# Project Euler 557
# Cutting Triangles
# Enumerate (s,a,d) with s=t+a, bc=a^2*d/s integer, disc square; sum areas t<=10000.
function gcd(a0: i64, b0: i64) -> i64 {
let mut a: i64 = a0
let mut b: i64 = b0
if a < 0 { a = -a }
if b < 0 { b = -b }
while b != 0 {
let t: i64 = a % b
a = b
b = t
}
return a
}
function isqrt(n: i64) -> i64 {
if n <= 0 { return 0 }
let mut x: i64 = n
let mut y: i64 = (x + 1) / 2
while y < x {
x = y
y = (x + n / x) / 2
}
return x
}
function S(N: i64) -> i64 {
let mut total: i64 = 0
let mut s: i64 = 3
while s <= 2 * N {
let mut a_min: i64 = s - N
if a_min < 1 { a_min = 1 }
let a_max: i64 = (s - 3) / 2
if a_min <= a_max {
let mut a: i64 = a_min
while a <= a_max {
let a2: i64 = a * a
let g: i64 = gcd(s, a2)
if g > 1 {
let step: i64 = s / g
let max_k: i64 = (s - 2 * a - 2) / step
if max_k > 0 {
let base_prod: i64 = a2 / g
let mut k: i64 = 1
while k <= max_k {
let d: i64 = step * k
let w: i64 = s - 2 * a - d
let prod: i64 = base_prod * k
let disc: i64 = w * w - 4 * prod
if disc >= 0 {
let r: i64 = isqrt(disc)
if r * r == disc {
if ((w - r) & 1) == 0 {
let b: i64 = (w - r) / 2
if b > 0 {
let c: i64 = (w + r) / 2
if b <= c {
total = total + (s - a)
}
}
}
}
}
k = k + 1
}
}
}
a = a + 1
}
}
s = s + 1
}
return total
}
function main() -> i32 {
printf("%lld\n", S(10000))
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 isqrt_i64(int64_t n);
int64_t S_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;
if (a < 0) {
a = (-a);
}
if (b < 0) {
b = (-b);
}
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t isqrt_i64(int64_t n) {
if (n <= 0) {
return 0;
}
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 S_i64(int64_t N) {
int64_t total = 0;
int64_t s = 3;
while (s <= (2 * N)) {
int64_t a_min = (s - N);
if (a_min < 1) {
a_min = 1;
}
int64_t a_max = FLOW_CHECKED_DIV(((s - 3)), (2));
if (a_min <= a_max) {
int64_t a = a_min;
while (a <= a_max) {
int64_t a2 = (a * a);
int64_t g = gcd_i64_i64(s, a2);
if (g > 1) {
int64_t step = FLOW_CHECKED_DIV((s), (g));
int64_t max_k = FLOW_CHECKED_DIV((((s - (2 * a)) - 2)), (step));
if (max_k > 0) {
int64_t base_prod = FLOW_CHECKED_DIV((a2), (g));
int64_t k = 1;
while (k <= max_k) {
int64_t d = (step * k);
int64_t w = ((s - (2 * a)) - d);
int64_t prod = (base_prod * k);
int64_t disc = ((w * w) - (4 * prod));
if (disc >= 0) {
int64_t r = isqrt_i64(disc);
if ((r * r) == disc) {
if (((w - r) & 1) == 0) {
int64_t b = FLOW_CHECKED_DIV(((w - r)), (2));
if (b > 0) {
int64_t c = FLOW_CHECKED_DIV(((w + r)), (2));
if (b <= c) {
total = (total + (s - a));
}
}
}
}
}
k = (k + 1);
}
}
}
a = (a + 1);
}
}
s = (s + 1);
}
return total;
}
int32_t main(void) {
printf("%lld\n", S_i64(10000));
return 0;
}