# Project Euler 348
# Sum of five smallest palindromes that are square+cube in exactly 4 ways.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function ipow10(e: i32) -> i64 {
let mut r: i64 = 1
let mut i: i32 = 0
while i < e {
r = r * 10
i = i + 1
}
return r
}
function reverse_int(n0: i64) -> i64 {
let mut n: i64 = n0
let mut r: i64 = 0
while n > 0 {
r = 10 * r + n % 10
n = n / 10
}
return r
}
function digit_len(n0: i64) -> i32 {
let mut n: i64 = n0
let mut L: i32 = 0
while n > 0 {
L = L + 1
n = n / 10
}
return L
}
function make_pal(prefix: i64, odd: bool) -> i64 {
if odd {
let L: i32 = digit_len(prefix)
return prefix * ipow10(L - 1) + reverse_int(prefix / 10)
}
let L: i32 = digit_len(prefix)
return prefix * ipow10(L) + reverse_int(prefix)
}
function count_ways(n: i64) -> i32 {
let mut ways: i32 = 0
let mut b: i64 = 2
while b * b * b <= n - 4 {
let rem: i64 = n - b * b * b
let r: i64 = isqrt(rem)
if r >= 2 && r * r == rem {
ways = ways + 1
if ways > 4 { return ways }
}
b = b + 1
}
return ways
}
function main() -> i32 {
let mut found: i64 = 0
let mut sum: i64 = 0
let mut digits: i32 = 1
while found < 5 {
let half: i32 = (digits + 1) / 2
let mut start: i64 = 1
if half > 1 { start = ipow10(half - 1) }
let stop: i64 = ipow10(half)
let odd: bool = digits % 2 == 1
let mut prefix: i64 = start
while prefix < stop {
let n: i64 = make_pal(prefix, odd)
if n >= 12 {
if count_ways(n) == 4 {
sum = sum + n
found = found + 1
if found == 5 { break }
}
}
prefix = prefix + 1
}
if found == 5 { break }
digits = digits + 1
}
printf("%lld\n", sum)
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 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);
int64_t ipow10_i32(int32_t e);
int64_t reverse_int_i64(int64_t n0);
int32_t digit_len_i64(int64_t n0);
int64_t make_pal_i64_bool(int64_t prefix, bool odd);
int32_t count_ways_i64(int64_t n);
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;
}
int64_t ipow10_i32(int32_t e) {
int64_t r = 1;
int32_t i = 0;
while (i < e) {
r = (r * 10);
i = (i + 1);
}
return r;
}
int64_t reverse_int_i64(int64_t n0) {
int64_t n = n0;
int64_t r = 0;
while (n > 0) {
r = ((10 * r) + FLOW_CHECKED_MOD((n), (10)));
n = FLOW_CHECKED_DIV((n), (10));
}
return r;
}
int32_t digit_len_i64(int64_t n0) {
int64_t n = n0;
int32_t L = 0;
while (n > 0) {
L = (L + 1);
n = FLOW_CHECKED_DIV((n), (10));
}
return L;
}
int64_t make_pal_i64_bool(int64_t prefix, bool odd) {
if (odd) {
int32_t L = digit_len_i64(prefix);
return ((prefix * ipow10_i32((L - 1))) + reverse_int_i64(FLOW_CHECKED_DIV((prefix), (10))));
}
int32_t L = digit_len_i64(prefix);
return ((prefix * ipow10_i32(L)) + reverse_int_i64(prefix));
}
int32_t count_ways_i64(int64_t n) {
int32_t ways = 0;
int64_t b = 2;
while (((b * b) * b) <= (n - 4)) {
int64_t rem = (n - ((b * b) * b));
int64_t r = isqrt_i64(rem);
if ((r >= 2 && (r * r) == rem)) {
ways = (ways + 1);
if (ways > 4) {
return ways;
}
}
b = (b + 1);
}
return ways;
}
int32_t main(void) {
int64_t found = 0;
int64_t sum = 0;
int32_t digits = 1;
while (found < 5) {
int32_t half = FLOW_CHECKED_DIV(((digits + 1)), (2));
int64_t start = 1;
if (half > 1) {
start = ipow10_i32((half - 1));
}
int64_t stop = ipow10_i32(half);
bool odd = FLOW_CHECKED_MOD((digits), (2)) == 1;
int64_t prefix = start;
while (prefix < stop) {
int64_t n = make_pal_i64_bool(prefix, odd);
if (n >= 12) {
if (count_ways_i64(n) == 4) {
sum = (sum + n);
found = (found + 1);
if (found == 5) {
break;
}
}
}
prefix = (prefix + 1);
}
if (found == 5) {
break;
}
digits = (digits + 1);
}
printf("%lld\n", sum);
return 0;
}