Problem 104

Least Fibonacci index where first and last nine digits are 1-9 pandigital.

Answer329468
Output329468
StatusPASS
Native helperno
Runtime0 ms
Peak memory1072 KB
Time complexityO(n) (estimated)
Space complexityO(1) (estimated)

Performance comparison

MetricOur solutionBest known
Time complexityO(n)O(log n)
Space complexityO(1)O(1)
ApproachFlow solutionMatrix exponentiation
VerdictSuboptimal

Flow source

# Project Euler 104
# Least Fibonacci index where first and last nine digits are 1-9 pandigital.

function is_pandigital9(n: i64) -> bool {
    if n < 100000000 || n > 999999999 { return false }
    let mut seen: i32 = 0
    let mut x: i64 = n
    let mut i: i32 = 0
    while i < 9 {
        let d: i32 = (x % 10) as i32
        if d == 0 { return false }
        let bit: i32 = 1 << d
        if (seen & bit) != 0 { return false }
        seen = seen | bit
        x = x / 10
        i = i + 1
    }
    return seen == 1022  # bits 1..9 = 0x3FE
}

function first9_fib(k: i64) -> i64 {
    # log10(F_k) ≈ k*log10(phi) - log10(sqrt(5))
    let log_phi: f64 = 0.20898764024997873
    let log_sqrt5: f64 = 0.3494850021680094
    let t: f64 = (k as f64) * log_phi - log_sqrt5
    let mut frac: f64 = t - ((t as i64) as f64)
    if frac < 0.0 {
        frac = frac + 1.0
    }
    # 10^frac via exp(frac * ln10)
    let ln10: f64 = 2.302585092994046
    let x: f64 = frac * ln10
    let mut term: f64 = 1.0
    let mut sum: f64 = 1.0
    let mut n: i32 = 1
    while n < 50 {
        term = term * x / (n as f64)
        sum = sum + term
        n = n + 1
    }
    let val: f64 = sum * 100000000.0
    return (val as i64)
}

function main() -> i32 {
    let mod: i64 = 1000000000
    let mut a: i64 = 1
    let mut b: i64 = 1
    let mut k: i64 = 2
    while k < 2000000 {
        k = k + 1
        let c: i64 = (a + b) % mod
        a = b
        b = c
        if is_pandigital9(b) {
            if is_pandigital9(first9_fib(k)) {
                printf("%lld\n", k)
                return 0
            }
        }
    }
    printf("0\n")
    return 1
}

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; }

bool is_pandigital9_i64(int64_t n);
int64_t first9_fib_i64(int64_t k);
int32_t main(void);

bool is_pandigital9_i64(int64_t n) {
    if ((n < 100000000 || n > 999999999)) {
        return 0;
    }
    int32_t seen = 0;
    int64_t x = n;
    int32_t i = 0;
    while (i < 9) {
        int32_t d = ((int32_t)(FLOW_CHECKED_MOD((x), (10))));
        if (d == 0) {
            return 0;
        }
        int32_t bit = FLOW_CHECKED_SHL((1), (d));
        if ((seen & bit) != 0) {
            return 0;
        }
        seen = (seen | bit);
        x = FLOW_CHECKED_DIV((x), (10));
        i = (i + 1);
    }
    return seen == 1022;
}

int64_t first9_fib_i64(int64_t k) {
    double log_phi = 0.20898764024997873;
    double log_sqrt5 = 0.3494850021680094;
    double t = ((((double)(k)) * log_phi) - log_sqrt5);
    double frac = (t - ((double)(((int64_t)(t)))));
    if (frac < 0.0) {
        frac = (frac + 1.0);
    }
    double ln10 = 2.302585092994046;
    double x = (frac * ln10);
    double term = 1.0;
    double sum = 1.0;
    int32_t n = 1;
    while (n < 50) {
        term = ((term * x) / ((double)(n)));
        sum = (sum + term);
        n = (n + 1);
    }
    double val = (sum * 100000000.0);
    return ((int64_t)(val));
}

int32_t main(void) {
    int64_t mod = 1000000000;
    int64_t a = 1;
    int64_t b = 1;
    int64_t k = 2;
    while (k < 2000000) {
        k = (k + 1);
        int64_t c = FLOW_CHECKED_MOD(((a + b)), (mod));
        a = b;
        b = c;
        if (is_pandigital9_i64(b)) {
            if (is_pandigital9_i64(first9_fib_i64(k))) {
                printf("%lld\n", k);
                return 0;
            }
        }
    }
    printf("0\n");
    return 1;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  llvm.mlir.global internal constant @str_1("0\n\00") {addr_space = 0 : i32} : !llvm.array<3 x i8>
  func.func @is_pandigital9(%arg0: i64) -> i1 {
    %0 = arith.constant 100000000 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi slt, %arg0, %2 : i64
    %3 = scf.if %1 -> (i1) {
      %4 = arith.constant true
      scf.yield %4 : i1
    } else {
      %5 = arith.constant 999999999 : i32
      %7 = arith.extsi %5 : i32 to i64
      %6 = arith.cmpi sgt, %arg0, %7 : i64
      scf.yield %6 : i1
    }
    cf.cond_br %3, ^bb0, ^bb1
    ^bb0:
      %8 = arith.constant 0 : i1
      func.return %8 : i1
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %9 = arith.constant 0 : i32
    %10 = llvm.mlir.constant(1 : i64) : i64
    %11 = llvm.alloca %10 x i32 : (i64) -> !llvm.ptr
    llvm.store %9, %11 : i32, !llvm.ptr
    %12 = llvm.mlir.constant(1 : i64) : i64
    %13 = llvm.alloca %12 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %13 : i64, !llvm.ptr
    %14 = arith.constant 0 : i32
    %15 = llvm.mlir.constant(1 : i64) : i64
    %16 = llvm.alloca %15 x i32 : (i64) -> !llvm.ptr
    llvm.store %14, %16 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %17 = llvm.load %16 : !llvm.ptr -> i32
    %18 = arith.constant 9 : i32
    %19 = arith.cmpi slt, %17, %18 : i32
    cf.cond_br %19, ^bb4, ^bb5
    ^bb4:
      %20 = llvm.load %13 : !llvm.ptr -> i64
      %21 = arith.constant 10 : i32
      %23 = arith.extsi %21 : i32 to i64
      %22 = arith.remsi %20, %23 : i64
      %24 = arith.trunci %22 : i64 to i32
      %25 = arith.constant 0 : i32
      %26 = arith.cmpi eq, %24, %25 : i32
      cf.cond_br %26, ^bb6, ^bb7
      ^bb6:
        %27 = arith.constant 0 : i1
        func.return %27 : i1
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %28 = arith.constant 1 : i32
      %29 = arith.shli %28, %24 : i32
      %30 = llvm.load %11 : !llvm.ptr -> i32
      %31 = arith.andi %30, %29 : i32
      %32 = arith.constant 0 : i32
      %33 = arith.cmpi ne, %31, %32 : i32
      cf.cond_br %33, ^bb9, ^bb10
      ^bb9:
        %34 = arith.constant 0 : i1
        func.return %34 : i1
      ^bb10:
        cf.br ^bb11
      ^bb11:
      %35 = llvm.load %11 : !llvm.ptr -> i32
      %36 = arith.ori %35, %29 : i32
      llvm.store %36, %11 : i32, !llvm.ptr
      %37 = llvm.load %13 : !llvm.ptr -> i64
      %38 = arith.constant 10 : i32
      %40 = arith.extsi %38 : i32 to i64
      %39 = arith.divsi %37, %40 : i64
      llvm.store %39, %13 : i64, !llvm.ptr
      %41 = llvm.load %16 : !llvm.ptr -> i32
      %42 = arith.constant 1 : i32
      %43 = arith.addi %41, %42 : i32
      llvm.store %43, %16 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    %44 = llvm.load %11 : !llvm.ptr -> i32
    %45 = arith.constant 1022 : i32
    %46 = arith.cmpi eq, %44, %45 : i32
    func.return %46 : i1
  }
  func.func @first9_fib(%arg0: i64) -> i64 {
    %47 = arith.constant 0.20898764024997873 : f32
    %48 = arith.extf %47 : f32 to f64
    %49 = arith.constant 0.3494850021680094 : f32
    %50 = arith.extf %49 : f32 to f64
    %51 = arith.sitofp %arg0 : i64 to f64
    %52 = arith.mulf %51, %48 : f64
    %53 = arith.subf %52, %50 : f64
    %54 = arith.fptosi %53 : f64 to i64
    %55 = arith.sitofp %54 : i64 to f64
    %56 = arith.subf %53, %55 : f64
    %57 = llvm.mlir.constant(1 : i64) : i64
    %58 = llvm.alloca %57 x f64 : (i64) -> !llvm.ptr
    llvm.store %56, %58 : f64, !llvm.ptr
    %59 = llvm.load %58 : !llvm.ptr -> f64
    %60 = arith.constant 0.0 : f32
    %62 = arith.extf %60 : f32 to f64
    %61 = arith.cmpf olt, %59, %62 : f64
    cf.cond_br %61, ^bb12, ^bb13
    ^bb12:
      %63 = llvm.load %58 : !llvm.ptr -> f64
      %64 = arith.constant 1.0 : f32
      %66 = arith.extf %64 : f32 to f64
      %65 = arith.addf %63, %66 : f64
      llvm.store %65, %58 : f64, !llvm.ptr
      cf.br ^bb14
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %67 = arith.constant 2.302585092994046 : f32
    %68 = arith.extf %67 : f32 to f64
    %69 = llvm.load %58 : !llvm.ptr -> f64
    %70 = arith.mulf %69, %68 : f64
    %71 = arith.constant 1.0 : f32
    %72 = arith.extf %71 : f32 to f64
    %73 = llvm.mlir.constant(1 : i64) : i64
    %74 = llvm.alloca %73 x f64 : (i64) -> !llvm.ptr
    llvm.store %72, %74 : f64, !llvm.ptr
    %75 = arith.constant 1.0 : f32
    %76 = arith.extf %75 : f32 to f64
    %77 = llvm.mlir.constant(1 : i64) : i64
    %78 = llvm.alloca %77 x f64 : (i64) -> !llvm.ptr
    llvm.store %76, %78 : f64, !llvm.ptr
    %79 = arith.constant 1 : i32
    %80 = llvm.mlir.constant(1 : i64) : i64
    %81 = llvm.alloca %80 x i32 : (i64) -> !llvm.ptr
    llvm.store %79, %81 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %82 = llvm.load %81 : !llvm.ptr -> i32
    %83 = arith.constant 50 : i32
    %84 = arith.cmpi slt, %82, %83 : i32
    cf.cond_br %84, ^bb16, ^bb17
    ^bb16:
      %85 = llvm.load %74 : !llvm.ptr -> f64
      %86 = arith.mulf %85, %70 : f64
      %87 = llvm.load %81 : !llvm.ptr -> i32
      %88 = arith.sitofp %87 : i32 to f64
      %89 = arith.divf %86, %88 : f64
      llvm.store %89, %74 : f64, !llvm.ptr
      %90 = llvm.load %78 : !llvm.ptr -> f64
      %91 = llvm.load %74 : !llvm.ptr -> f64
      %92 = arith.addf %90, %91 : f64
      llvm.store %92, %78 : f64, !llvm.ptr
      %93 = llvm.load %81 : !llvm.ptr -> i32
      %94 = arith.constant 1 : i32
      %95 = arith.addi %93, %94 : i32
      llvm.store %95, %81 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %96 = llvm.load %78 : !llvm.ptr -> f64
    %97 = arith.constant 100000000.0 : f32
    %99 = arith.extf %97 : f32 to f64
    %98 = arith.mulf %96, %99 : f64
    %100 = arith.fptosi %98 : f64 to i64
    func.return %100 : i64
  }
  func.func @main() -> i32 {
    %101 = arith.constant 1000000000 : i32
    %102 = arith.extsi %101 : i32 to i64
    %103 = arith.constant 1 : i32
    %104 = arith.extsi %103 : i32 to i64
    %105 = llvm.mlir.constant(1 : i64) : i64
    %106 = llvm.alloca %105 x i64 : (i64) -> !llvm.ptr
    llvm.store %104, %106 : i64, !llvm.ptr
    %107 = arith.constant 1 : i32
    %108 = arith.extsi %107 : i32 to i64
    %109 = llvm.mlir.constant(1 : i64) : i64
    %110 = llvm.alloca %109 x i64 : (i64) -> !llvm.ptr
    llvm.store %108, %110 : i64, !llvm.ptr
    %111 = arith.constant 2 : i32
    %112 = arith.extsi %111 : i32 to i64
    %113 = llvm.mlir.constant(1 : i64) : i64
    %114 = llvm.alloca %113 x i64 : (i64) -> !llvm.ptr
    llvm.store %112, %114 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %115 = llvm.load %114 : !llvm.ptr -> i64
    %116 = arith.constant 2000000 : i32
    %118 = arith.extsi %116 : i32 to i64
    %117 = arith.cmpi slt, %115, %118 : i64
    cf.cond_br %117, ^bb19, ^bb20
    ^bb19:
      %119 = llvm.load %114 : !llvm.ptr -> i64
      %120 = arith.constant 1 : i32
      %122 = arith.extsi %120 : i32 to i64
      %121 = arith.addi %119, %122 : i64
      llvm.store %121, %114 : i64, !llvm.ptr
      %123 = llvm.load %106 : !llvm.ptr -> i64
      %124 = llvm.load %110 : !llvm.ptr -> i64
      %125 = arith.addi %123, %124 : i64
      %126 = arith.remsi %125, %102 : i64
      %127 = llvm.load %110 : !llvm.ptr -> i64
      llvm.store %127, %106 : i64, !llvm.ptr
      llvm.store %126, %110 : i64, !llvm.ptr
      %129 = llvm.load %110 : !llvm.ptr -> i64
      %128 = func.call @is_pandigital9(%129) : (i64) -> i1
      cf.cond_br %128, ^bb21, ^bb22
      ^bb21:
        %132 = llvm.load %114 : !llvm.ptr -> i64
        %131 = func.call @first9_fib(%132) : (i64) -> i64
        %130 = func.call @is_pandigital9(%131) : (i64) -> i1
        cf.cond_br %130, ^bb24, ^bb25
        ^bb24:
          %133 = llvm.mlir.addressof @str_0 : !llvm.ptr
          %134 = llvm.load %114 : !llvm.ptr -> i64
          %135 = llvm.call @printf(%133, %134) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
          %136 = arith.constant 0 : i32
          func.return %136 : i32
        ^bb25:
          cf.br ^bb26
        ^bb26:
        cf.br ^bb23
      ^bb22:
        cf.br ^bb23
      ^bb23:
      cf.br ^bb18
    ^bb20:
    %137 = llvm.mlir.addressof @str_1 : !llvm.ptr
    %138 = llvm.call @printf(%137) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr) -> i32
    %139 = arith.constant 1 : i32
    func.return %139 : i32
  }
}