# Project Euler 973
# Computed via S_k_value and X(n) with modular arithmetic mod 10^9+7.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000007
const INV2: i64 = 500000004
const N: i64 = 10000
function mod(x: i64) -> i64 {
let mut r: i64 = x % MOD
if r < 0 { r = r + MOD }
return r
}
function powmod(base0: i64, exp0: i64, m: i64) -> i64 {
let mut result: i64 = 1 % m
let mut base: i64 = base0 % m
if base < 0 { base = base + m }
let mut exp: i64 = exp0
while exp > 0 {
if (exp & 1) != 0 {
result = ((result as i128) * (base as i128) % (m as i128)) as i64
}
base = ((base as i128) * (base as i128) % (m as i128)) as i64
exp = exp >> 1
}
return result
}
function S_k_value(n: i64, k: i64) -> i64 {
if k == 0 {
if n == 0 { return 1 }
return mod(0 - powmod(MOD - 2, n - 1, MOD))
}
let B: i64 = 1 << k
let period: i64 = B << 1
let per_mask: i64 = period - 1
let S: ptr<i64> = calloc(n + 1, 8)
let P: ptr<i64> = calloc(n + 1, 8)
S[0] = 1
P[0] = 1
let mut nn: i64 = 1
while nn <= n {
let mut val: i64 = 0
let mut s: i64 = 1
while s <= nn {
let p: i64 = s & per_mask
let mut sign: i64 = 1
let mut e: i64 = 0
if p < B {
sign = 1
e = s + (B - p) - 1
} else {
sign = -1
e = s + (period - p) - 1
}
if e > nn { e = nn }
let t_lo: i64 = nn - e
let t_hi: i64 = nn - s
let mut sum_range: i64 = 0
if t_lo == 0 {
sum_range = P[t_hi]
} else {
sum_range = P[t_hi] - P[t_lo - 1]
}
val = val + sign * sum_range
s = e + 1
}
S[nn] = mod(val)
P[nn] = mod(P[nn - 1] + S[nn])
nn = nn + 1
}
let result: i64 = S[n]
free(S)
free(P)
return result
}
function X(n: i64) -> i64 {
if n <= 0 { return 0 }
let P: i64 = powmod(2, n - 1, MOD)
let mut total: i64 = 0
let mut k: i64 = 0
while k < 14 {
let Sk: i64 = S_k_value(n, k)
let Ak: i64 = mod(((P - Sk) % MOD) * INV2 % MOD)
total = (total + powmod(2, k, MOD) * Ak) % MOD
k = k + 1
}
total = mod(total - (n & 1))
return total
}
function main() -> i32 {
printf("%lld\n", X(N))
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 mod_i64(int64_t x);
int64_t powmod_i64_i64_i64(int64_t base0, int64_t exp0, int64_t m);
int64_t S_k_value_i64_i64(int64_t n, int64_t k);
int64_t X_i64(int64_t n);
int32_t main(void);
static const int64_t MOD = 1000000007;
static const int64_t INV2 = 500000004;
static const int64_t N = 10000;
int64_t mod_i64(int64_t x) {
int64_t r = FLOW_CHECKED_MOD((x), (MOD));
if (r < 0) {
r = (r + MOD);
}
return r;
}
int64_t powmod_i64_i64_i64(int64_t base0, int64_t exp0, int64_t m) {
int64_t result = FLOW_CHECKED_MOD((1), (m));
int64_t base = FLOW_CHECKED_MOD((base0), (m));
if (base < 0) {
base = (base + m);
}
int64_t exp = exp0;
while (exp > 0) {
if ((exp & 1) != 0) {
result = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(result)) * ((__int128)(base)))), (((__int128)(m))))));
}
base = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(base)) * ((__int128)(base)))), (((__int128)(m))))));
exp = FLOW_CHECKED_SHR((exp), (1));
}
return result;
}
int64_t S_k_value_i64_i64(int64_t n, int64_t k) {
if (k == 0) {
if (n == 0) {
return 1;
}
return mod_i64((0 - powmod_i64_i64_i64((MOD - 2), (n - 1), MOD)));
}
int64_t B = FLOW_CHECKED_SHL((1), (k));
int64_t period = FLOW_CHECKED_SHL((B), (1));
int64_t per_mask = (period - 1);
int64_t* S = (int64_t*)(calloc((n + 1), 8));
int64_t* P = (int64_t*)(calloc((n + 1), 8));
S[0] = 1;
P[0] = 1;
int64_t nn = 1;
while (nn <= n) {
int64_t val = 0;
int64_t s = 1;
while (s <= nn) {
int64_t p = (s & per_mask);
int64_t sign = 1;
int64_t e = 0;
if (p < B) {
sign = 1;
e = ((s + (B - p)) - 1);
} else {
sign = (-1);
e = ((s + (period - p)) - 1);
}
if (e > nn) {
e = nn;
}
int64_t t_lo = (nn - e);
int64_t t_hi = (nn - s);
int64_t sum_range = 0;
if (t_lo == 0) {
sum_range = P[t_hi];
} else {
sum_range = (P[t_hi] - P[(t_lo - 1)]);
}
val = (val + (sign * sum_range));
s = (e + 1);
}
S[nn] = mod_i64(val);
P[nn] = mod_i64((P[(nn - 1)] + S[nn]));
nn = (nn + 1);
}
int64_t result = S[n];
free(S);
free(P);
return result;
}
int64_t X_i64(int64_t n) {
if (n <= 0) {
return 0;
}
int64_t P = powmod_i64_i64_i64(2, (n - 1), MOD);
int64_t total = 0;
int64_t k = 0;
while (k < 14) {
int64_t Sk = S_k_value_i64_i64(n, k);
int64_t Ak = mod_i64(FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((P - Sk)), (MOD)) * INV2)), (MOD)));
total = FLOW_CHECKED_MOD(((total + (powmod_i64_i64_i64(2, k, MOD) * Ak))), (MOD));
k = (k + 1);
}
total = mod_i64((total - (n & 1)));
return total;
}
int32_t main(void) {
printf("%lld\n", X_i64(N));
return 0;
}