21位花朵数

花朵数是这么一个N位数，它的各个位数字的N次方之和为它的本身，比如：

1^3+5^3+3^3=153

现要求三分钟之内求解21位的水仙花数。

#include <stdio.h>#include <memory.h>#include <stdlib.h>#include <sys/time.h>  #define N 21#define NUMBER_LENGTH_MAX 30struct number{  char digits[NUMBER_LENGTH_MAX];  int length;};struct counter{  int digits[10];  int offset;};void assign(struct number *a, int b){  a->length = 0;  memset(&a->digits[0], 0, NUMBER_LENGTH_MAX);  if (b == 0) a->length = 1;  while(b > 0)  {    a->digits[a->length++] = b % 10;    b /= 10;  }}void copy(struct number *src, struct number *dst){  dst->length = src->length;  memcpy(&dst->digits[0], &src->digits[0], NUMBER_LENGTH_MAX);}void print(struct number *a){  char *p = &(a->digits[0]);  char *endp = &(a->digits[0]) + a->length;  do  {    endp--;    printf("%c", "0123456789"[(int)*endp]);  }while(endp != p);}void add(struct number *a, struct number *b){  int len = (a->length > b->length) ? a->length : b->length;  int i;  int carry = 0;  int d;  for (i = 0; i < len; i++)  {    d = (a->digits[i] + b->digits[i] + carry);    a->digits[i] = d % 10;    carry = d / 10;  }  if (carry > 0)  {    a->digits[len] = carry;    len++;  }  a->length = len;}void mul(struct number *a, int b){  int carry = 0;  char *p = &(a->digits[0]);  char *endp = &(a->digits[0]) + a->length;  while(p != endp)  {    int d = carry + *p * b;    *p = d % 10;    carry = d / 10;    p++;  }  if (carry > 0)  {    *p = carry;    a->length++;  }}int judge(struct counter *ctr, struct number *b, struct number *table){  static struct number t;  static int i;  assign(b, 0);  for (i = 9; i >= ctr->offset; i--)  {    if (ctr->digits[i] > 0)    {      copy(&table[(i * (N + 1)) + ctr->digits[i]], &t);      add(b, &t);    }  }  static struct counter new_ctr;  memset(&new_ctr, 0, sizeof(new_ctr));  new_ctr.offset = 0;  char *p = b->digits;  char *endp = b->digits + b->length;  if (b->length != N) return 0;  while (p != endp)  {    new_ctr.digits[(int)*p]++;    p++;  }  for (i = 0; i < ctr->offset; i++)  {    if (new_ctr.digits[i] != 0) return 0;  }  for (i = ctr->offset + 1; i < 10; i++)  {    if (ctr->digits[i] != new_ctr.digits[i]) return 0;  }  return 1;}int iter(struct number *table){  struct counter ctr;  ctr.offset = 9;  int remain = 0;  ctr.digits[9] = N;  while (1){    if (remain == 0)    {      struct number sum;      if (judge(&ctr, &sum, table))      {        print(&sum);printf("\n");      }      if (ctr.digits[ctr.offset] > 0)      {        ctr.digits[ctr.offset]--;        remain++;      }      else      {        while (ctr.digits[ctr.offset] == 0) ctr.offset++;      }    }    else    {      if (ctr.offset > 0)      {        ctr.offset--;        ctr.digits[ctr.offset] = remain;        remain = 0;      }      else      {        if (ctr.offset == 0 && remain == N) return 0;        while (ctr.digits[ctr.offset] == 0) ctr.offset++;        ctr.digits[ctr.offset]--;        remain++;      }    }  }  return 0;}void init_table(struct number *table){  int i, j;  for (i = 0; i < 10; i++)  {    assign(&table[i * (N + 1)], 0);    assign(&table[i * (N + 1) + 1], i);    for (j = 0; j < N - 1; j++)    {      mul(&table[i * (N + 1) + 1], i);    }    for (j = 2; j <= N; j++)    {      copy(&table[i * (N + 1) + j - 1], &table[i * (N + 1) + j]);      add(&table[i * (N + 1) + j], &table[i * (N + 1) + 1]);    }  }}int main(int argc, const char *argv[]){  struct number *table = (struct number *)malloc(sizeof(struct number) * ((N + 1) * 10));  struct timeval time1, time2;  gettimeofday(&time1, NULL);  init_table(table);  iter(table);  free(table);  gettimeofday(&time2, NULL);  printf("time:%lu:%lu\n", time2.tv_sec - time1.tv_sec, time2.tv_usec - time1.tv_usec);  return 0;}