Problem 862

Larger Digit Permutation — S(12) via digit-multiset enumeration.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 862
# Larger Digit Permutation — S(12) via digit-multiset enumeration.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

let mut FACT: ptr<i64> = null
let mut TOTAL: i64 = 0
let mut D0: i64 = 0
let mut R: i64 = 0
let mut FK1: i64 = 0

function rec(digit: i64, rem: i64, denom_prod: i64) -> void {
    if digit == 10 {
        if rem != 0 { return }
        let denom: i64 = FACT[D0] * denom_prod
        let M: i64 = (R * FK1) / denom
        TOTAL = TOTAL + M * (M - 1) / 2
        return
    }
    if digit == 9 {
        rec(10, 0, denom_prod * FACT[rem])
        return
    }
    let mut c: i64 = 0
    while c <= rem {
        rec(digit + 1, rem - c, denom_prod * FACT[c])
        c = c + 1
    }
}

function S(k: i64) -> i64 {
    if k <= 1 { return 0 }
    FACT = calloc(k + 1, 8)
    FACT[0] = 1
    let mut i: i64 = 1
    while i <= k {
        FACT[i] = FACT[i - 1] * i
        i = i + 1
    }
    FK1 = FACT[k - 1]
    TOTAL = 0
    D0 = 0
    while D0 <= k {
        R = k - D0
        if R > 0 {
            rec(1, R, 1)
        }
        D0 = D0 + 1
    }
    let ans: i64 = TOTAL
    free(FACT)
    return ans
}

function main() -> i32 {
    printf("%lld\n", S(12))
    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; }

void rec_i64_i64_i64(int64_t digit, int64_t rem, int64_t denom_prod);
int64_t S_i64(int64_t k);
int32_t main(void);

/* Module statics */
static int64_t* FACT = NULL;
static int64_t TOTAL = 0;
static int64_t D0 = 0;
static int64_t R = 0;
static int64_t FK1 = 0;



void rec_i64_i64_i64(int64_t digit, int64_t rem, int64_t denom_prod) {
    if (digit == 10) {
        if (rem != 0) {
            return;
        }
        int64_t denom = (FACT[D0] * denom_prod);
        int64_t M = FLOW_CHECKED_DIV(((R * FK1)), (denom));
        TOTAL = (TOTAL + FLOW_CHECKED_DIV(((M * (M - 1))), (2)));
        return;
    }
    if (digit == 9) {
        rec_i64_i64_i64(10, 0, (denom_prod * FACT[rem]));
        return;
    }
    int64_t c = 0;
    while (c <= rem) {
        rec_i64_i64_i64((digit + 1), (rem - c), (denom_prod * FACT[c]));
        c = (c + 1);
    }
}

int64_t S_i64(int64_t k) {
    if (k <= 1) {
        return 0;
    }
    FACT = calloc((k + 1), 8);
    FACT[0] = 1;
    int64_t i = 1;
    while (i <= k) {
        FACT[i] = (FACT[(i - 1)] * i);
        i = (i + 1);
    }
    FK1 = FACT[(k - 1)];
    TOTAL = 0;
    D0 = 0;
    while (D0 <= k) {
        R = (k - D0);
        if (R > 0) {
            rec_i64_i64_i64(1, R, 1);
        }
        D0 = (D0 + 1);
    }
    int64_t ans = TOTAL;
    free(FACT);
    return ans;
}

int32_t main(void) {
    printf("%lld\n", S_i64(12));
    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 private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  // Module static: FACT
  llvm.mlir.global internal @FACT() {addr_space = 0 : i32} : !llvm.ptr {
    %0 = llvm.mlir.zero : !llvm.ptr
    llvm.return %0 : !llvm.ptr
  }
  // Module static: TOTAL
  llvm.mlir.global internal @TOTAL(0 : i64) : i64
  // Module static: D0
  llvm.mlir.global internal @D0(0 : i64) : i64
  // Module static: R
  llvm.mlir.global internal @R(0 : i64) : i64
  // Module static: FK1
  llvm.mlir.global internal @FK1(0 : i64) : i64
  func.func @rec(%arg0: i64, %arg1: i64, %arg2: i64) -> () {
    %1 = arith.constant 10 : i32
    %3 = arith.extsi %1 : i32 to i64
    %2 = arith.cmpi eq, %arg0, %3 : i64
    cf.cond_br %2, ^bb0, ^bb1
    ^bb0:
      %4 = arith.constant 0 : i32
      %6 = arith.extsi %4 : i32 to i64
      %5 = arith.cmpi ne, %arg1, %6 : i64
      cf.cond_br %5, ^bb3, ^bb4
      ^bb3:
        func.return
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %8 = llvm.mlir.addressof @FACT : !llvm.ptr
      %9 = llvm.load %8 : !llvm.ptr -> !llvm.ptr
      %10 = llvm.mlir.addressof @D0 : !llvm.ptr
      %11 = llvm.load %10 : !llvm.ptr -> i64
      %12 = llvm.getelementptr %9[%11] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %7 = llvm.load %12 : !llvm.ptr -> i64
      %13 = arith.muli %7, %arg2 : i64
      %14 = llvm.mlir.addressof @R : !llvm.ptr
      %15 = llvm.load %14 : !llvm.ptr -> i64
      %16 = llvm.mlir.addressof @FK1 : !llvm.ptr
      %17 = llvm.load %16 : !llvm.ptr -> i64
      %18 = arith.muli %15, %17 : i64
      %19 = arith.divsi %18, %13 : i64
      %20 = llvm.mlir.addressof @TOTAL : !llvm.ptr
      %21 = llvm.load %20 : !llvm.ptr -> i64
      %22 = arith.constant 1 : i32
      %24 = arith.extsi %22 : i32 to i64
      %23 = arith.subi %19, %24 : i64
      %25 = arith.muli %19, %23 : i64
      %26 = arith.constant 2 : i32
      %28 = arith.extsi %26 : i32 to i64
      %27 = arith.divsi %25, %28 : i64
      %29 = arith.addi %21, %27 : i64
      %30 = llvm.mlir.addressof @TOTAL : !llvm.ptr
      llvm.store %29, %30 : i64, !llvm.ptr
      func.return
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %31 = arith.constant 9 : i32
    %33 = arith.extsi %31 : i32 to i64
    %32 = arith.cmpi eq, %arg0, %33 : i64
    cf.cond_br %32, ^bb6, ^bb7
    ^bb6:
      %35 = arith.constant 10 : i32
      %36 = arith.constant 0 : i32
      %38 = llvm.mlir.addressof @FACT : !llvm.ptr
      %39 = llvm.load %38 : !llvm.ptr -> !llvm.ptr
      %40 = llvm.getelementptr %39[%arg1] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %37 = llvm.load %40 : !llvm.ptr -> i64
      %41 = arith.muli %arg2, %37 : i64
      %42 = arith.extsi %35 : i32 to i64
      %43 = arith.extsi %36 : i32 to i64
      func.call @rec(%42, %43, %41) : (i64, i64, i64) -> ()
      func.return
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %44 = arith.constant 0 : i32
    %45 = arith.extsi %44 : i32 to i64
    %46 = llvm.mlir.constant(1 : i64) : i64
    %47 = llvm.alloca %46 x i64 : (i64) -> !llvm.ptr
    llvm.store %45, %47 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %48 = llvm.load %47 : !llvm.ptr -> i64
    %49 = arith.cmpi sle, %48, %arg1 : i64
    cf.cond_br %49, ^bb10, ^bb11
    ^bb10:
      %51 = arith.constant 1 : i32
      %53 = arith.extsi %51 : i32 to i64
      %52 = arith.addi %arg0, %53 : i64
      %54 = llvm.load %47 : !llvm.ptr -> i64
      %55 = arith.subi %arg1, %54 : i64
      %57 = llvm.mlir.addressof @FACT : !llvm.ptr
      %58 = llvm.load %57 : !llvm.ptr -> !llvm.ptr
      %59 = llvm.load %47 : !llvm.ptr -> i64
      %60 = llvm.getelementptr %58[%59] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %56 = llvm.load %60 : !llvm.ptr -> i64
      %61 = arith.muli %arg2, %56 : i64
      func.call @rec(%52, %55, %61) : (i64, i64, i64) -> ()
      %62 = llvm.load %47 : !llvm.ptr -> i64
      %63 = arith.constant 1 : i32
      %65 = arith.extsi %63 : i32 to i64
      %64 = arith.addi %62, %65 : i64
      llvm.store %64, %47 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    func.return
  }
  func.func @S(%arg0: i64) -> i64 {
    %66 = arith.constant 1 : i32
    %68 = arith.extsi %66 : i32 to i64
    %67 = arith.cmpi sle, %arg0, %68 : i64
    cf.cond_br %67, ^bb12, ^bb13
    ^bb12:
      %69 = arith.constant 0 : i32
      %70 = arith.extsi %69 : i32 to i64
      func.return %70 : i64
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %72 = arith.constant 1 : i32
    %74 = arith.extsi %72 : i32 to i64
    %73 = arith.addi %arg0, %74 : i64
    %75 = arith.constant 8 : i32
    %76 = arith.extsi %75 : i32 to i64
    %71 = func.call @calloc(%73, %76) : (i64, i64) -> !llvm.ptr
    %77 = llvm.mlir.addressof @FACT : !llvm.ptr
    llvm.store %71, %77 : !llvm.ptr, !llvm.ptr
    %78 = arith.constant 1 : i32
    %79 = llvm.mlir.addressof @FACT : !llvm.ptr
    %80 = llvm.load %79 : !llvm.ptr -> !llvm.ptr
    %81 = arith.constant 0 : i32
    %82 = arith.extsi %78 : i32 to i64
    %83 = arith.extsi %81 : i32 to i64
    %84 = llvm.getelementptr %80[%83] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %82, %84 : i64, !llvm.ptr
    %85 = arith.constant 1 : i32
    %86 = arith.extsi %85 : i32 to i64
    %87 = llvm.mlir.constant(1 : i64) : i64
    %88 = llvm.alloca %87 x i64 : (i64) -> !llvm.ptr
    llvm.store %86, %88 : i64, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %89 = llvm.load %88 : !llvm.ptr -> i64
    %90 = arith.cmpi sle, %89, %arg0 : i64
    cf.cond_br %90, ^bb16, ^bb17
    ^bb16:
      %92 = llvm.mlir.addressof @FACT : !llvm.ptr
      %93 = llvm.load %92 : !llvm.ptr -> !llvm.ptr
      %94 = llvm.load %88 : !llvm.ptr -> i64
      %95 = arith.constant 1 : i32
      %97 = arith.extsi %95 : i32 to i64
      %96 = arith.subi %94, %97 : i64
      %98 = llvm.getelementptr %93[%96] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %91 = llvm.load %98 : !llvm.ptr -> i64
      %99 = llvm.load %88 : !llvm.ptr -> i64
      %100 = arith.muli %91, %99 : i64
      %101 = llvm.mlir.addressof @FACT : !llvm.ptr
      %102 = llvm.load %101 : !llvm.ptr -> !llvm.ptr
      %103 = llvm.load %88 : !llvm.ptr -> i64
      %104 = llvm.getelementptr %102[%103] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %100, %104 : i64, !llvm.ptr
      %105 = llvm.load %88 : !llvm.ptr -> i64
      %106 = arith.constant 1 : i32
      %108 = arith.extsi %106 : i32 to i64
      %107 = arith.addi %105, %108 : i64
      llvm.store %107, %88 : i64, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %110 = llvm.mlir.addressof @FACT : !llvm.ptr
    %111 = llvm.load %110 : !llvm.ptr -> !llvm.ptr
    %112 = arith.constant 1 : i32
    %114 = arith.extsi %112 : i32 to i64
    %113 = arith.subi %arg0, %114 : i64
    %115 = llvm.getelementptr %111[%113] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %109 = llvm.load %115 : !llvm.ptr -> i64
    %116 = llvm.mlir.addressof @FK1 : !llvm.ptr
    llvm.store %109, %116 : i64, !llvm.ptr
    %117 = arith.constant 0 : i32
    %118 = arith.extsi %117 : i32 to i64
    %119 = llvm.mlir.addressof @TOTAL : !llvm.ptr
    llvm.store %118, %119 : i64, !llvm.ptr
    %120 = arith.constant 0 : i32
    %121 = arith.extsi %120 : i32 to i64
    %122 = llvm.mlir.addressof @D0 : !llvm.ptr
    llvm.store %121, %122 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %123 = llvm.mlir.addressof @D0 : !llvm.ptr
    %124 = llvm.load %123 : !llvm.ptr -> i64
    %125 = arith.cmpi sle, %124, %arg0 : i64
    cf.cond_br %125, ^bb19, ^bb20
    ^bb19:
      %126 = llvm.mlir.addressof @D0 : !llvm.ptr
      %127 = llvm.load %126 : !llvm.ptr -> i64
      %128 = arith.subi %arg0, %127 : i64
      %129 = llvm.mlir.addressof @R : !llvm.ptr
      llvm.store %128, %129 : i64, !llvm.ptr
      %130 = llvm.mlir.addressof @R : !llvm.ptr
      %131 = llvm.load %130 : !llvm.ptr -> i64
      %132 = arith.constant 0 : i32
      %134 = arith.extsi %132 : i32 to i64
      %133 = arith.cmpi sgt, %131, %134 : i64
      cf.cond_br %133, ^bb21, ^bb22
      ^bb21:
        %136 = arith.constant 1 : i32
        %137 = llvm.mlir.addressof @R : !llvm.ptr
        %138 = llvm.load %137 : !llvm.ptr -> i64
        %139 = arith.constant 1 : i32
        %140 = arith.extsi %136 : i32 to i64
        %141 = arith.extsi %139 : i32 to i64
        func.call @rec(%140, %138, %141) : (i64, i64, i64) -> ()
        cf.br ^bb23
      ^bb22:
        cf.br ^bb23
      ^bb23:
      %142 = llvm.mlir.addressof @D0 : !llvm.ptr
      %143 = llvm.load %142 : !llvm.ptr -> i64
      %144 = arith.constant 1 : i32
      %146 = arith.extsi %144 : i32 to i64
      %145 = arith.addi %143, %146 : i64
      %147 = llvm.mlir.addressof @D0 : !llvm.ptr
      llvm.store %145, %147 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %148 = llvm.mlir.addressof @TOTAL : !llvm.ptr
    %149 = llvm.load %148 : !llvm.ptr -> i64
    %151 = llvm.mlir.addressof @FACT : !llvm.ptr
    %152 = llvm.load %151 : !llvm.ptr -> !llvm.ptr
    func.call @free(%152) : (!llvm.ptr) -> ()
    func.return %149 : i64
  }
  func.func @main() -> i32 {
    %153 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %155 = arith.constant 12 : i32
    %156 = arith.extsi %155 : i32 to i64
    %154 = func.call @S(%156) : (i64) -> i64
    %157 = llvm.call @printf(%153, %154) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %158 = arith.constant 0 : i32
    func.return %158 : i32
  }
}