Problem 600

Integer sided equiangular hexagons with perimeter <= 55106. H(n) = # ways to write n-6 as 1a+2b+3c+4d+6e (coin DP).

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 600
# Integer sided equiangular hexagons with perimeter <= 55106.
# H(n) = # ways to write n-6 as 1a+2b+3c+4d+6e (coin DP).

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

function H(n: i64) -> i64 {
    let m: i64 = n - 6
    if m < 0 { return 0 }
    let dp: ptr<i64> = calloc(m + 1, 8)
    if dp == null { return -1 }
    dp[0] = 1
    let coins: ptr<i64> = calloc(5, 8)
    coins[0] = 1
    coins[1] = 2
    coins[2] = 3
    coins[3] = 4
    coins[4] = 6
    let mut ci: i64 = 0
    while ci < 5 {
        let c: i64 = coins[ci]
        let mut i: i64 = c
        while i <= m {
            dp[i] = dp[i] + dp[i - c]
            i = i + 1
        }
        ci = ci + 1
    }
    let ans: i64 = dp[m]
    free(coins)
    free(dp)
    return ans
}

function main() -> i32 {
    printf("%lld\n", H(55106))
    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 H_i64(int64_t n);
int32_t main(void);



int64_t H_i64(int64_t n) {
    int64_t m = (n - 6);
    if (m < 0) {
        return 0;
    }
    int64_t* dp = (int64_t*)(calloc((m + 1), 8));
    if (dp == NULL) {
        return (-1);
    }
    dp[0] = 1;
    int64_t* coins = (int64_t*)(calloc(5, 8));
    coins[0] = 1;
    coins[1] = 2;
    coins[2] = 3;
    coins[3] = 4;
    coins[4] = 6;
    int64_t ci = 0;
    while (ci < 5) {
        int64_t c = coins[ci];
        int64_t i = c;
        while (i <= m) {
            dp[i] = (dp[i] + dp[(i - c)]);
            i = (i + 1);
        }
        ci = (ci + 1);
    }
    int64_t ans = dp[m];
    free(coins);
    free(dp);
    return ans;
}

int32_t main(void) {
    printf("%lld\n", H_i64(55106));
    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) -> ()
  func.func @H(%arg0: i64) -> i64 {
    %0 = arith.constant 6 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.subi %arg0, %2 : i64
    %3 = arith.constant 0 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.cmpi slt, %1, %5 : i64
    cf.cond_br %4, ^bb0, ^bb1
    ^bb0:
      %6 = arith.constant 0 : i32
      %7 = arith.extsi %6 : i32 to i64
      func.return %7 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %9 = arith.constant 1 : i32
    %11 = arith.extsi %9 : i32 to i64
    %10 = arith.addi %1, %11 : i64
    %12 = arith.constant 8 : i32
    %13 = arith.extsi %12 : i32 to i64
    %8 = func.call @calloc(%10, %13) : (i64, i64) -> !llvm.ptr
    %14 = llvm.mlir.zero : !llvm.ptr
    %15 = llvm.icmp "eq" %8, %14 : !llvm.ptr
    cf.cond_br %15, ^bb3, ^bb4
    ^bb3:
      %16 = arith.constant 1 : i32
      %18 = arith.constant 0 : i32
      %17 = arith.subi %18, %16 : i32
      %19 = arith.extsi %17 : i32 to i64
      func.return %19 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %20 = arith.constant 1 : i32
    %21 = arith.constant 0 : i32
    %22 = arith.extsi %20 : i32 to i64
    %23 = arith.extsi %21 : i32 to i64
    %24 = llvm.getelementptr %8[%23] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %22, %24 : i64, !llvm.ptr
    %26 = arith.constant 5 : i32
    %27 = arith.constant 8 : i32
    %28 = arith.extsi %26 : i32 to i64
    %29 = arith.extsi %27 : i32 to i64
    %25 = func.call @calloc(%28, %29) : (i64, i64) -> !llvm.ptr
    %30 = arith.constant 1 : i32
    %31 = arith.constant 0 : i32
    %32 = arith.extsi %30 : i32 to i64
    %33 = arith.extsi %31 : i32 to i64
    %34 = llvm.getelementptr %25[%33] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %32, %34 : i64, !llvm.ptr
    %35 = arith.constant 2 : i32
    %36 = arith.constant 1 : i32
    %37 = arith.extsi %35 : i32 to i64
    %38 = arith.extsi %36 : i32 to i64
    %39 = llvm.getelementptr %25[%38] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %37, %39 : i64, !llvm.ptr
    %40 = arith.constant 3 : i32
    %41 = arith.constant 2 : i32
    %42 = arith.extsi %40 : i32 to i64
    %43 = arith.extsi %41 : i32 to i64
    %44 = llvm.getelementptr %25[%43] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %42, %44 : i64, !llvm.ptr
    %45 = arith.constant 4 : i32
    %46 = arith.constant 3 : i32
    %47 = arith.extsi %45 : i32 to i64
    %48 = arith.extsi %46 : i32 to i64
    %49 = llvm.getelementptr %25[%48] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %47, %49 : i64, !llvm.ptr
    %50 = arith.constant 6 : i32
    %51 = arith.constant 4 : i32
    %52 = arith.extsi %50 : i32 to i64
    %53 = arith.extsi %51 : i32 to i64
    %54 = llvm.getelementptr %25[%53] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %52, %54 : i64, !llvm.ptr
    %55 = arith.constant 0 : i32
    %56 = arith.extsi %55 : i32 to i64
    %57 = llvm.mlir.constant(1 : i64) : i64
    %58 = llvm.alloca %57 x i64 : (i64) -> !llvm.ptr
    llvm.store %56, %58 : i64, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %59 = llvm.load %58 : !llvm.ptr -> i64
    %60 = arith.constant 5 : i32
    %62 = arith.extsi %60 : i32 to i64
    %61 = arith.cmpi slt, %59, %62 : i64
    cf.cond_br %61, ^bb7, ^bb8
    ^bb7:
      %64 = llvm.load %58 : !llvm.ptr -> i64
      %65 = llvm.getelementptr %25[%64] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %63 = llvm.load %65 : !llvm.ptr -> i64
      %66 = llvm.mlir.constant(1 : i64) : i64
      %67 = llvm.alloca %66 x i64 : (i64) -> !llvm.ptr
      llvm.store %63, %67 : i64, !llvm.ptr
      cf.br ^bb9
      ^bb9:
      %68 = llvm.load %67 : !llvm.ptr -> i64
      %69 = arith.cmpi sle, %68, %1 : i64
      cf.cond_br %69, ^bb10, ^bb11
      ^bb10:
        %71 = llvm.load %67 : !llvm.ptr -> i64
        %72 = llvm.getelementptr %8[%71] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %70 = llvm.load %72 : !llvm.ptr -> i64
        %74 = llvm.load %67 : !llvm.ptr -> i64
        %75 = arith.subi %74, %63 : i64
        %76 = llvm.getelementptr %8[%75] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %73 = llvm.load %76 : !llvm.ptr -> i64
        %77 = arith.addi %70, %73 : i64
        %78 = llvm.load %67 : !llvm.ptr -> i64
        %79 = llvm.getelementptr %8[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        llvm.store %77, %79 : i64, !llvm.ptr
        %80 = llvm.load %67 : !llvm.ptr -> i64
        %81 = arith.constant 1 : i32
        %83 = arith.extsi %81 : i32 to i64
        %82 = arith.addi %80, %83 : i64
        llvm.store %82, %67 : i64, !llvm.ptr
        cf.br ^bb9
      ^bb11:
      %84 = llvm.load %58 : !llvm.ptr -> i64
      %85 = arith.constant 1 : i32
      %87 = arith.extsi %85 : i32 to i64
      %86 = arith.addi %84, %87 : i64
      llvm.store %86, %58 : i64, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %89 = llvm.getelementptr %8[%1] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %88 = llvm.load %89 : !llvm.ptr -> i64
    func.call @free(%25) : (!llvm.ptr) -> ()
    func.call @free(%8) : (!llvm.ptr) -> ()
    func.return %88 : i64
  }
  func.func @main() -> i32 {
    %92 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %94 = arith.constant 55106 : i32
    %95 = arith.extsi %94 : i32 to i64
    %93 = func.call @H(%95) : (i64) -> i64
    %96 = llvm.call @printf(%92, %93) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %97 = arith.constant 0 : i32
    func.return %97 : i32
  }
}