Problem 158

Max over n of p(n): strings of length n from 26 letters with exactly one character lexicographically after its left neighbour.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 158
# Max over n of p(n): strings of length n from 26 letters with exactly one
# character lexicographically after its left neighbour.

function choose(n0: i64, k0: i64) -> i64 {
    let mut n: i64 = n0
    let mut result: i64 = 1
    let mut inv: i64 = 1
    while inv <= k0 {
        result = result * n / inv
        n = n - 1
        inv = inv + 1
    }
    return result
}

function count(n: i64, alphabet: i64) -> i64 {
    if n > alphabet { return 0 }
    let mut result: i64 = 0
    let mut i: i64 = 1
    while i < n {
        result = result + choose(n, i) - 1
        i = i + 1
    }
    return result * choose(alphabet, n)
}

function main() -> i32 {
    let mut best: i64 = 0
    let mut i: i64 = 2
    while i <= 26 {
        let cur: i64 = count(i, 26)
        if cur > best { best = cur }
        i = i + 1
    }
    printf("%lld\n", best)
    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 choose_i64_i64(int64_t n0, int64_t k0);
int64_t count_i64_i64(int64_t n, int64_t alphabet);
int32_t main(void);

int64_t choose_i64_i64(int64_t n0, int64_t k0) {
    int64_t n = n0;
    int64_t result = 1;
    int64_t inv = 1;
    while (inv <= k0) {
        result = FLOW_CHECKED_DIV(((result * n)), (inv));
        n = (n - 1);
        inv = (inv + 1);
    }
    return result;
}

int64_t count_i64_i64(int64_t n, int64_t alphabet) {
    if (n > alphabet) {
        return 0;
    }
    int64_t result = 0;
    int64_t i = 1;
    while (i < n) {
        result = ((result + choose_i64_i64(n, i)) - 1);
        i = (i + 1);
    }
    return (result * choose_i64_i64(alphabet, n));
}

int32_t main(void) {
    int64_t best = 0;
    int64_t i = 2;
    while (i <= 26) {
        int64_t cur = count_i64_i64(i, 26);
        if (cur > best) {
            best = cur;
        }
        i = (i + 1);
    }
    printf("%lld\n", best);
    return 0;
}

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>
  func.func @choose(%arg0: i64, %arg1: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %1 : i64, !llvm.ptr
    %2 = arith.constant 1 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = llvm.mlir.constant(1 : i64) : i64
    %5 = llvm.alloca %4 x i64 : (i64) -> !llvm.ptr
    llvm.store %3, %5 : i64, !llvm.ptr
    %6 = arith.constant 1 : i32
    %7 = arith.extsi %6 : i32 to i64
    %8 = llvm.mlir.constant(1 : i64) : i64
    %9 = llvm.alloca %8 x i64 : (i64) -> !llvm.ptr
    llvm.store %7, %9 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %10 = llvm.load %9 : !llvm.ptr -> i64
    %11 = arith.cmpi sle, %10, %arg1 : i64
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %12 = llvm.load %5 : !llvm.ptr -> i64
      %13 = llvm.load %1 : !llvm.ptr -> i64
      %14 = arith.muli %12, %13 : i64
      %15 = llvm.load %9 : !llvm.ptr -> i64
      %16 = arith.divsi %14, %15 : i64
      llvm.store %16, %5 : i64, !llvm.ptr
      %17 = llvm.load %1 : !llvm.ptr -> i64
      %18 = arith.constant 1 : i32
      %20 = arith.extsi %18 : i32 to i64
      %19 = arith.subi %17, %20 : i64
      llvm.store %19, %1 : i64, !llvm.ptr
      %21 = llvm.load %9 : !llvm.ptr -> i64
      %22 = arith.constant 1 : i32
      %24 = arith.extsi %22 : i32 to i64
      %23 = arith.addi %21, %24 : i64
      llvm.store %23, %9 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %25 = llvm.load %5 : !llvm.ptr -> i64
    func.return %25 : i64
  }
  func.func @count(%arg0: i64, %arg1: i64) -> i64 {
    %26 = arith.cmpi sgt, %arg0, %arg1 : i64
    cf.cond_br %26, ^bb3, ^bb4
    ^bb3:
      %27 = arith.constant 0 : i32
      %28 = arith.extsi %27 : i32 to i64
      func.return %28 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %29 = arith.constant 0 : i32
    %30 = arith.extsi %29 : i32 to i64
    %31 = llvm.mlir.constant(1 : i64) : i64
    %32 = llvm.alloca %31 x i64 : (i64) -> !llvm.ptr
    llvm.store %30, %32 : i64, !llvm.ptr
    %33 = arith.constant 1 : i32
    %34 = arith.extsi %33 : i32 to i64
    %35 = llvm.mlir.constant(1 : i64) : i64
    %36 = llvm.alloca %35 x i64 : (i64) -> !llvm.ptr
    llvm.store %34, %36 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %37 = llvm.load %36 : !llvm.ptr -> i64
    %38 = arith.cmpi slt, %37, %arg0 : i64
    cf.cond_br %38, ^bb7, ^bb8
    ^bb7:
      %39 = llvm.load %32 : !llvm.ptr -> i64
      %41 = llvm.load %36 : !llvm.ptr -> i64
      %40 = func.call @choose(%arg0, %41) : (i64, i64) -> i64
      %42 = arith.addi %39, %40 : i64
      %43 = arith.constant 1 : i32
      %45 = arith.extsi %43 : i32 to i64
      %44 = arith.subi %42, %45 : i64
      llvm.store %44, %32 : i64, !llvm.ptr
      %46 = llvm.load %36 : !llvm.ptr -> i64
      %47 = arith.constant 1 : i32
      %49 = arith.extsi %47 : i32 to i64
      %48 = arith.addi %46, %49 : i64
      llvm.store %48, %36 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %50 = llvm.load %32 : !llvm.ptr -> i64
    %51 = func.call @choose(%arg1, %arg0) : (i64, i64) -> i64
    %52 = arith.muli %50, %51 : i64
    func.return %52 : i64
  }
  func.func @main() -> i32 {
    %53 = arith.constant 0 : i32
    %54 = arith.extsi %53 : i32 to i64
    %55 = llvm.mlir.constant(1 : i64) : i64
    %56 = llvm.alloca %55 x i64 : (i64) -> !llvm.ptr
    llvm.store %54, %56 : i64, !llvm.ptr
    %57 = arith.constant 2 : i32
    %58 = arith.extsi %57 : i32 to i64
    %59 = llvm.mlir.constant(1 : i64) : i64
    %60 = llvm.alloca %59 x i64 : (i64) -> !llvm.ptr
    llvm.store %58, %60 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %61 = llvm.load %60 : !llvm.ptr -> i64
    %62 = arith.constant 26 : i32
    %64 = arith.extsi %62 : i32 to i64
    %63 = arith.cmpi sle, %61, %64 : i64
    cf.cond_br %63, ^bb10, ^bb11
    ^bb10:
      %66 = llvm.load %60 : !llvm.ptr -> i64
      %67 = arith.constant 26 : i32
      %68 = arith.extsi %67 : i32 to i64
      %65 = func.call @count(%66, %68) : (i64, i64) -> i64
      %69 = llvm.load %56 : !llvm.ptr -> i64
      %70 = arith.cmpi sgt, %65, %69 : i64
      cf.cond_br %70, ^bb12, ^bb13
      ^bb12:
        llvm.store %65, %56 : i64, !llvm.ptr
        cf.br ^bb14
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %71 = llvm.load %60 : !llvm.ptr -> i64
      %72 = arith.constant 1 : i32
      %74 = arith.extsi %72 : i32 to i64
      %73 = arith.addi %71, %74 : i64
      llvm.store %73, %60 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %75 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %76 = llvm.load %56 : !llvm.ptr -> i64
    %77 = llvm.call @printf(%75, %76) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %78 = arith.constant 0 : i32
    func.return %78 : i32
  }
}