# Project Euler 070
# Find n, 1 < n < 10^7, minimizing n/φ(n) among n where φ(n) is a permutation of n.
# Optimum is a product of two primes near sqrt(limit).
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function is_perm(a: i64, b: i64, ca: ptr<i32>) -> bool {
let mut i: i32 = 0
while i < 10 {
ca[i] = 0
i = i + 1
}
let mut x: i64 = a
let mut y: i64 = b
while x > 0 {
ca[(x % 10) as i32] = ca[(x % 10) as i32] + 1
x = x / 10
}
while y > 0 {
ca[(y % 10) as i32] = ca[(y % 10) as i32] - 1
y = y / 10
}
i = 0
while i < 10 {
if ca[i] != 0 { return false }
i = i + 1
}
return true
}
function main() -> i32 {
# Generate primes up to ~5000 (sqrt(1e7)≈3162, search a bit wider)
let plim: i64 = 5000
let sieve: ptr<i8> = calloc(plim, 1)
let primes: ptr<i64> = calloc(1000, 8)
if sieve == null || primes == null { return 1 }
sieve[0] = 1
sieve[1] = 1
let mut p: i64 = 2
while p * p < plim {
if sieve[p] == 0 {
let mut m: i64 = p * p
while m < plim {
sieve[m] = 1
m = m + p
}
}
p = p + 1
}
let mut pc: i32 = 0
p = 2
while p < plim {
if sieve[p] == 0 {
primes[pc] = p
pc = pc + 1
}
p = p + 1
}
let ca: ptr<i32> = calloc(10, 4)
if ca == null { return 1 }
let mut best_n: i64 = 0
let mut best_phi: i64 = 1
let limit: i64 = 10000000
let mut i: i32 = 0
while i < pc {
let mut j: i32 = i
while j < pc {
let n: i64 = primes[i] * primes[j]
if n >= limit { break }
# φ(pq) = (p-1)(q-1) for p!=q; φ(p^2)=(p^2-p)
let mut ph: i64 = 0
if i == j {
ph = primes[i] * (primes[i] - 1)
} else {
ph = (primes[i] - 1) * (primes[j] - 1)
}
if is_perm(n, ph, ca) {
if best_n == 0 || n * best_phi < best_n * ph {
best_n = n
best_phi = ph
}
}
j = j + 1
}
i = i + 1
}
printf("%lld\n", best_n)
free(ca)
free(primes)
free(sieve)
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; }
bool is_perm_i64_i64_ptr_i32(int64_t a, int64_t b, int32_t* ca);
int32_t main(void);
bool is_perm_i64_i64_ptr_i32(int64_t a, int64_t b, int32_t* ca) {
int32_t i = 0;
while (i < 10) {
ca[i] = 0;
i = (i + 1);
}
int64_t x = a;
int64_t y = b;
while (x > 0) {
ca[((int32_t)(FLOW_CHECKED_MOD((x), (10))))] = (ca[((int32_t)(FLOW_CHECKED_MOD((x), (10))))] + 1);
x = FLOW_CHECKED_DIV((x), (10));
}
while (y > 0) {
ca[((int32_t)(FLOW_CHECKED_MOD((y), (10))))] = (ca[((int32_t)(FLOW_CHECKED_MOD((y), (10))))] - 1);
y = FLOW_CHECKED_DIV((y), (10));
}
i = 0;
while (i < 10) {
if (ca[i] != 0) {
return 0;
}
i = (i + 1);
}
return 1;
}
int32_t main(void) {
int64_t plim = 5000;
int8_t* sieve = (int8_t*)(calloc(plim, 1));
int64_t* primes = (int64_t*)(calloc(1000, 8));
if ((sieve == NULL || primes == NULL)) {
return 1;
}
sieve[0] = 1;
sieve[1] = 1;
int64_t p = 2;
while ((p * p) < plim) {
if (sieve[p] == 0) {
int64_t m = (p * p);
while (m < plim) {
sieve[m] = 1;
m = (m + p);
}
}
p = (p + 1);
}
int32_t pc = 0;
p = 2;
while (p < plim) {
if (sieve[p] == 0) {
primes[pc] = p;
pc = (pc + 1);
}
p = (p + 1);
}
int32_t* ca = (int32_t*)(calloc(10, 4));
if (ca == NULL) {
return 1;
}
int64_t best_n = 0;
int64_t best_phi = 1;
int64_t limit = 10000000;
int32_t i = 0;
while (i < pc) {
int32_t j = i;
while (j < pc) {
int64_t n = (primes[i] * primes[j]);
if (n >= limit) {
break;
}
int64_t ph = 0;
if (i == j) {
ph = (primes[i] * (primes[i] - 1));
} else {
ph = ((primes[i] - 1) * (primes[j] - 1));
}
if (is_perm_i64_i64_ptr_i32(n, ph, ca)) {
if ((best_n == 0 || (n * best_phi) < (best_n * ph))) {
best_n = n;
best_phi = ph;
}
}
j = (j + 1);
}
i = (i + 1);
}
printf("%lld\n", best_n);
free(ca);
free(primes);
free(sieve);
return 0;
}