# Project Euler 316
# Sum g(floor(10^16/n)) for n=2..999999 using KMP borders.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function digits_of(n: i64, buf: ptr<i8>) -> i32 {
# write decimal digits of n into buf, return length
if n == 0 {
buf[0] = 48
return 1
}
let tmp: ptr<i8> = calloc(24, 1)
let mut len: i32 = 0
let mut v: i64 = n
while v > 0 {
tmp[len] = ((v % 10) as i8) + 48
v = v / 10
len = len + 1
}
# reverse into buf
let mut i: i32 = 0
while i < len {
buf[i] = tmp[len - 1 - i]
i = i + 1
}
free(tmp)
return len
}
function g(n: i64) -> i64 {
let word: ptr<i8> = calloc(24, 1)
let length: i32 = digits_of(n, word)
let pi: ptr<i32> = calloc(length as i64, 4)
let mut matched: i32 = 0
let mut i: i32 = 1
while i < length {
while matched > 0 && word[i] != word[matched] {
matched = pi[matched - 1]
}
if word[i] == word[matched] {
matched = matched + 1
}
pi[i] = matched
i = i + 1
}
let mut expected_end: i64 = 0
let mut border: i32 = length
while border > 0 {
# POW10[border]
let mut p: i64 = 1
let mut e: i32 = 0
while e < border {
p = p * 10
e = e + 1
}
expected_end = expected_end + p
border = pi[border - 1]
}
let ans: i64 = expected_end - (length as i64) + 1
free(word); free(pi)
return ans
}
function main() -> i32 {
let mut total: i64 = 0
let divider: i64 = 10000000000000000
let mut n: i64 = 2
while n <= 999999 {
total = total + g(divider / n)
n = n + 1
}
printf("%lld\n", total)
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int32_t digits_of_i64_ptr_i8(int64_t n, int8_t* buf);
int64_t g_i64(int64_t n);
int32_t main(void);
int32_t digits_of_i64_ptr_i8(int64_t n, int8_t* buf) {
if (n == 0) {
buf[0] = 48;
return 1;
}
int8_t* tmp = (int8_t*)(calloc(24, 1));
int32_t len = 0;
int64_t v = n;
while (v > 0) {
tmp[len] = (((int8_t)(FLOW_CHECKED_MOD((v), (10)))) + 48);
v = FLOW_CHECKED_DIV((v), (10));
len = (len + 1);
}
int32_t i = 0;
while (i < len) {
buf[i] = tmp[((len - 1) - i)];
i = (i + 1);
}
free(tmp);
return len;
}
int64_t g_i64(int64_t n) {
int8_t* word = (int8_t*)(calloc(24, 1));
int32_t length = digits_of_i64_ptr_i8(n, word);
int32_t* pi = (int32_t*)(calloc(((int64_t)(length)), 4));
int32_t matched = 0;
int32_t i = 1;
while (i < length) {
while ((matched > 0 && word[i] != word[matched])) {
matched = pi[(matched - 1)];
}
if (word[i] == word[matched]) {
matched = (matched + 1);
}
pi[i] = matched;
i = (i + 1);
}
int64_t expected_end = 0;
int32_t border = length;
while (border > 0) {
int64_t p = 1;
int32_t e = 0;
while (e < border) {
p = (p * 10);
e = (e + 1);
}
expected_end = (expected_end + p);
border = pi[(border - 1)];
}
int64_t ans = ((expected_end - ((int64_t)(length))) + 1);
free(word);
free(pi);
return ans;
}
int32_t main(void) {
int64_t total = 0;
int64_t divider = 10000000000000000;
int64_t n = 2;
while (n <= 999999) {
total = (total + g_i64(FLOW_CHECKED_DIV((divider), (n))));
n = (n + 1);
}
printf("%lld\n", total);
return 0;
}