Problem 122

Sum of m(k) for 1≤k≤200 — minimal multiplication-chain length to reach k.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 122
# Sum of m(k) for 1≤k≤200 — minimal multiplication-chain length to reach k.

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

function dfs(chain: ptr<i32>, len: i32, depth: i32, limit: i32, best: ptr<i32>) -> void {
    let cur: i32 = chain[len - 1]
    if depth > best[cur] {
        return
    }
    best[cur] = depth
    let mut i: i32 = len - 1
    while i >= 0 {
        let nxt: i32 = cur + chain[i]
        if nxt <= limit {
            if depth + 1 <= best[nxt] {
                chain[len] = nxt
                dfs(chain, len + 1, depth + 1, limit, best)
            }
        }
        i = i - 1
    }
}

function main() -> i32 {
    let limit: i32 = 200
    let best: ptr<i32> = calloc((limit + 1) as i64, 4)
    let chain: ptr<i32> = calloc(64, 4)
    if best == null || chain == null { return 1 }
    let mut i: i32 = 0
    while i <= limit {
        best[i] = 999
        i = i + 1
    }
    chain[0] = 1
    dfs(chain, 1, 0, limit, best)
    let mut total: i64 = 0
    i = 1
    while i <= limit {
        total = total + (best[i] as i64)
        i = i + 1
    }
    printf("%lld\n", total)
    free(chain)
    free(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; }

void dfs_ptr_i32_i32_i32_i32_ptr_i32(int32_t* chain, int32_t len, int32_t depth, int32_t limit, int32_t* best);
int32_t main(void);



void dfs_ptr_i32_i32_i32_i32_ptr_i32(int32_t* chain, int32_t len, int32_t depth, int32_t limit, int32_t* best) {
    int32_t cur = chain[(len - 1)];
    if (depth > best[cur]) {
        return;
    }
    best[cur] = depth;
    int32_t i = (len - 1);
    while (i >= 0) {
        int32_t nxt = (cur + chain[i]);
        if (nxt <= limit) {
            if ((depth + 1) <= best[nxt]) {
                chain[len] = nxt;
                dfs_ptr_i32_i32_i32_i32_ptr_i32(chain, (len + 1), (depth + 1), limit, best);
            }
        }
        i = (i - 1);
    }
}

int32_t main(void) {
    int32_t limit = 200;
    int32_t* best = (int32_t*)(calloc(((int64_t)((limit + 1))), 4));
    int32_t* chain = (int32_t*)(calloc(64, 4));
    if ((best == NULL || chain == NULL)) {
        return 1;
    }
    int32_t i = 0;
    while (i <= limit) {
        best[i] = 999;
        i = (i + 1);
    }
    chain[0] = 1;
    dfs_ptr_i32_i32_i32_i32_ptr_i32(chain, 1, 0, limit, best);
    int64_t total = 0;
    i = 1;
    while (i <= limit) {
        total = (total + ((int64_t)(best[i])));
        i = (i + 1);
    }
    printf("%lld\n", total);
    free(chain);
    free(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 private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @dfs(%arg0: !llvm.ptr, %arg1: i32, %arg2: i32, %arg3: i32, %arg4: !llvm.ptr) -> () {
    %1 = arith.constant 1 : i32
    %2 = arith.subi %arg1, %1 : i32
    %3 = arith.extsi %2 : i32 to i64
    %4 = llvm.getelementptr %arg0[%3] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    %0 = llvm.load %4 : !llvm.ptr -> i32
    %6 = arith.extsi %0 : i32 to i64
    %7 = llvm.getelementptr %arg4[%6] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    %5 = llvm.load %7 : !llvm.ptr -> i32
    %8 = arith.cmpi sgt, %arg2, %5 : i32
    cf.cond_br %8, ^bb0, ^bb1
    ^bb0:
      func.return
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %9 = arith.extsi %0 : i32 to i64
    %10 = llvm.getelementptr %arg4[%9] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    llvm.store %arg2, %10 : i32, !llvm.ptr
    %11 = arith.constant 1 : i32
    %12 = arith.subi %arg1, %11 : i32
    %13 = llvm.mlir.constant(1 : i64) : i64
    %14 = llvm.alloca %13 x i32 : (i64) -> !llvm.ptr
    llvm.store %12, %14 : i32, !llvm.ptr
    cf.br ^bb3
    ^bb3:
    %15 = llvm.load %14 : !llvm.ptr -> i32
    %16 = arith.constant 0 : i32
    %17 = arith.cmpi sge, %15, %16 : i32
    cf.cond_br %17, ^bb4, ^bb5
    ^bb4:
      %19 = llvm.load %14 : !llvm.ptr -> i32
      %20 = arith.extsi %19 : i32 to i64
      %21 = llvm.getelementptr %arg0[%20] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %18 = llvm.load %21 : !llvm.ptr -> i32
      %22 = arith.addi %0, %18 : i32
      %23 = arith.cmpi sle, %22, %arg3 : i32
      cf.cond_br %23, ^bb6, ^bb7
      ^bb6:
        %24 = arith.constant 1 : i32
        %25 = arith.addi %arg2, %24 : i32
        %27 = arith.extsi %22 : i32 to i64
        %28 = llvm.getelementptr %arg4[%27] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %26 = llvm.load %28 : !llvm.ptr -> i32
        %29 = arith.cmpi sle, %25, %26 : i32
        cf.cond_br %29, ^bb9, ^bb10
        ^bb9:
          %30 = arith.extsi %arg1 : i32 to i64
          %31 = llvm.getelementptr %arg0[%30] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %22, %31 : i32, !llvm.ptr
          %33 = arith.constant 1 : i32
          %34 = arith.addi %arg1, %33 : i32
          %35 = arith.constant 1 : i32
          %36 = arith.addi %arg2, %35 : i32
          func.call @dfs(%arg0, %34, %36, %arg3, %arg4) : (!llvm.ptr, i32, i32, i32, !llvm.ptr) -> ()
          cf.br ^bb11
        ^bb10:
          cf.br ^bb11
        ^bb11:
        cf.br ^bb8
      ^bb7:
        cf.br ^bb8
      ^bb8:
      %37 = llvm.load %14 : !llvm.ptr -> i32
      %38 = arith.constant 1 : i32
      %39 = arith.subi %37, %38 : i32
      llvm.store %39, %14 : i32, !llvm.ptr
      cf.br ^bb3
    ^bb5:
    func.return
  }
  func.func @main() -> i32 {
    %40 = arith.constant 200 : i32
    %42 = arith.constant 1 : i32
    %43 = arith.addi %40, %42 : i32
    %44 = arith.extsi %43 : i32 to i64
    %45 = arith.constant 4 : i32
    %46 = arith.extsi %45 : i32 to i64
    %41 = func.call @calloc(%44, %46) : (i64, i64) -> !llvm.ptr
    %48 = arith.constant 64 : i32
    %49 = arith.constant 4 : i32
    %50 = arith.extsi %48 : i32 to i64
    %51 = arith.extsi %49 : i32 to i64
    %47 = func.call @calloc(%50, %51) : (i64, i64) -> !llvm.ptr
    %52 = llvm.mlir.zero : !llvm.ptr
    %53 = llvm.icmp "eq" %41, %52 : !llvm.ptr
    %54 = scf.if %53 -> (i1) {
      %55 = arith.constant true
      scf.yield %55 : i1
    } else {
      %56 = llvm.mlir.zero : !llvm.ptr
      %57 = llvm.icmp "eq" %47, %56 : !llvm.ptr
      scf.yield %57 : i1
    }
    cf.cond_br %54, ^bb12, ^bb13
    ^bb12:
      %58 = arith.constant 1 : i32
      func.return %58 : i32
    ^bb13:
      cf.br ^bb14
    ^bb14:
    %59 = arith.constant 0 : i32
    %60 = llvm.mlir.constant(1 : i64) : i64
    %61 = llvm.alloca %60 x i32 : (i64) -> !llvm.ptr
    llvm.store %59, %61 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %62 = llvm.load %61 : !llvm.ptr -> i32
    %63 = arith.cmpi sle, %62, %40 : i32
    cf.cond_br %63, ^bb16, ^bb17
    ^bb16:
      %64 = arith.constant 999 : i32
      %65 = llvm.load %61 : !llvm.ptr -> i32
      %66 = arith.extsi %65 : i32 to i64
      %67 = llvm.getelementptr %41[%66] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %64, %67 : i32, !llvm.ptr
      %68 = llvm.load %61 : !llvm.ptr -> i32
      %69 = arith.constant 1 : i32
      %70 = arith.addi %68, %69 : i32
      llvm.store %70, %61 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %71 = arith.constant 1 : i32
    %72 = arith.constant 0 : i32
    %73 = arith.extsi %72 : i32 to i64
    %74 = llvm.getelementptr %47[%73] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    llvm.store %71, %74 : i32, !llvm.ptr
    %76 = arith.constant 1 : i32
    %77 = arith.constant 0 : i32
    func.call @dfs(%47, %76, %77, %40, %41) : (!llvm.ptr, i32, i32, i32, !llvm.ptr) -> ()
    %78 = arith.constant 0 : i32
    %79 = arith.extsi %78 : i32 to i64
    %80 = llvm.mlir.constant(1 : i64) : i64
    %81 = llvm.alloca %80 x i64 : (i64) -> !llvm.ptr
    llvm.store %79, %81 : i64, !llvm.ptr
    %82 = arith.constant 1 : i32
    llvm.store %82, %61 : i32, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %83 = llvm.load %61 : !llvm.ptr -> i32
    %84 = arith.cmpi sle, %83, %40 : i32
    cf.cond_br %84, ^bb19, ^bb20
    ^bb19:
      %85 = llvm.load %81 : !llvm.ptr -> i64
      %87 = llvm.load %61 : !llvm.ptr -> i32
      %88 = arith.extsi %87 : i32 to i64
      %89 = llvm.getelementptr %41[%88] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %86 = llvm.load %89 : !llvm.ptr -> i32
      %90 = arith.extsi %86 : i32 to i64
      %91 = arith.addi %85, %90 : i64
      llvm.store %91, %81 : i64, !llvm.ptr
      %92 = llvm.load %61 : !llvm.ptr -> i32
      %93 = arith.constant 1 : i32
      %94 = arith.addi %92, %93 : i32
      llvm.store %94, %61 : i32, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %95 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %96 = llvm.load %81 : !llvm.ptr -> i64
    %97 = llvm.call @printf(%95, %96) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%47) : (!llvm.ptr) -> ()
    func.call @free(%41) : (!llvm.ptr) -> ()
    %100 = arith.constant 0 : i32
    func.return %100 : i32
  }
}