# Project Euler 914
# Triangles inside Circles — max inradius of primitive Pythagorean
# triple with hypotenuse < 2R. F(10^18).
extern {
function sqrt(x: f64) -> f64
}
function igcd(a: i64, b: i64) -> i64 {
let mut x: i64 = a
let mut y: i64 = b
while y != 0 {
let t: i64 = x % y
x = y
y = t
}
return x
}
function isqrt(n: i64) -> i64 {
if n <= 0 { return 0 }
let mut x: i64 = sqrt(n as f64) as i64
while (x + 1) * (x + 1) <= n { x = x + 1 }
while x > 0 && x * x > n { x = x - 1 }
return x
}
function F(R: i64) -> i64 {
if R <= 0 { return 0 }
let limit: i64 = 2 * R - 1
if limit <= 0 { return 0 }
let sqrt2: f64 = sqrt(2.0)
let n0: i64 = sqrt(R as f64 / (2.0 + sqrt2)) as i64
let mut W: i64 = n0 / 2000 + 10000
if W < 10000 { W = 10000 }
let mut best: i64 = 0
let mut lo: i64 = n0 - W
if lo < 1 { lo = 1 }
let hi: i64 = n0 + W
let mut n: i64 = lo
while n <= hi {
let t: i64 = limit - n * n
if t > 0 {
let mut m: i64 = isqrt(t)
if m > n {
if ((m - n) & 1) == 0 {
m = m - 1
}
while m > n && igcd(m, n) != 1 {
m = m - 2
}
if m > n {
let r: i64 = n * (m - n)
if r > best { best = r }
}
}
}
n = n + 1
}
return best
}
function main() -> i32 {
printf("%lld\n", F(1000000000000000000))
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 igcd_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t F_i64(int64_t R);
int32_t main(void);
int64_t igcd_i64_i64(int64_t a, int64_t b) {
int64_t x = a;
int64_t y = b;
while (y != 0) {
int64_t t = FLOW_CHECKED_MOD((x), (y));
x = y;
y = t;
}
return x;
}
int64_t isqrt_i64(int64_t n) {
if (n <= 0) {
return 0;
}
int64_t x = ((int64_t)(sqrt(((double)(n)))));
while (((x + 1) * (x + 1)) <= n) {
x = (x + 1);
}
while ((x > 0 && (x * x) > n)) {
x = (x - 1);
}
return x;
}
int64_t F_i64(int64_t R) {
if (R <= 0) {
return 0;
}
int64_t limit = ((2 * R) - 1);
if (limit <= 0) {
return 0;
}
double sqrt2 = sqrt(2.0);
int64_t n0 = ((int64_t)(sqrt((((double)(R)) / (2.0 + sqrt2)))));
int64_t W = (FLOW_CHECKED_DIV((n0), (2000)) + 10000);
if (W < 10000) {
W = 10000;
}
int64_t best = 0;
int64_t lo = (n0 - W);
if (lo < 1) {
lo = 1;
}
int64_t hi = (n0 + W);
int64_t n = lo;
while (n <= hi) {
int64_t t = (limit - (n * n));
if (t > 0) {
int64_t m = isqrt_i64(t);
if (m > n) {
if (((m - n) & 1) == 0) {
m = (m - 1);
}
while ((m > n && igcd_i64_i64(m, n) != 1)) {
m = (m - 2);
}
if (m > n) {
int64_t r = (n * (m - n));
if (r > best) {
best = r;
}
}
}
}
n = (n + 1);
}
return best;
}
int32_t main(void) {
printf("%lld\n", F_i64(1000000000000000000));
return 0;
}