# Project Euler 528
# Constrained Sums — inclusion-exclusion for S(10^k,k,k), k=10..15.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000007
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % mod
let mut e: i64 = exp0
while e > 0 {
if (e & 1) == 1 {
r = ((r as i128) * (b as i128) % (mod as i128)) as i64
}
b = ((b as i128) * (b as i128) % (mod as i128)) as i64
e = e / 2
}
return r
}
function constrained(n: i64, k: i32, b: i64, w: ptr<i64>) -> i64 {
let mut pw: i64 = 1
let mut i: i32 = 0
while i < k {
pw = pw * b
w[i] = pw + 1
i = i + 1
}
let mut fact: i64 = 1
i = 2
while i <= k {
fact = (fact * (i as i64)) % MOD
i = i + 1
}
let invk: i64 = modpow(fact, MOD - 2, MOD)
let m: i32 = 1 << k
let mut ans: i64 = 0
let mut mask: i32 = 0
while mask < m {
let mut shift: i64 = 0
let mut bits: i32 = 0
let mut bit: i32 = 0
while bit < k {
if (mask & (1 << bit)) != 0 {
bits = bits + 1
shift = shift + w[bit]
}
bit = bit + 1
}
let budget: i64 = n - shift
if budget >= 0 {
let N: i64 = budget + (k as i64)
let mut prod: i64 = 1
let mut j: i32 = 0
while j < k {
let mut termn: i64 = (N - (j as i64)) % MOD
if termn < 0 { termn = termn + MOD }
prod = ((prod as i128) * (termn as i128) % (MOD as i128)) as i64
j = j + 1
}
let term: i64 = ((prod as i128) * (invk as i128) % (MOD as i128)) as i64
if (bits & 1) == 1 {
ans = ans - term
} else {
ans = ans + term
}
ans = ans % MOD
if ans < 0 { ans = ans + MOD }
}
mask = mask + 1
}
return ans
}
function main() -> i32 {
let w: ptr<i64> = calloc(16, 8)
if w == null { return 1 }
let mut total: i64 = 0
let mut k: i32 = 10
while k <= 15 {
let mut n: i64 = 1
let mut i: i32 = 0
while i < k {
n = n * 10
i = i + 1
}
total = (total + constrained(n, k, k as i64, w)) % MOD
k = k + 1
}
printf("%lld\n", total)
free(w)
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 base0, int64_t exp0, int64_t mod);
int64_t constrained_i64_i32_i64_ptr_i64(int64_t n, int32_t k, int64_t b, int64_t* w);
int32_t main(void);
static const int64_t MOD = 1000000007;
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (mod));
int64_t e = exp0;
while (e > 0) {
if ((e & 1) == 1) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t constrained_i64_i32_i64_ptr_i64(int64_t n, int32_t k, int64_t b, int64_t* w) {
int64_t pw = 1;
int32_t i = 0;
while (i < k) {
pw = (pw * b);
w[i] = (pw + 1);
i = (i + 1);
}
int64_t fact = 1;
i = 2;
while (i <= k) {
fact = FLOW_CHECKED_MOD(((fact * ((int64_t)(i)))), (MOD));
i = (i + 1);
}
int64_t invk = modpow_i64_i64_i64(fact, (MOD - 2), MOD);
int32_t m = FLOW_CHECKED_SHL((1), (k));
int64_t ans = 0;
int32_t mask = 0;
while (mask < m) {
int64_t shift = 0;
int32_t bits = 0;
int32_t bit = 0;
while (bit < k) {
if ((mask & FLOW_CHECKED_SHL((1), (bit))) != 0) {
bits = (bits + 1);
shift = (shift + w[bit]);
}
bit = (bit + 1);
}
int64_t budget = (n - shift);
if (budget >= 0) {
int64_t N = (budget + ((int64_t)(k)));
int64_t prod = 1;
int32_t j = 0;
while (j < k) {
int64_t termn = FLOW_CHECKED_MOD(((N - ((int64_t)(j)))), (MOD));
if (termn < 0) {
termn = (termn + MOD);
}
prod = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(prod)) * ((__int128)(termn)))), (((__int128)(MOD))))));
j = (j + 1);
}
int64_t term = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(prod)) * ((__int128)(invk)))), (((__int128)(MOD))))));
if ((bits & 1) == 1) {
ans = (ans - term);
} else {
ans = (ans + term);
}
ans = FLOW_CHECKED_MOD((ans), (MOD));
if (ans < 0) {
ans = (ans + MOD);
}
}
mask = (mask + 1);
}
return ans;
}
int32_t main(void) {
int64_t* w = (int64_t*)(calloc(16, 8));
if (w == NULL) {
return 1;
}
int64_t total = 0;
int32_t k = 10;
while (k <= 15) {
int64_t n = 1;
int32_t i = 0;
while (i < k) {
n = (n * 10);
i = (i + 1);
}
total = FLOW_CHECKED_MOD(((total + constrained_i64_i32_i64_ptr_i64(n, k, ((int64_t)(k)), w))), (MOD));
k = (k + 1);
}
printf("%lld\n", total);
free(w);
return 0;
}