# Project Euler 359
# Hilbert's Hotel: sum P(2^a * 3^b, 2^{27-a}*3^{12-b}) mod 10^8.
function mulmod(a: i64, b: i64, mod: i64) -> i64 {
# (a * b) % mod with a,b reduced; uses i128 via double-and-add for safety
let mut x: i64 = a % mod
if x < 0 { x = x + mod }
let mut y: i64 = b % mod
if y < 0 { y = y + mod }
let mut res: i64 = 0
while y > 0 {
if y % 2 == 1 {
res = res + x
if res >= mod { res = res - mod }
}
x = x + x
if x >= mod { x = x - mod }
y = y / 2
}
return res
}
function p_value(floor: i64, room: i64, mod: i64) -> i64 {
# result = ((floor+1)//2)*floor [- (floor+1)//2 if floor odd > 1]
let half: i64 = (floor + 1) / 2
let mut result: i64 = mulmod(half, floor, mod)
if floor % 2 == 1 && floor > 1 {
result = result - (half % mod)
if result < 0 { result = result + mod }
}
let mut increment_even: i64 = 1
if floor % 2 == 0 {
increment_even = 2 * floor + 1
}
let mut increment_odd: i64 = 2
if floor % 2 == 1 {
increment_odd = 2 * floor
}
if floor == 1 {
increment_odd = 3
increment_even = 2
}
let num_even: i64 = room / 2
let num_odd: i64 = (room - 1) / 2
# triangle_even*2 cancelled: num_even*(num_even+1)
# triangle_odd*2 cancelled: num_odd*(num_odd+1)
let te: i64 = mulmod(num_even, num_even + 1, mod)
let tod: i64 = mulmod(num_odd, num_odd + 1, mod)
let ie: i64 = increment_even - 2
let io: i64 = increment_odd - 2
result = (result + mulmod(num_even, ie, mod)) % mod
if result < 0 { result = result + mod }
result = (result + te) % mod
result = (result + mulmod(num_odd, io, mod)) % mod
if result < 0 { result = result + mod }
result = (result + tod) % mod
return result
}
function main() -> i32 {
let mod: i64 = 100000000
let number: i64 = 134217728 # 2^27
number = number * 531441 # * 3^12
let mut total: i64 = 0
let mut two: i64 = 1
let mut a: i32 = 0
while a <= 27 {
let mut three: i64 = 1
let mut b: i32 = 0
while b <= 12 {
let floor: i64 = two * three
let room: i64 = number / floor
total = (total + p_value(floor, room, mod)) % mod
three = three * 3
b = b + 1
}
two = two * 2
a = a + 1
}
printf("%lld\n", total)
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 mulmod_i64_i64_i64(int64_t a, int64_t b, int64_t mod);
int64_t p_value_i64_i64_i64(int64_t floor, int64_t room, int64_t mod);
int32_t main(void);
int64_t mulmod_i64_i64_i64(int64_t a, int64_t b, int64_t mod) {
int64_t x = FLOW_CHECKED_MOD((a), (mod));
if (x < 0) {
x = (x + mod);
}
int64_t y = FLOW_CHECKED_MOD((b), (mod));
if (y < 0) {
y = (y + mod);
}
int64_t res = 0;
while (y > 0) {
if (FLOW_CHECKED_MOD((y), (2)) == 1) {
res = (res + x);
if (res >= mod) {
res = (res - mod);
}
}
x = (x + x);
if (x >= mod) {
x = (x - mod);
}
y = FLOW_CHECKED_DIV((y), (2));
}
return res;
}
int64_t p_value_i64_i64_i64(int64_t floor, int64_t room, int64_t mod) {
int64_t half = FLOW_CHECKED_DIV(((floor + 1)), (2));
int64_t result = mulmod_i64_i64_i64(half, floor, mod);
if ((FLOW_CHECKED_MOD((floor), (2)) == 1 && floor > 1)) {
result = (result - FLOW_CHECKED_MOD((half), (mod)));
if (result < 0) {
result = (result + mod);
}
}
int64_t increment_even = 1;
if (FLOW_CHECKED_MOD((floor), (2)) == 0) {
increment_even = ((2 * floor) + 1);
}
int64_t increment_odd = 2;
if (FLOW_CHECKED_MOD((floor), (2)) == 1) {
increment_odd = (2 * floor);
}
if (floor == 1) {
increment_odd = 3;
increment_even = 2;
}
int64_t num_even = FLOW_CHECKED_DIV((room), (2));
int64_t num_odd = FLOW_CHECKED_DIV(((room - 1)), (2));
int64_t te = mulmod_i64_i64_i64(num_even, (num_even + 1), mod);
int64_t tod = mulmod_i64_i64_i64(num_odd, (num_odd + 1), mod);
int64_t ie = (increment_even - 2);
int64_t io = (increment_odd - 2);
result = FLOW_CHECKED_MOD(((result + mulmod_i64_i64_i64(num_even, ie, mod))), (mod));
if (result < 0) {
result = (result + mod);
}
result = FLOW_CHECKED_MOD(((result + te)), (mod));
result = FLOW_CHECKED_MOD(((result + mulmod_i64_i64_i64(num_odd, io, mod))), (mod));
if (result < 0) {
result = (result + mod);
}
result = FLOW_CHECKED_MOD(((result + tod)), (mod));
return result;
}
int32_t main(void) {
int64_t mod = 100000000;
int64_t number = 134217728;
number = (number * 531441);
int64_t total = 0;
int64_t two = 1;
int32_t a = 0;
while (a <= 27) {
int64_t three = 1;
int32_t b = 0;
while (b <= 12) {
int64_t floor = (two * three);
int64_t room = FLOW_CHECKED_DIV((number), (floor));
total = FLOW_CHECKED_MOD(((total + p_value_i64_i64_i64(floor, room, mod))), (mod));
three = (three * 3);
b = (b + 1);
}
two = (two * 2);
a = (a + 1);
}
printf("%lld\n", total);
return 0;
}