# Project Euler 364
# Comfortable distance seating sequences mod 100000007, N=10^6.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function modpow(base: i64, exp: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base % mod
let mut e: i64 = exp
while e > 0 {
if e % 2 == 1 { r = (r * b) % mod }
b = (b * b) % mod
e = e / 2
}
return r
}
function nCk(n: i64, k: i64, fact: ptr<i64>, invfact: ptr<i64>, mod: i64) -> i64 {
if k < 0 || k > n { return 0 }
return ((fact[n] * invfact[k]) % mod * invfact[n - k]) % mod
}
function T(n: i64, fact: ptr<i64>, invfact: ptr<i64>, pow2: ptr<i64>, mod: i64) -> i64 {
let mut res: i64 = 0
let mut a: i64 = 1
while a <= 2 {
let mut b: i64 = 0
while b <= 1 {
let L: i64 = n - a - b
if L >= 0 {
let mut e: i64 = 0
if a == 2 { e = e + 1 }
if b == 1 { e = e + 1 }
let start_p: i64 = L % 2
let max_p: i64 = L / 3
let mut p: i64 = start_p
while p <= max_p {
let rem: i64 = L - 3 * p
let q: i64 = rem / 2
let k: i64 = 1 + p + q
let mut term: i64 = nCk(k - 1, p, fact, invfact, mod)
term = (term * pow2[p]) % mod
term = (term * fact[k]) % mod
term = (term * fact[p + e]) % mod
term = (term * fact[k - 1]) % mod
res = (res + term) % mod
p = p + 2
}
}
b = b + 1
}
a = a + 1
}
return res
}
function main() -> i32 {
let MOD: i64 = 100000007
let N: i64 = 1000000
let fact: ptr<i64> = calloc(N + 1, 8)
let invfact: ptr<i64> = calloc(N + 1, 8)
let pow2: ptr<i64> = calloc(N / 3 + 4, 8)
if fact == null || invfact == null || pow2 == null { return 1 }
fact[0] = 1
let mut i: i64 = 1
while i <= N {
fact[i] = (fact[i - 1] * i) % MOD
i = i + 1
}
invfact[N] = modpow(fact[N], MOD - 2, MOD)
i = N
while i > 0 {
invfact[i - 1] = (invfact[i] * i) % MOD
i = i - 1
}
pow2[0] = 1
i = 1
while i <= N / 3 + 3 {
pow2[i] = (pow2[i - 1] * 2) % MOD
i = i + 1
}
let ans: i64 = T(N, fact, invfact, pow2, MOD)
printf("%lld\n", ans)
free(pow2)
free(invfact)
free(fact)
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 modpow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
int64_t nCk_i64_i64_ptr_i64_ptr_i64_i64(int64_t n, int64_t k, int64_t* fact, int64_t* invfact, int64_t mod);
int64_t T_i64_ptr_i64_ptr_i64_ptr_i64_i64(int64_t n, int64_t* fact, int64_t* invfact, int64_t* pow2, int64_t mod);
int32_t main(void);
int64_t modpow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
r = FLOW_CHECKED_MOD(((r * b)), (mod));
}
b = FLOW_CHECKED_MOD(((b * b)), (mod));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t nCk_i64_i64_ptr_i64_ptr_i64_i64(int64_t n, int64_t k, int64_t* fact, int64_t* invfact, int64_t mod) {
if ((k < 0 || k > n)) {
return 0;
}
return FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((fact[n] * invfact[k])), (mod)) * invfact[(n - k)])), (mod));
}
int64_t T_i64_ptr_i64_ptr_i64_ptr_i64_i64(int64_t n, int64_t* fact, int64_t* invfact, int64_t* pow2, int64_t mod) {
int64_t res = 0;
int64_t a = 1;
while (a <= 2) {
int64_t b = 0;
while (b <= 1) {
int64_t L = ((n - a) - b);
if (L >= 0) {
int64_t e = 0;
if (a == 2) {
e = (e + 1);
}
if (b == 1) {
e = (e + 1);
}
int64_t start_p = FLOW_CHECKED_MOD((L), (2));
int64_t max_p = FLOW_CHECKED_DIV((L), (3));
int64_t p = start_p;
while (p <= max_p) {
int64_t rem = (L - (3 * p));
int64_t q = FLOW_CHECKED_DIV((rem), (2));
int64_t k = ((1 + p) + q);
int64_t term = nCk_i64_i64_ptr_i64_ptr_i64_i64((k - 1), p, fact, invfact, mod);
term = FLOW_CHECKED_MOD(((term * pow2[p])), (mod));
term = FLOW_CHECKED_MOD(((term * fact[k])), (mod));
term = FLOW_CHECKED_MOD(((term * fact[(p + e)])), (mod));
term = FLOW_CHECKED_MOD(((term * fact[(k - 1)])), (mod));
res = FLOW_CHECKED_MOD(((res + term)), (mod));
p = (p + 2);
}
}
b = (b + 1);
}
a = (a + 1);
}
return res;
}
int32_t main(void) {
int64_t MOD = 100000007;
int64_t N = 1000000;
int64_t* fact = (int64_t*)(calloc((N + 1), 8));
int64_t* invfact = (int64_t*)(calloc((N + 1), 8));
int64_t* pow2 = (int64_t*)(calloc((FLOW_CHECKED_DIV((N), (3)) + 4), 8));
if (((fact == NULL || invfact == NULL) || pow2 == NULL)) {
return 1;
}
fact[0] = 1;
int64_t i = 1;
while (i <= N) {
fact[i] = FLOW_CHECKED_MOD(((fact[(i - 1)] * i)), (MOD));
i = (i + 1);
}
invfact[N] = modpow_i64_i64_i64(fact[N], (MOD - 2), MOD);
i = N;
while (i > 0) {
invfact[(i - 1)] = FLOW_CHECKED_MOD(((invfact[i] * i)), (MOD));
i = (i - 1);
}
pow2[0] = 1;
i = 1;
while (i <= (FLOW_CHECKED_DIV((N), (3)) + 3)) {
pow2[i] = FLOW_CHECKED_MOD(((pow2[(i - 1)] * 2)), (MOD));
i = (i + 1);
}
int64_t ans = T_i64_ptr_i64_ptr_i64_ptr_i64_i64(N, fact, invfact, pow2, MOD);
printf("%lld\n", ans);
free(pow2);
free(invfact);
free(fact);
return 0;
}