# Project Euler 221
# 150000th Alexandrian integer.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function mul_ok(a: i64, b: i64) -> bool {
if a == 0 || b == 0 { return true }
let MAX: i64 = 9223372036854775807
return a <= MAX / b
}
function main() -> i32 {
let K: i64 = 150000
let heap: ptr<i64> = calloc(K, 8)
if heap == null { return 1 }
let mut hn: i64 = 0
let mut p: i64 = 1
while true {
let n: i64 = p * p + 1
let root: i64 = isqrt(n)
for d in 1..(root + 1) {
if n % d == 0 {
let e: i64 = n / d
if mul_ok(p, p + d) && mul_ok(p * (p + d), p + e) {
let value: i64 = p * (p + d) * (p + e)
if hn < K {
let mut i: i64 = hn
heap[i] = value
while i > 0 {
let par: i64 = (i - 1) / 2
if heap[par] >= heap[i] { break }
let t: i64 = heap[par]; heap[par] = heap[i]; heap[i] = t
i = par
}
hn = hn + 1
} elif value < heap[0] {
heap[0] = value
let mut i: i64 = 0
while true {
let l: i64 = 2 * i + 1
let r: i64 = 2 * i + 2
let mut best: i64 = i
if l < hn && heap[l] > heap[best] { best = l }
if r < hn && heap[r] > heap[best] { best = r }
if best == i { break }
let t: i64 = heap[i]; heap[i] = heap[best]; heap[best] = t
i = best
}
}
}
}
}
p = p + 1
if hn == K {
if !mul_ok(p, p + 1) || !mul_ok(p * (p + 1), p + 1) || p * (p + 1) * (p + 1) > heap[0] {
printf("%lld\n", heap[0])
free(heap)
return 0
}
}
}
return 1
}
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 gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
bool mul_ok_i64_i64(int64_t a, int64_t b);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
bool mul_ok_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 1;
}
int64_t MAX = 9223372036854775807;
return a <= FLOW_CHECKED_DIV((MAX), (b));
}
int32_t main(void) {
int64_t K = 150000;
int64_t* heap = (int64_t*)(calloc(K, 8));
if (heap == NULL) {
return 1;
}
int64_t hn = 0;
int64_t p = 1;
while (1) {
int64_t n = ((p * p) + 1);
int64_t root = isqrt_i64(n);
int32_t __flow_step_1 = 1;
for (int32_t d = 1; (1 <= (root + 1)) ? d < (root + 1) : d > (root + 1); d += (1 <= (root + 1)) ? 1 : -1) {
if (FLOW_CHECKED_MOD((n), (d)) == 0) {
int64_t e = FLOW_CHECKED_DIV((n), (d));
if ((mul_ok_i64_i64(p, (p + d)) && mul_ok_i64_i64((p * (p + d)), (p + e)))) {
int64_t value = ((p * (p + d)) * (p + e));
if (hn < K) {
int64_t i = hn;
heap[i] = value;
while (i > 0) {
int64_t par = FLOW_CHECKED_DIV(((i - 1)), (2));
if (heap[par] >= heap[i]) {
break;
}
int64_t t = heap[par];
heap[par] = heap[i];
heap[i] = t;
i = par;
}
hn = (hn + 1);
} else if (value < heap[0]) {
heap[0] = value;
int64_t i = 0;
while (1) {
int64_t l = ((2 * i) + 1);
int64_t r = ((2 * i) + 2);
int64_t best = i;
if ((l < hn && heap[l] > heap[best])) {
best = l;
}
if ((r < hn && heap[r] > heap[best])) {
best = r;
}
if (best == i) {
break;
}
int64_t t = heap[i];
heap[i] = heap[best];
heap[best] = t;
i = best;
}
}
}
}
}
p = (p + 1);
if (hn == K) {
if ((((!(mul_ok_i64_i64(p, (p + 1)))) || (!(mul_ok_i64_i64((p * (p + 1)), (p + 1))))) || ((p * (p + 1)) * (p + 1)) > heap[0])) {
printf("%lld\n", heap[0]);
free(heap);
return 0;
}
}
}
return 1;
}