175, 171, 62, 23, 161, 12, 76, 210, 68, 184, 93, 243, 48, 209, 174, 200, 121, 123, 36, 173, 140, 133, 145, 6, 110, 152, 142, 241, 55, 138, 147, 193, 213, 127, 7, 34, 66, 153, 26, 13, 162, 183, 239, 78, 249, 221, 28, 194, 16, 35, 33, 82, 195, 148, 216, 119, 166, 197]

Python 3 (con PyPy) - puntuación: 607771

Editar: creo que el error está solucionado, pero todavía no estoy convencido de que esto funcione hasta que demuestre que funciona

def d(a, b, N):
    a, b = a%N, b%N

    if a >= b:
        return a-b
    else:
        return a+(N-b)

def gt(a, b, N):
    if a == N and b == 1:
        return False
    if a == 1 and b == N:
        return True
    return a > b

def solve(numbers):
    N = len(numbers)
    best_move = None
    target = sorted(numbers)

    if N == 2:
      return "" if numbers == [1,2] else "P"

    for b in range(N):
        nums = numbers[:]
        moves = []
        head_ptr = 0 # Which element should be at the start of the list if we actually moved stuff
        reference = target[b:]+target[:b]
        ref_d = {t:i for i,t in enumerate(reference)}

        while True:
            for pops in range(N):
                ptr = (head_ptr + pops) % N

                # Magic
                d1 = d(ref_d[nums[ptr-1]],ptr-1,N)+d(ptr,ref_d[nums[ptr]],N)
                d2 = d(ref_d[nums[ptr]],ptr,N)+d(ptr-1,ref_d[nums[ptr-1]],N)

                if d1 > d2 or (d1 == d2 and gt(nums[ptr-1], nums[ptr], N)):
                    moves.append("P"*pops + "S")
                    head_ptr = (head_ptr + pops) % N
                    nums[ptr-1],nums[ptr] = nums[ptr],nums[ptr-1]
                    break

            else:
                if nums[nums.index(1):]+nums[:nums.index(1)] != target:
                    print("This algorithm is seriously broken.\n")
                moves.append("P"*((N+nums.index(1)-head_ptr)%N))
                break

        moves = "".join(moves)

        if not best_move or len(moves) < len(best_move):
            best_move = moves

    return best_move

Uso

solve([3, 4, 2, 1, 5])

Explicación

El programa solo realiza intercambios de clasificación de burbujas, utilizando la observación de que:
S: n 1 2 3 ... n-1 0 PS: 0 2 3 ... n-1 n 1 PPS: 1 3 ... n-1 n 0 2 PPPS: 2 ... n-1 n 0 1 3 ...

En otras palabras, los iempujes seguidos de un intercambio significa que el elemento ise intercambia con el elemento i-1, el ajuste de los índices. Sin embargo, debemos hacer un seguimiento del hecho de que la lista se modifica al hacerlo.

Para hacerlo mejor que el tipo de burbuja habitual, tratamos de aplicar una heurística para asegurarnos de no hacer demasiados intercambios inútiles, haciendo cumplir que cualquier intercambio acerque ambos elementos a sus respectivos objetivos (no lo he demostrado formalmente es correcto, pero parece funcionar hasta ahora). Luego tomamos la mejor solución de muchas configuraciones (CPython lleva un tiempo, pero PyPy hace este trabajo relativamente rápido).

Tanteo

Salida en Pastebin.

Anterior ingenua burbuja ordenar ver. (puntuación: 1126232)

Este definitivamente funciona.

def cyclic_sorted(nums):
    for i in range(len(nums)):
        if nums[i:] + nums[:i] == sorted(nums):
            return i
    return False

def solve(nums):
    N = len(nums)

    def gt(a, b):
        if a == 1 and b == N:
            return True
        if a == N and b == 1:
            return False
        return a > b

    moves = []
    head_ptr = 0 # Which element should be at the start of the list if we actually moved stuff

    while nums != sorted(nums):
        pops = 0
        ptr_offset = 0

        while pops < N:
            ptr = (head_ptr + pops) % N

            if (not moves or pops > 0) and gt(nums[ptr-1], nums[ptr]):
                moves.append("P"*pops + "S")
                head_ptr = (head_ptr + pops) % N

                nums[ptr-1],nums[ptr] = nums[ptr],nums[ptr-1]
                break

            pops += 1

        else:
            moves.append("P"*cyclic_sorted(nums[head_ptr:]+nums[:head_ptr]))
            break

    return "".join(moves)

Javascript ES6 - 607,771

function popsort( iData ) {
    var sSP, iLen,
        sSP_Opt = popsortimpl( iData.slice( 0 ), 0 ),
        iOptLen = sSP_Opt.length;

    for( var n = iData.length, i = 2; i <= n; i++ )
        if( (iLen = (sSP = popsortimpl( iData.slice( 0 ), i - 1 )).length) < iOptLen ) {
            iOptLen = iLen;
            sSP_Opt = sSP;
        }

    return sSP_Opt;
}

function popsortimpl( iData, iPivIdx ) {
    function issorted()
        { return iData.every( (_,i_) => _ == i_+1 ); }

    function swap() {
        var i_ = iData[0];

        iData[0] = iData[n-1];
        iData[n-1] = i_;

        sSP.push( 'S' );
    }

    function pop() {
        iData.push( iData.shift() );
        if( --iPivIdx < 0 )
            iPivIdx += n;

        sSP.push( 'P' );
    }

    function dist2home( iIdx_, i_ ) {
        var iHome_ = (iPivIdx + i_) %n,
            iDist1_ = iIdx_ - iHome_,
            iDist2_ = iHome_ - iIdx_;

        if( iDist1_ < 0 )
            iDist1_ += n;
        if( iDist2_ < 0 )
            iDist2_ += n;

        return Math.min( iDist1_, iDist2_*Math.max( 1, n/50 ) );
    }

    var n = iData.length,
        sSP = [];

    while( !issorted() ) {
        var iDistP = Math.max( dist2home( 0, iData[0] ), dist2home( n - 1, iData[n - 1] ) ),
            iDistS = Math.max( dist2home( n - 1, iData[0] ), dist2home( 0, iData[n - 1] ) );

        if( iDistS < iDistP )
            swap();
        else pop();
    }
    return sSP.join('');
}

Implementa un tipo de burbuja del "extremo más cercano" que burbujea elementos hacia arriba o hacia abajo según la ruta más corta (burbuja hacia arriba o hacia abajo) a una posición de referencia.

No creo que la rutina sea óptima, pero debería estar razonablemente cerca de ella. Como beneficio adicional, ejecuta el conjunto completo de vectores de prueba en milisegundos.

Actualizado para iterar sobre el punto de pivote para mejorar la competitividad. También introduje la heurística para compensar el hecho de que los elementos tienen una movilidad más baja moviéndose "hacia arriba" en la lista que moviéndose "hacia abajo" (un fenómeno análogo a la diferencia en la movilidad de electrones y huecos en un semiconductor). Existen grandes diferencias entre esta implementación y las de Sp3000, de ahí que el hecho de que ambas obtengan exactamente 607,771 es espeluznante. Halloween espeluznante

La rutina ahora tarda unos 20 segundos en ejecutarse.

Salida de muestra

popsort( [2, 7, 5, 3, 4, 6, 1] )

rendimientos

PSPPSPSPPPS

OCaml, puntuación: 1136707 1136599

Editar: me equivoqué! Había leído Sque intercambiaría elementos adyacentes y me perdí que el primer y el último elemento se intercambian. Esta implementación se basa en esto como es obvio de la evalimplementación. Editar²: Lo arreglé utilizando la observación de que puedes escribir lo que pensé que era SP como P S. También cambié a la versión con mejor puntuación con algunas optimizaciones para hacerlo menos lento.

El tiempo de ejecución es 1.33 18 1.01 segundos en mi sistema usando el binario compilado por el intérprete .

type sp = S | P

let string_of_sp = function
  | S -> "S"
  | P -> "P"

let rec eval (e : sp list) (xs : int list) : int list =
  match e, xs with
  | [], xs -> xs
  | P :: S :: e, x1 :: x2 :: xs -> eval e (x1 :: xs @ [x2])
  | P :: e, x :: xs -> eval e (xs @ [x])
  | _ -> assert false

let generate_sp_sequence xs : sp list =
  let sorted = List.sort compare xs in
  let rec generate_sp_sequence ((xs, ys) : int list * int list) acc : sp list =
    if sorted = ys @ List.rev xs
    then acc
    else 
      match ys with
      | v1 :: v2 :: ys' ->
         if v1 > v2
         then generate_sp_sequence (v2 :: xs, v1 :: ys') (S :: P :: acc)
         else generate_sp_sequence (v1 :: xs, v2 :: ys') (P :: acc)
      | [x] ->
         let ys = List.rev (x :: xs) in
         generate_sp_sequence ([], ys) (P :: acc)
      | [] ->
         assert false
  in List.rev @@ generate_sp_sequence ([], xs) []


(** Uncomment to run tests **)
(*
let test =
  QCheck.(mk_test
            ~n:1000
            ~name:"generate_sp_sequence sorting test"
            ~pp:PP.(list int)
            Arbitrary.(list ~start:2 ~stop:256 small_int)
            (fun xs ->
             Prop.assume (List.length xs >= 2);
             eval (generate_sp_sequence ([], xs))
                  xs
             = List.sort compare xs))

let _ = QCheck.run test
 *)

let score_test = ... (* not included for brevity *)

let score =
  List.map (fun xs -> generate_sp_sequence ([], xs)) score_test
  |> List.map List.length
  |> List.fold_left (+) 0

let _ =
  print_string "The score is: ";
  print_int score;
  print_newline ()

generate_sp_sequence simplemente ejecuta bubbleort y genera los pasos en términos de S y P. Puede generar pasos innecesarios.

C, puntuación: 607771

Resulta que mi solución es muy similar a la solución Python de Sp3000 (que explica el puntaje idéntico). Nunca he usado Python, así que no puedo decirlo con certeza, pero creo que el concepto es exactamente el mismo:

Para cada número r en 0..n-1, establezca una meta de una matriz ordenada rotada r veces desde la posición inicial (es decir, que contenga P pops con r = P mod n), y encuentre una serie de movimientos que resulten en esta configuración. Registre la secuencia más corta de movimientos para cualquier r.
Realice intercambios solo cuando el intercambio se acerque, sea cual sea el elemento que esté más alejado de su posición de meta (mirando en cualquier dirección), o cuando el intercambio acerque ambos elementos si ambos están igualmente lejos.

Código

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Returns true if the array is sorted starting at position 'offset' */
int is_sorted(int *array, int n, int offset)
{
    int i;
    for (i = 0; i < n && array[(offset+i)%n] == i+1; i++);
    return i == n;
}

/* Find moves that would sort the array, assuming the first element will
   be at position (offset + n/2) % n */
int get_moves(int *array, int n, int offset, int stop_after, char *moves)
{
    int tmp, posA = n-1, posB = 0, counter = 0;
    /* Repeat until sorted or reaching the maximum number of moves (previous
       best, or the worst case upper bound if no previous solution) */
    for (; counter < stop_after && !is_sorted(array, n, posB); posA = (posA+1)%n, posB = (posB+1)%n, moves[counter++] = 'P')
    {
        /* Perform a swap if it would move whichever element is further away
           closer to its target */
        if ((array[posA] - posA + offset + n) % n >
            (array[posB] - posB + offset + n) % n)
        {
            tmp = array[posA];
            array[posA] = array[posB];
            array[posB] = tmp;
            moves[counter++] = 'S';
            if (is_sorted(array, n, posB))
            {
                break;
            }
        }
    }
    return counter;
}

int *parse_input(int _argc, char **_argv)
{
    int i;
    int *array = NULL;
    if (_argc > 1)
    {
        array = malloc((_argc-1) * sizeof(int));
        _argv[1]++; /* remove initial square bracket */
        for (i = 1; i < _argc; i++)
        {
            array[i-1] = atoi(_argv[i]);
        }
    }
    return array;
}

int main(int _argc, char **_argv)
{
    int *orig_array = parse_input(_argc, _argv);
    if (orig_array != NULL)
    {
        int n = _argc - 1;
        /* Safe worst case upper bound representing n^2 "SP" moves */
        int worst_move_count = 2*n*n;

        int i, move_count, offset;
        int best_offset, best_move_count = worst_move_count;

        char *best_moves = malloc(worst_move_count + 1);
        char *moves = malloc(worst_move_count + 1);
        int *array = malloc(n * sizeof(int));

        memset(best_moves, 0, worst_move_count + 1);
        /* Try all offsets from 0 to n-1; i.e. find solutions for:
           1, 2, 3, ..., n-2, n-1, n
           2, 3, 4, ..., n-1, n,   1
           3, 4, 5, ..., n,   1,   2
           ...
           n, 1, 2, ..., n-3, n-2, n-1
        */
        for (offset = 0; offset < n; offset++)
        {
            memset(moves, 0, worst_move_count + 1);
            memcpy(array, orig_array, n*sizeof(int));
            move_count = get_moves(array, n, offset, best_move_count, moves);
            if (move_count < best_move_count)
            {
                strcpy(best_moves, moves);
                best_move_count = move_count;
                best_offset = offset;
            }
        }
        printf("%s\n", best_moves);

        free(best_moves);
        free(moves);
        free(array);
        free(orig_array);
    }
    return 0;
}

Uso

$ gcc -Ofast -o popswap popswap.c
$ ./popswap [2, 7, 5, 3, 4, 6, 1]
PSPPSPSPPPS
$ ./popswap [2, 7, 5, 3, 4, 6, 1]|tr -d '\n'|wc -c
11

Tanteo

Guión:

#!/bin/sh
grep ^\\[ input.txt|while read line; do
    len=`echo $line|wc -w`;
    score=`./popswap $line|tr -d '\n'|wc -c`;
    echo "    $len $score";
done

Resultados:

$ ./scoring.sh |cut -d' ' -f 6|paste -sd+|bc
607771
$ time ./scoring.sh > /dev/null

real    0m1.926s
user    0m1.879s
sys     0m0.122s
$ ./scoring.sh
3 2
7 11
41 893
52 1546
65 2543
69 2686
75 3391
80 3728
103 6483
108 0
109 7103
151 14371
173 18663
177 19728
192 22824
201 24828
201 24752
205 25573
211 27509
226 32221
227 31928
230 33630
238 34603
241 36676
241 36505
244 37759
246 38106
250 38264
253 40040
256 41405

C ++ 11, puntaje: 1122052

Implementación muy ingenua que no tiene en cuenta los agujeros en la secuencia de entrada pero tiene en cuenta el valor mínimo en la secuencia.

La lista de argumentos es solo la secuencia de números, sin comas ni corchetes (por ejemplo: "./a.out 2 7 5")

#include <iostream>
#include <cstring>
#include <string>
using namespace std;

int* input  = 0;
int s_count = 0;
int p_count = 0;
int len;
int last;

void do_swap()
{
  int a = input[0];
  input[0] = input[last];
  input[last] = a;
  s_count++;
  cerr << "S";
}

void do_pop()
{
  int a = input[0];
  memmove(&input[0], &input[1], sizeof(int) * last);
  input[last] = a;
  p_count++;
  cerr << "P";
}

bool is_sorted()
{
  int i = 0;
  while (input[i] < input[i+1]) { if (++i == last) return true; }
  return false;
}

int main(int argc, char** args)
{
  int min_val = 256;

  len = argc - 1;
  last = len - 1;
  if (len <= 1)
    return 1;

  input = new int[len];
  for (int i = 2; i <= argc; i++)
  {
    int j = stoi(args[i-1]);
    input[i-2] = j;
    min_val = min(min_val, j);
  }

  while (!is_sorted())
  {
    if ((input[0]) == min_val)
      do_pop();
    else if (input[0] < input[last])
      do_swap();
    else if (input[0] > input[last])
      do_pop();
  }

  cerr << endl;
  cout << len << " " << (s_count + p_count) << endl;
  delete [] input;
  return 0;
}

Tanteo

3 2
7 19
41 1642
52 3236
65 4787
69 4966
75 6644
80 6090
103 12142
108 0
109 13774
151 24976
173 34061
177 37835
192 41994
201 48316
201 47276
205 49439
211 51551
226 58859
227 56824
230 58994
238 64227
241 65774
241 66287
244 71345
246 73426
250 71766
253 68629
256 77171