# Project Euler 497
# Drunken Tower of Hanoi — sum E(n,10^n,3^n,6^n,9^n) last 9 digits.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1000000000
const LIMIT: i64 = 10000
# Flattened dp[fr][dst][st][edge]
# Edges: (0,1),(0,2),(1,0),(1,2),(2,0),(2,1)
function edge_idx(u: i32, v: i32) -> i32 {
if u == 0 {
if v == 1 { return 0 }
return 1
}
if u == 1 {
if v == 0 { return 2 }
return 3
}
if v == 0 { return 4 }
return 5
}
function dp_idx(fr: i32, dst: i32, st: i32, e: i32) -> i64 {
return ((((fr * 3 + dst) * 3 + st) * 6 + e) as i64)
}
function dist_lt(i: i64, j: i64) -> i64 {
let mut a: i64 = (j - i) % MOD
if a < 0 { a = a + MOD }
let mut b: i64 = (j + i - 2) % MOD
if b < 0 { b = b + MOD }
return ((a as i128) * (b as i128) % (MOD as i128)) as i64
}
function dist_gt(i: i64, j: i64, k: i64) -> i64 {
let mut a: i64 = (i - j) % MOD
if a < 0 { a = a + MOD }
let mut b: i64 = (2 * k - i - j) % MOD
if b < 0 { b = b + MOD }
return ((a as i128) * (b as i128) % (MOD as i128)) as i64
}
function init_counts(dp: ptr<i64>) -> void {
let mut fr: i32 = 0
while fr < 3 {
let mut dst: i32 = 0
while dst < 3 {
if fr != dst {
let mut st: i32 = 0
while st < 3 {
let mut e: i32 = 0
while e < 6 {
dp[dp_idx(fr, dst, st, e)] = 0
e = e + 1
}
if st != fr {
let ei: i32 = edge_idx(st, fr)
dp[dp_idx(fr, dst, st, ei)] = dp[dp_idx(fr, dst, st, ei)] + 1
}
let ej: i32 = edge_idx(fr, dst)
dp[dp_idx(fr, dst, st, ej)] = dp[dp_idx(fr, dst, st, ej)] + 1
st = st + 1
}
}
dst = dst + 1
}
fr = fr + 1
}
}
function step_counts(dp: ptr<i64>, newdp: ptr<i64>) -> void {
let mut fr: i32 = 0
while fr < 3 {
let mut dst: i32 = 0
while dst < 3 {
if fr != dst {
let aux: i32 = 3 - fr - dst
let mut st: i32 = 0
while st < 3 {
let mut e: i32 = 0
while e < 6 {
let v1: i64 = dp[dp_idx(fr, aux, st, e)]
let v2: i64 = dp[dp_idx(aux, dst, dst, e)]
newdp[dp_idx(fr, dst, st, e)] = (v1 + v2) % MOD
e = e + 1
}
let e1: i32 = edge_idx(aux, fr)
let e2: i32 = edge_idx(fr, dst)
newdp[dp_idx(fr, dst, st, e1)] = (newdp[dp_idx(fr, dst, st, e1)] + 1) % MOD
newdp[dp_idx(fr, dst, st, e2)] = (newdp[dp_idx(fr, dst, st, e2)] + 1) % MOD
st = st + 1
}
}
dst = dst + 1
}
fr = fr + 1
}
}
function main() -> i32 {
let sz: i64 = 3 * 3 * 3 * 6
let dp: ptr<i64> = calloc(sz, 8)
let newdp: ptr<i64> = calloc(sz, 8)
if dp == null || newdp == null { return 1 }
init_counts(dp)
let mut a: i64 = 1
let mut b: i64 = 1
let mut c: i64 = 1
let mut k: i64 = 1
let mut total: i64 = 0
let mut n: i64 = 1
while n <= LIMIT {
a = (a * 3) % MOD
b = (b * 6) % MOD
c = (c * 9) % MOD
k = (k * 10) % MOD
if n > 1 {
step_counts(dp, newdp)
let mut i: i64 = 0
while i < sz {
dp[i] = newdp[i]
i = i + 1
}
}
let d01: i64 = dist_lt(a, b)
let d02: i64 = dist_lt(a, c)
let d10: i64 = dist_gt(b, a, k)
let d12: i64 = dist_lt(b, c)
let d20: i64 = dist_gt(c, a, k)
let d21: i64 = dist_gt(c, b, k)
let mut e: i128 = 0
e = e + (dp[dp_idx(0, 2, 1, 0)] as i128) * (d01 as i128)
e = e + (dp[dp_idx(0, 2, 1, 1)] as i128) * (d02 as i128)
e = e + (dp[dp_idx(0, 2, 1, 2)] as i128) * (d10 as i128)
e = e + (dp[dp_idx(0, 2, 1, 3)] as i128) * (d12 as i128)
e = e + (dp[dp_idx(0, 2, 1, 4)] as i128) * (d20 as i128)
e = e + (dp[dp_idx(0, 2, 1, 5)] as i128) * (d21 as i128)
total = ((total as i128 + e) % (MOD as i128)) as i64
n = n + 1
}
printf("%lld\n", total)
free(newdp)
free(dp)
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; }
int32_t edge_idx_i32_i32(int32_t u, int32_t v);
int64_t dp_idx_i32_i32_i32_i32(int32_t fr, int32_t dst, int32_t st, int32_t e);
int64_t dist_lt_i64_i64(int64_t i, int64_t j);
int64_t dist_gt_i64_i64_i64(int64_t i, int64_t j, int64_t k);
void init_counts_ptr_i64(int64_t* dp);
void step_counts_ptr_i64_ptr_i64(int64_t* dp, int64_t* newdp);
int32_t main(void);
static const int64_t MOD = 1000000000;
static const int64_t LIMIT = 10000;
int32_t edge_idx_i32_i32(int32_t u, int32_t v) {
if (u == 0) {
if (v == 1) {
return 0;
}
return 1;
}
if (u == 1) {
if (v == 0) {
return 2;
}
return 3;
}
if (v == 0) {
return 4;
}
return 5;
}
int64_t dp_idx_i32_i32_i32_i32(int32_t fr, int32_t dst, int32_t st, int32_t e) {
return ((int64_t)(((((((fr * 3) + dst) * 3) + st) * 6) + e)));
}
int64_t dist_lt_i64_i64(int64_t i, int64_t j) {
int64_t a = FLOW_CHECKED_MOD(((j - i)), (MOD));
if (a < 0) {
a = (a + MOD);
}
int64_t b = FLOW_CHECKED_MOD((((j + i) - 2)), (MOD));
if (b < 0) {
b = (b + MOD);
}
return ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(a)) * ((__int128)(b)))), (((__int128)(MOD))))));
}
int64_t dist_gt_i64_i64_i64(int64_t i, int64_t j, int64_t k) {
int64_t a = FLOW_CHECKED_MOD(((i - j)), (MOD));
if (a < 0) {
a = (a + MOD);
}
int64_t b = FLOW_CHECKED_MOD(((((2 * k) - i) - j)), (MOD));
if (b < 0) {
b = (b + MOD);
}
return ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(a)) * ((__int128)(b)))), (((__int128)(MOD))))));
}
void init_counts_ptr_i64(int64_t* dp) {
int32_t fr = 0;
while (fr < 3) {
int32_t dst = 0;
while (dst < 3) {
if (fr != dst) {
int32_t st = 0;
while (st < 3) {
int32_t e = 0;
while (e < 6) {
dp[dp_idx_i32_i32_i32_i32(fr, dst, st, e)] = 0;
e = (e + 1);
}
if (st != fr) {
int32_t ei = edge_idx_i32_i32(st, fr);
dp[dp_idx_i32_i32_i32_i32(fr, dst, st, ei)] = (dp[dp_idx_i32_i32_i32_i32(fr, dst, st, ei)] + 1);
}
int32_t ej = edge_idx_i32_i32(fr, dst);
dp[dp_idx_i32_i32_i32_i32(fr, dst, st, ej)] = (dp[dp_idx_i32_i32_i32_i32(fr, dst, st, ej)] + 1);
st = (st + 1);
}
}
dst = (dst + 1);
}
fr = (fr + 1);
}
}
void step_counts_ptr_i64_ptr_i64(int64_t* dp, int64_t* newdp) {
int32_t fr = 0;
while (fr < 3) {
int32_t dst = 0;
while (dst < 3) {
if (fr != dst) {
int32_t aux = ((3 - fr) - dst);
int32_t st = 0;
while (st < 3) {
int32_t e = 0;
while (e < 6) {
int64_t v1 = dp[dp_idx_i32_i32_i32_i32(fr, aux, st, e)];
int64_t v2 = dp[dp_idx_i32_i32_i32_i32(aux, dst, dst, e)];
newdp[dp_idx_i32_i32_i32_i32(fr, dst, st, e)] = FLOW_CHECKED_MOD(((v1 + v2)), (MOD));
e = (e + 1);
}
int32_t e1 = edge_idx_i32_i32(aux, fr);
int32_t e2 = edge_idx_i32_i32(fr, dst);
newdp[dp_idx_i32_i32_i32_i32(fr, dst, st, e1)] = FLOW_CHECKED_MOD(((newdp[dp_idx_i32_i32_i32_i32(fr, dst, st, e1)] + 1)), (MOD));
newdp[dp_idx_i32_i32_i32_i32(fr, dst, st, e2)] = FLOW_CHECKED_MOD(((newdp[dp_idx_i32_i32_i32_i32(fr, dst, st, e2)] + 1)), (MOD));
st = (st + 1);
}
}
dst = (dst + 1);
}
fr = (fr + 1);
}
}
int32_t main(void) {
int64_t sz = (((3 * 3) * 3) * 6);
int64_t* dp = (int64_t*)(calloc(sz, 8));
int64_t* newdp = (int64_t*)(calloc(sz, 8));
if ((dp == NULL || newdp == NULL)) {
return 1;
}
init_counts_ptr_i64(dp);
int64_t a = 1;
int64_t b = 1;
int64_t c = 1;
int64_t k = 1;
int64_t total = 0;
int64_t n = 1;
while (n <= LIMIT) {
a = FLOW_CHECKED_MOD(((a * 3)), (MOD));
b = FLOW_CHECKED_MOD(((b * 6)), (MOD));
c = FLOW_CHECKED_MOD(((c * 9)), (MOD));
k = FLOW_CHECKED_MOD(((k * 10)), (MOD));
if (n > 1) {
step_counts_ptr_i64_ptr_i64(dp, newdp);
int64_t i = 0;
while (i < sz) {
dp[i] = newdp[i];
i = (i + 1);
}
}
int64_t d01 = dist_lt_i64_i64(a, b);
int64_t d02 = dist_lt_i64_i64(a, c);
int64_t d10 = dist_gt_i64_i64_i64(b, a, k);
int64_t d12 = dist_lt_i64_i64(b, c);
int64_t d20 = dist_gt_i64_i64_i64(c, a, k);
int64_t d21 = dist_gt_i64_i64_i64(c, b, k);
__int128 e = 0;
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 0)])) * ((__int128)(d01))));
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 1)])) * ((__int128)(d02))));
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 2)])) * ((__int128)(d10))));
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 3)])) * ((__int128)(d12))));
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 4)])) * ((__int128)(d20))));
e = (e + (((__int128)(dp[dp_idx_i32_i32_i32_i32(0, 2, 1, 5)])) * ((__int128)(d21))));
total = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(total)) + e)), (((__int128)(MOD))))));
n = (n + 1);
}
printf("%lld\n", total);
free(newdp);
free(dp);
return 0;
}