# Project Euler 326
# f(10^12, 10^6): count subarray sums ≡ 0 mod M via period 6M.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function a_n(n: i64) -> i64 {
let r: i64 = n % 6
if r == 0 || r == 2 { return n / 2 }
if r == 1 { return (2 * n + 1) / 3 }
if r == 3 { return (n - 3) / 6 }
if r == 4 { return n - 1 }
return (n - 5) / 6
}
function main() -> i32 {
let N: i64 = 1000000000000
let M: i64 = 1000000
let P: i64 = 6 * M
let q: i64 = N / P
let r: i64 = N % P
let freq: ptr<i64> = calloc(M, 8)
if freq == null { return 1 }
freq[0] = q + 1
let mut s: i64 = 0
if q == 0 {
let mut i: i64 = 1
while i <= r {
s = (s + a_n(i)) % M
freq[s] = freq[s] + 1
i = i + 1
}
} else {
let mut i: i64 = 1
while i < P {
s = (s + a_n(i)) % M
if i <= r {
freq[s] = freq[s] + (q + 1)
} else {
freq[s] = freq[s] + q
}
i = i + 1
}
}
let mut ans: i64 = 0
let mut i: i64 = 0
while i < M {
let c: i64 = freq[i]
if c > 1 {
ans = ans + c * (c - 1) / 2
}
i = i + 1
}
printf("%lld\n", ans)
free(freq)
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 a_n_i64(int64_t n);
int32_t main(void);
int64_t a_n_i64(int64_t n) {
int64_t r = FLOW_CHECKED_MOD((n), (6));
if ((r == 0 || r == 2)) {
return FLOW_CHECKED_DIV((n), (2));
}
if (r == 1) {
return FLOW_CHECKED_DIV((((2 * n) + 1)), (3));
}
if (r == 3) {
return FLOW_CHECKED_DIV(((n - 3)), (6));
}
if (r == 4) {
return (n - 1);
}
return FLOW_CHECKED_DIV(((n - 5)), (6));
}
int32_t main(void) {
int64_t N = 1000000000000;
int64_t M = 1000000;
int64_t P = (6 * M);
int64_t q = FLOW_CHECKED_DIV((N), (P));
int64_t r = FLOW_CHECKED_MOD((N), (P));
int64_t* freq = (int64_t*)(calloc(M, 8));
if (freq == NULL) {
return 1;
}
freq[0] = (q + 1);
int64_t s = 0;
if (q == 0) {
int64_t i = 1;
while (i <= r) {
s = FLOW_CHECKED_MOD(((s + a_n_i64(i))), (M));
freq[s] = (freq[s] + 1);
i = (i + 1);
}
} else {
int64_t i = 1;
while (i < P) {
s = FLOW_CHECKED_MOD(((s + a_n_i64(i))), (M));
if (i <= r) {
freq[s] = (freq[s] + (q + 1));
} else {
freq[s] = (freq[s] + q);
}
i = (i + 1);
}
}
int64_t ans = 0;
int64_t i = 0;
while (i < M) {
int64_t c = freq[i];
if (c > 1) {
ans = (ans + FLOW_CHECKED_DIV(((c * (c - 1))), (2)));
}
i = (i + 1);
}
printf("%lld\n", ans);
free(freq);
return 0;
}