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#include <stdio.h>
#include <stdint.h>
#include <assert.h>
#define MAXLEN 14
int64_t power10tab[MAXLEN + 1];
void init_pwr10()
{
power10tab[0] = 1;
for (size_t i = 1; i <= MAXLEN; i++) {
power10tab[i] = power10tab[i - 1] * 10;
}
}
int num_len(int64_t v)
{
// find the length of v
int len = MAXLEN;
for (size_t i = 0; i < MAXLEN; i++) {
if (v < power10tab[i]) {
len = i;
break;
}
}
assert(len < MAXLEN);
return len;
}
// split a number at digit position {s0,s1,...} and add the numbers
// v[s0:0], v[s1:s0+1],...,v[len-1:s[last]]
// split = (1 << s0) | (1 << s1) | ...
int64_t split_num(int64_t v, int len, int split)
{
int64_t sum = 0;
int lastsplit = 0;
for (int i = 0; i < len; i++) {
if (split & 1) {
int64_t segment = (v / power10tab[lastsplit])
% power10tab[i + 1 - lastsplit];
lastsplit = i + 1;
sum += segment;
// printf("%ld ", segment);
}
split >>= 1;
}
// last split is v[len-1:lastsplit]
int64_t segment = (v / power10tab[lastsplit])
% power10tab[len + 1 - lastsplit];
sum += segment;
// printf("%ld\n", segment);
return sum;
}
int64_t split_test(int64_t v, int split)
{
return split_num(v, num_len(v), split);
}
int main()
{
init_pwr10();
// split 6724 as {6,72,4} => 0b101
printf("sum = %ld\n", split_test(6724, 5));
// split 8281 as {8,2,81} => 0b110
printf("sum = %ld\n", split_test(8281, 6));
// split 8281 as {8281}
printf("sum = %ld\n", split_test(8281, 0));
// split 0
printf("sum = %ld\n", split_test(0, 0));
// split 10^12
printf("sum = %ld\n", split_test(1000000LL * 1000000LL, 0));
int64_t sum_s = 0;
// calculate T(1000000*1000000)
// S-numbers should be able to be splitted to 2 or more numbers, so
// an S-number is at least 4*4
for (int64_t i = 4; i <= 1000000; i++) {
int64_t square = i * i;
int L = num_len(square);
int maxsp = 1 << L;
// we need at least (L+1)/2 digits in the highest split
int minsp = 1 << ((L / 2) - 1);
for (int sp = minsp; sp < maxsp; sp++) {
if (split_num(square, L, sp) == i) {
printf("%ld is an S-number.\n", square);
sum_s += square;
break;
}
}
}
printf("The sum of S-numbers is %ld\n", sum_s);
}
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