# Project Euler 849
# The Tournament — F(100) mod 10^9+7.
#
# DP over tournament steps with a sliding-window prefix sum.
# State is (height, displacement) tracked in flat arrays.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
function malloc(n: i64) -> ptr<void>
}
const MOD: i64 = 1000000007
function main() -> i32 {
let n: i32 = 100
let vmax: i32 = 2 * (n - 1)
let off: i32 = vmax
let v: i32 = 2 * vmax + 1
let maxh: ptr<i32> = malloc(((n + 1) as i64) * 4)
let mut i: i32 = 0
while i <= n {
maxh[i] = 2 * i * (n - i)
i = i + 1
}
let mh: i32 = maxh[1]
let mut dp: ptr<i64> = calloc(((mh + 1) as i64) * ((v as i64)), 8)
let mut d: i32 = 0
while d <= vmax {
dp[((d as i64) * (v as i64)) + ((d + off) as i64)] = 1
d = d + 1
}
let mut step: i32 = 1
while step < n {
let mh_cur: i32 = maxh[step]
let mh_next: i32 = maxh[step + 1]
let nxt: ptr<i64> = calloc(((mh_next + 1) as i64) * ((v as i64)), 8)
let mut h: i32 = 0
while h <= mh_cur {
let row_base: i64 = (h as i64) * (v as i64)
let mut cum: i64 = 0
let base: i32 = h - off - 4
let mut vi_start: i32 = -base
if vi_start < 4 {
vi_start = 4
}
if vi_start > v {
vi_start = v
}
let mut vi_end: i32 = mh_next - base
if vi_end > v - 1 {
vi_end = v - 1
}
let mut vi: i32 = 0
while vi < vi_start {
cum = cum + dp[row_base + (vi as i64)]
if cum >= MOD {
cum = cum - MOD
}
vi = vi + 1
}
if vi_start <= vi_end {
vi = vi_start
while vi <= vi_end {
cum = cum + dp[row_base + (vi as i64)]
if cum >= MOD {
cum = cum - MOD
}
let h2: i32 = base + vi
let idx2: i32 = vi - 4
let val: i64 = nxt[((h2 as i64) * (v as i64)) + (idx2 as i64)] + cum
let mut val2: i64 = val
if val2 >= MOD {
val2 = val2 - MOD
}
nxt[((h2 as i64) * (v as i64)) + (idx2 as i64)] = val2
vi = vi + 1
}
vi = vi_end + 1
while vi < v {
cum = cum + dp[row_base + (vi as i64)]
if cum >= MOD {
cum = cum - MOD
}
vi = vi + 1
}
}
else {
vi = vi_start
while vi < v {
cum = cum + dp[row_base + (vi as i64)]
if cum >= MOD {
cum = cum - MOD
}
vi = vi + 1
}
}
let total: i64 = cum
if total != 0 {
let base_h: i32 = h - off
vi = v - 4
while vi < v {
let h2: i32 = base_h + vi
if 0 <= h2 && h2 <= mh_next {
let val: i64 = nxt[((h2 as i64) * (v as i64)) + (vi as i64)] + total
let mut val2: i64 = val
if val2 >= MOD {
val2 = val2 - MOD
}
nxt[((h2 as i64) * (v as i64)) + (vi as i64)] = val2
}
vi = vi + 1
}
}
h = h + 1
}
free(dp)
dp = nxt
step = step + 1
}
let mut ans: i64 = 0
let mut vi: i32 = 0
while vi < v {
ans = ans + dp[(vi as i64)]
if ans >= MOD {
ans = ans - MOD
}
vi = vi + 1
}
free(dp)
free(maxh)
printf("%lld\n", ans)
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 main(void);
static const int64_t MOD = 1000000007;
int32_t main(void) {
int32_t n = 100;
int32_t vmax = (2 * (n - 1));
int32_t off = vmax;
int32_t v = ((2 * vmax) + 1);
int32_t* maxh = (int32_t*)(malloc((((int64_t)((n + 1))) * 4)));
int32_t i = 0;
while (i <= n) {
maxh[i] = ((2 * i) * (n - i));
i = (i + 1);
}
int32_t mh = maxh[1];
int64_t* dp = (int64_t*)(calloc((((int64_t)((mh + 1))) * ((int64_t)(v))), 8));
int32_t d = 0;
while (d <= vmax) {
dp[((((int64_t)(d)) * ((int64_t)(v))) + ((int64_t)((d + off))))] = 1;
d = (d + 1);
}
int32_t step = 1;
while (step < n) {
int32_t mh_cur = maxh[step];
int32_t mh_next = maxh[(step + 1)];
int64_t* nxt = (int64_t*)(calloc((((int64_t)((mh_next + 1))) * ((int64_t)(v))), 8));
int32_t h = 0;
while (h <= mh_cur) {
int64_t row_base = (((int64_t)(h)) * ((int64_t)(v)));
int64_t cum = 0;
int32_t base = ((h - off) - 4);
int32_t vi_start = (-base);
if (vi_start < 4) {
vi_start = 4;
}
if (vi_start > v) {
vi_start = v;
}
int32_t vi_end = (mh_next - base);
if (vi_end > (v - 1)) {
vi_end = (v - 1);
}
int32_t vi = 0;
while (vi < vi_start) {
cum = (cum + dp[(row_base + ((int64_t)(vi)))]);
if (cum >= MOD) {
cum = (cum - MOD);
}
vi = (vi + 1);
}
if (vi_start <= vi_end) {
vi = vi_start;
while (vi <= vi_end) {
cum = (cum + dp[(row_base + ((int64_t)(vi)))]);
if (cum >= MOD) {
cum = (cum - MOD);
}
int32_t h2 = (base + vi);
int32_t idx2 = (vi - 4);
int64_t val = (nxt[((((int64_t)(h2)) * ((int64_t)(v))) + ((int64_t)(idx2)))] + cum);
int64_t val2 = val;
if (val2 >= MOD) {
val2 = (val2 - MOD);
}
nxt[((((int64_t)(h2)) * ((int64_t)(v))) + ((int64_t)(idx2)))] = val2;
vi = (vi + 1);
}
vi = (vi_end + 1);
while (vi < v) {
cum = (cum + dp[(row_base + ((int64_t)(vi)))]);
if (cum >= MOD) {
cum = (cum - MOD);
}
vi = (vi + 1);
}
} else {
vi = vi_start;
while (vi < v) {
cum = (cum + dp[(row_base + ((int64_t)(vi)))]);
if (cum >= MOD) {
cum = (cum - MOD);
}
vi = (vi + 1);
}
}
int64_t total = cum;
if (total != 0) {
int32_t base_h = (h - off);
vi = (v - 4);
while (vi < v) {
int32_t h2 = (base_h + vi);
if ((0 <= h2 && h2 <= mh_next)) {
int64_t val = (nxt[((((int64_t)(h2)) * ((int64_t)(v))) + ((int64_t)(vi)))] + total);
int64_t val2 = val;
if (val2 >= MOD) {
val2 = (val2 - MOD);
}
nxt[((((int64_t)(h2)) * ((int64_t)(v))) + ((int64_t)(vi)))] = val2;
}
vi = (vi + 1);
}
}
h = (h + 1);
}
free(dp);
dp = nxt;
step = (step + 1);
}
int64_t ans = 0;
int32_t vi = 0;
while (vi < v) {
ans = (ans + dp[((int64_t)(vi))]);
if (ans >= MOD) {
ans = (ans - MOD);
}
vi = (vi + 1);
}
free(dp);
free(maxh);
printf("%lld\n", ans);
return 0;
}