# Project Euler 202
# Laserbeam reflections exiting at C after 12017639147 bounces.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function count_ways(N: i64) -> i64 {
if N % 2 == 0 { return 0 }
let M: i64 = (N + 3) / 2
if M % 3 == 0 { return 0 }
# factorize M into primes[0..pc)
let primes: ptr<i64> = calloc(64, 8)
if primes == null { return 0 }
let mut pc: i32 = 0
let mut n: i64 = M
if n % 2 == 0 {
primes[pc] = 2
pc = pc + 1
while n % 2 == 0 { n = n / 2 }
}
while n % 3 == 0 {
if pc == 0 || primes[pc - 1] != 3 {
primes[pc] = 3
pc = pc + 1
}
n = n / 3
}
let mut f: i64 = 5
let mut step: i64 = 2
while f * f <= n {
if n % f == 0 {
primes[pc] = f
pc = pc + 1
while n % f == 0 { n = n / f }
}
f = f + step
step = 6 - step
}
if n > 1 {
primes[pc] = n
pc = pc + 1
}
let mut phi_M: i64 = M
let mut i: i32 = 0
while i < pc {
let p: i64 = primes[i]
phi_M = phi_M / p * (p - 1)
i = i + 1
}
let mut has_p1: bool = false
i = 0
while i < pc {
if primes[i] % 3 == 1 { has_p1 = true }
i = i + 1
}
if !has_p1 {
let mut G: i64 = 0 - 1
if M % 3 == 1 { G = 1 }
let mut tw: i64 = 1
let mut j: i32 = 0
while j < pc {
tw = tw * 2
j = j + 1
}
phi_M = phi_M - G * tw
}
free(primes)
return phi_M / 3
}
function main() -> i32 {
printf("%lld\n", count_ways(12017639147))
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; }
int64_t count_ways_i64(int64_t N);
int32_t main(void);
int64_t count_ways_i64(int64_t N) {
if (FLOW_CHECKED_MOD((N), (2)) == 0) {
return 0;
}
int64_t M = FLOW_CHECKED_DIV(((N + 3)), (2));
if (FLOW_CHECKED_MOD((M), (3)) == 0) {
return 0;
}
int64_t* primes = (int64_t*)(calloc(64, 8));
if (primes == NULL) {
return 0;
}
int32_t pc = 0;
int64_t n = M;
if (FLOW_CHECKED_MOD((n), (2)) == 0) {
primes[pc] = 2;
pc = (pc + 1);
while (FLOW_CHECKED_MOD((n), (2)) == 0) {
n = FLOW_CHECKED_DIV((n), (2));
}
}
while (FLOW_CHECKED_MOD((n), (3)) == 0) {
if ((pc == 0 || primes[(pc - 1)] != 3)) {
primes[pc] = 3;
pc = (pc + 1);
}
n = FLOW_CHECKED_DIV((n), (3));
}
int64_t f = 5;
int64_t step = 2;
while ((f * f) <= n) {
if (FLOW_CHECKED_MOD((n), (f)) == 0) {
primes[pc] = f;
pc = (pc + 1);
while (FLOW_CHECKED_MOD((n), (f)) == 0) {
n = FLOW_CHECKED_DIV((n), (f));
}
}
f = (f + step);
step = (6 - step);
}
if (n > 1) {
primes[pc] = n;
pc = (pc + 1);
}
int64_t phi_M = M;
int32_t i = 0;
while (i < pc) {
int64_t p = primes[i];
phi_M = (FLOW_CHECKED_DIV((phi_M), (p)) * (p - 1));
i = (i + 1);
}
bool has_p1 = 0;
i = 0;
while (i < pc) {
if (FLOW_CHECKED_MOD((primes[i]), (3)) == 1) {
has_p1 = 1;
}
i = (i + 1);
}
if ((!(has_p1))) {
int64_t G = (0 - 1);
if (FLOW_CHECKED_MOD((M), (3)) == 1) {
G = 1;
}
int64_t tw = 1;
int32_t j = 0;
while (j < pc) {
tw = (tw * 2);
j = (j + 1);
}
phi_M = (phi_M - (G * tw));
}
free(primes);
return FLOW_CHECKED_DIV((phi_M), (3));
}
int32_t main(void) {
printf("%lld\n", count_ways_i64(12017639147));
return 0;
}