# Project Euler 906
# A Collective Decision — Condorcet winner probability P(20000).
function agreement_probability(n: i64) -> f64 {
if n == 1 { return 1.0 }
let N: i64 = n - 1
let factor: f64 = (N + 1) as f64 / ((n * n) as f64)
let mut s: f64 = 0.0
let mut c: f64 = 0.0
let mut a: i64 = 0
while a <= N {
let bmax: i64 = N - a
let mut term: f64 = 1.0 / ((a + 1) as f64)
let mut y: f64 = term - c
let mut t: f64 = s + y
c = (t - s) - y
s = t
let mut g: f64 = 1.0
let mut num: f64 = (N - a) as f64
let mut den: f64 = N as f64
let mut b: i64 = 1
while b <= bmax {
g = g * (num / den)
num = num - 1.0
den = den - 1.0
term = g / ((a + b + 1) as f64)
y = term - c
t = s + y
c = (t - s) - y
s = t
let rem: i64 = bmax - b
if rem > 0 && term * (rem as f64) < 1e-20 {
break
}
b = b + 1
}
a = a + 1
}
return factor * s
}
function main() -> i32 {
printf("%.10f\n", agreement_probability(20000))
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; }
double agreement_probability_i64(int64_t n);
int32_t main(void);
double agreement_probability_i64(int64_t n) {
if (n == 1) {
return 1.0;
}
int64_t N = (n - 1);
double factor = (((double)((N + 1))) / ((double)((n * n))));
double s = 0.0;
double c = 0.0;
int64_t a = 0;
while (a <= N) {
int64_t bmax = (N - a);
double term = (1.0 / ((double)((a + 1))));
double y = (term - c);
double t = (s + y);
c = ((t - s) - y);
s = t;
double g = 1.0;
double num = ((double)((N - a)));
double den = ((double)(N));
int64_t b = 1;
while (b <= bmax) {
g = (g * (num / den));
num = (num - 1.0);
den = (den - 1.0);
term = (g / ((double)(((a + b) + 1))));
y = (term - c);
t = (s + y);
c = ((t - s) - y);
s = t;
int64_t rem = (bmax - b);
if ((rem > 0 && (term * ((double)(rem))) < 1e-20)) {
break;
}
b = (b + 1);
}
a = (a + 1);
}
return (factor * s);
}
int32_t main(void) {
printf("%.10f\n", agreement_probability_i64(20000));
return 0;
}