Problem 951

Count length 2n strings with n R, n B and no maximal run of length 2. Answer = C(2n,n) - count_balanced_no_run2(n) for n=26.

Answer495568995495726
Output495568995495726
StatusPASS
Native helperno
Runtime0 ms
Peak memory1072 KB
Time complexityO(1) (estimated)
Space complexityO(n) (estimated)

Performance comparison

MetricOur solutionBest known
Time complexityO(1)?
Space complexityO(n)?
ApproachFlow solutionNot curated
VerdictUnknown

Flow source

# Project Euler 951: Unique Subsets
# Count length 2n strings with n R, n B and no maximal run of length 2.
# Answer = C(2n,n) - count_balanced_no_run2(n) for n=26.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function memset(dst: ptr<void>, val: i32, n: i64) -> void
}

function comb(n: i32, k0: i32) -> i64 {
    if k0 < 0 || k0 > n { return 0 }
    let mut k: i32 = k0
    if k > n - k { k = n - k }
    let mut result: i64 = 1
    let mut i: i32 = 0
    while i < k {
        result = result * (n - i) as i64 / (i + 1) as i64
        i = i + 1
    }
    return result
}

function idx(r: i32, last: i32, rs: i32) -> i64 {
    return (r as i64) * 6 + (last as i64) * 3 + (rs as i64)
}

function count_balanced_no_run2(n: i32) -> i64 {
    if n <= 0 {
        if n == 0 { return 1 }
        return 0
    }
    let L: i32 = 2 * n
    let R: i32 = n + 1
    let sz: i64 = (R as i64) * 6
    let mut dp: ptr<i64> = calloc(sz, 8)
    let mut nw: ptr<i64> = calloc(sz, 8)

    dp[idx(1, 0, 0)] = 1
    dp[idx(0, 1, 0)] = 1

    let mut pos: i32 = 1
    while pos < L {
        memset(nw as ptr<void>, 0, sz * 8)
        let mut r: i32 = 0
        while r <= n {
            let b: i32 = pos - r
            if b < 0 || b > n {
                r = r + 1
                continue
            }
            let mut last: i32 = 0
            while last < 2 {
                let mut rs: i32 = 0
                while rs < 3 {
                    let val: i64 = dp[idx(r, last, rs)]
                    if val != 0 {
                        let rscat: i32 = rs + 1

                        if r + 1 <= n {
                            if last == 0 {
                                let mut nrs: i32 = rscat + 1
                                if rscat >= 3 { nrs = 3 }
                                nw[idx(r + 1, 0, nrs - 1)] = nw[idx(r + 1, 0, nrs - 1)] + val
                            } else {
                                if rscat != 2 {
                                    nw[idx(r + 1, 0, 0)] = nw[idx(r + 1, 0, 0)] + val
                                }
                            }
                        }
                        if b + 1 <= n {
                            if last == 1 {
                                let mut nrs: i32 = rscat + 1
                                if rscat >= 3 { nrs = 3 }
                                nw[idx(r, 1, nrs - 1)] = nw[idx(r, 1, nrs - 1)] + val
                            } else {
                                if rscat != 2 {
                                    nw[idx(r, 1, 0)] = nw[idx(r, 1, 0)] + val
                                }
                            }
                        }
                    }
                    rs = rs + 1
                }
                last = last + 1
            }
            r = r + 1
        }
        let tmp: ptr<i64> = dp
        dp = nw
        nw = tmp
        pos = pos + 1
    }

    let mut total: i64 = 0
    let mut last: i32 = 0
    while last < 2 {
        total = total + dp[idx(n, last, 0)]
        total = total + dp[idx(n, last, 2)]
        last = last + 1
    }
    free(dp)
    free(nw)
    return total
}

function main() -> i32 {
    let n: i32 = 26
    let total: i64 = comb(2 * n, n)
    let unfair: i64 = count_balanced_no_run2(n)
    printf("%lld\n", total - unfair)
    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 comb_i32_i32(int32_t n, int32_t k0);
int64_t idx_i32_i32_i32(int32_t r, int32_t last, int32_t rs);
int64_t count_balanced_no_run2_i32(int32_t n);
int32_t main(void);




int64_t comb_i32_i32(int32_t n, int32_t k0) {
    if ((k0 < 0 || k0 > n)) {
        return 0;
    }
    int32_t k = k0;
    if (k > (n - k)) {
        k = (n - k);
    }
    int64_t result = 1;
    int32_t i = 0;
    while (i < k) {
        result = FLOW_CHECKED_DIV(((result * ((int64_t)((n - i))))), (((int64_t)((i + 1)))));
        i = (i + 1);
    }
    return result;
}

int64_t idx_i32_i32_i32(int32_t r, int32_t last, int32_t rs) {
    return (((((int64_t)(r)) * 6) + (((int64_t)(last)) * 3)) + ((int64_t)(rs)));
}

int64_t count_balanced_no_run2_i32(int32_t n) {
    if (n <= 0) {
        if (n == 0) {
            return 1;
        }
        return 0;
    }
    int32_t L = (2 * n);
    int32_t R = (n + 1);
    int64_t sz = (((int64_t)(R)) * 6);
    int64_t* dp = (int64_t*)(calloc(sz, 8));
    int64_t* nw = (int64_t*)(calloc(sz, 8));
    dp[idx_i32_i32_i32(1, 0, 0)] = 1;
    dp[idx_i32_i32_i32(0, 1, 0)] = 1;
    int32_t pos = 1;
    while (pos < L) {
        memset(((void*)(nw)), 0, (sz * 8));
        int32_t r = 0;
        while (r <= n) {
            int32_t b = (pos - r);
            if ((b < 0 || b > n)) {
                r = (r + 1);
                continue;
            }
            int32_t last = 0;
            while (last < 2) {
                int32_t rs = 0;
                while (rs < 3) {
                    int64_t val = dp[idx_i32_i32_i32(r, last, rs)];
                    if (val != 0) {
                        int32_t rscat = (rs + 1);
                        if ((r + 1) <= n) {
                            if (last == 0) {
                                int32_t nrs = (rscat + 1);
                                if (rscat >= 3) {
                                    nrs = 3;
                                }
                                nw[idx_i32_i32_i32((r + 1), 0, (nrs - 1))] = (nw[idx_i32_i32_i32((r + 1), 0, (nrs - 1))] + val);
                            } else {
                                if (rscat != 2) {
                                    nw[idx_i32_i32_i32((r + 1), 0, 0)] = (nw[idx_i32_i32_i32((r + 1), 0, 0)] + val);
                                }
                            }
                        }
                        if ((b + 1) <= n) {
                            if (last == 1) {
                                int32_t nrs = (rscat + 1);
                                if (rscat >= 3) {
                                    nrs = 3;
                                }
                                nw[idx_i32_i32_i32(r, 1, (nrs - 1))] = (nw[idx_i32_i32_i32(r, 1, (nrs - 1))] + val);
                            } else {
                                if (rscat != 2) {
                                    nw[idx_i32_i32_i32(r, 1, 0)] = (nw[idx_i32_i32_i32(r, 1, 0)] + val);
                                }
                            }
                        }
                    }
                    rs = (rs + 1);
                }
                last = (last + 1);
            }
            r = (r + 1);
        }
        int64_t* tmp = (int64_t*)(dp);
        dp = nw;
        nw = tmp;
        pos = (pos + 1);
    }
    int64_t total = 0;
    int32_t last = 0;
    while (last < 2) {
        total = (total + dp[idx_i32_i32_i32(n, last, 0)]);
        total = (total + dp[idx_i32_i32_i32(n, last, 2)]);
        last = (last + 1);
    }
    free(dp);
    free(nw);
    return total;
}

int32_t main(void) {
    int32_t n = 26;
    int64_t total = comb_i32_i32((2 * n), n);
    int64_t unfair = count_balanced_no_run2_i32(n);
    printf("%lld\n", (total - unfair));
    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 private @memset(!llvm.ptr, i32, i64) -> ()
  func.func @comb(%arg0: i32, %arg1: i32) -> i64 {
    %0 = arith.constant 0 : i32
    %1 = arith.cmpi slt, %arg1, %0 : i32
    %2 = scf.if %1 -> (i1) {
      %3 = arith.constant true
      scf.yield %3 : i1
    } else {
      %4 = arith.cmpi sgt, %arg1, %arg0 : i32
      scf.yield %4 : i1
    }
    cf.cond_br %2, ^bb0, ^bb1
    ^bb0:
      %5 = arith.constant 0 : i32
      %6 = arith.extsi %5 : i32 to i64
      func.return %6 : i64
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i32 : (i64) -> !llvm.ptr
    llvm.store %arg1, %8 : i32, !llvm.ptr
    %9 = llvm.load %8 : !llvm.ptr -> i32
    %10 = llvm.load %8 : !llvm.ptr -> i32
    %11 = arith.subi %arg0, %10 : i32
    %12 = arith.cmpi sgt, %9, %11 : i32
    cf.cond_br %12, ^bb3, ^bb4
    ^bb3:
      %13 = llvm.load %8 : !llvm.ptr -> i32
      %14 = arith.subi %arg0, %13 : i32
      llvm.store %14, %8 : i32, !llvm.ptr
      cf.br ^bb5
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %15 = arith.constant 1 : i32
    %16 = arith.extsi %15 : i32 to i64
    %17 = llvm.mlir.constant(1 : i64) : i64
    %18 = llvm.alloca %17 x i64 : (i64) -> !llvm.ptr
    llvm.store %16, %18 : i64, !llvm.ptr
    %19 = arith.constant 0 : i32
    %20 = llvm.mlir.constant(1 : i64) : i64
    %21 = llvm.alloca %20 x i32 : (i64) -> !llvm.ptr
    llvm.store %19, %21 : i32, !llvm.ptr
    cf.br ^bb6
    ^bb6:
    %22 = llvm.load %21 : !llvm.ptr -> i32
    %23 = llvm.load %8 : !llvm.ptr -> i32
    %24 = arith.cmpi slt, %22, %23 : i32
    cf.cond_br %24, ^bb7, ^bb8
    ^bb7:
      %25 = llvm.load %18 : !llvm.ptr -> i64
      %26 = llvm.load %21 : !llvm.ptr -> i32
      %27 = arith.subi %arg0, %26 : i32
      %28 = arith.extsi %27 : i32 to i64
      %29 = arith.muli %25, %28 : i64
      %30 = llvm.load %21 : !llvm.ptr -> i32
      %31 = arith.constant 1 : i32
      %32 = arith.addi %30, %31 : i32
      %33 = arith.extsi %32 : i32 to i64
      %34 = arith.divsi %29, %33 : i64
      llvm.store %34, %18 : i64, !llvm.ptr
      %35 = llvm.load %21 : !llvm.ptr -> i32
      %36 = arith.constant 1 : i32
      %37 = arith.addi %35, %36 : i32
      llvm.store %37, %21 : i32, !llvm.ptr
      cf.br ^bb6
    ^bb8:
    %38 = llvm.load %18 : !llvm.ptr -> i64
    func.return %38 : i64
  }
  func.func @idx(%arg0: i32, %arg1: i32, %arg2: i32) -> i64 {
    %39 = arith.extsi %arg0 : i32 to i64
    %40 = arith.constant 6 : i32
    %42 = arith.extsi %40 : i32 to i64
    %41 = arith.muli %39, %42 : i64
    %43 = arith.extsi %arg1 : i32 to i64
    %44 = arith.constant 3 : i32
    %46 = arith.extsi %44 : i32 to i64
    %45 = arith.muli %43, %46 : i64
    %47 = arith.addi %41, %45 : i64
    %48 = arith.extsi %arg2 : i32 to i64
    %49 = arith.addi %47, %48 : i64
    func.return %49 : i64
  }
  func.func @count_balanced_no_run2(%arg0: i32) -> i64 {
    %50 = arith.constant 0 : i32
    %51 = arith.cmpi sle, %arg0, %50 : i32
    cf.cond_br %51, ^bb9, ^bb10
    ^bb9:
      %52 = arith.constant 0 : i32
      %53 = arith.cmpi eq, %arg0, %52 : i32
      cf.cond_br %53, ^bb12, ^bb13
      ^bb12:
        %54 = arith.constant 1 : i32
        %55 = arith.extsi %54 : i32 to i64
        func.return %55 : i64
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %56 = arith.constant 0 : i32
      %57 = arith.extsi %56 : i32 to i64
      func.return %57 : i64
    ^bb10:
      cf.br ^bb11
    ^bb11:
    %58 = arith.constant 2 : i32
    %59 = arith.muli %58, %arg0 : i32
    %60 = arith.constant 1 : i32
    %61 = arith.addi %arg0, %60 : i32
    %62 = arith.extsi %61 : i32 to i64
    %63 = arith.constant 6 : i32
    %65 = arith.extsi %63 : i32 to i64
    %64 = arith.muli %62, %65 : i64
    %67 = arith.constant 8 : i32
    %68 = arith.extsi %67 : i32 to i64
    %66 = func.call @calloc(%64, %68) : (i64, i64) -> !llvm.ptr
    %69 = llvm.mlir.constant(1 : i64) : i64
    %70 = llvm.alloca %69 x !llvm.ptr : (i64) -> !llvm.ptr
    llvm.store %66, %70 : !llvm.ptr, !llvm.ptr
    %72 = arith.constant 8 : i32
    %73 = arith.extsi %72 : i32 to i64
    %71 = func.call @calloc(%64, %73) : (i64, i64) -> !llvm.ptr
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x !llvm.ptr : (i64) -> !llvm.ptr
    llvm.store %71, %75 : !llvm.ptr, !llvm.ptr
    %76 = arith.constant 1 : i32
    %77 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
    %79 = arith.constant 1 : i32
    %80 = arith.constant 0 : i32
    %81 = arith.constant 0 : i32
    %78 = func.call @idx(%79, %80, %81) : (i32, i32, i32) -> i64
    %82 = arith.extsi %76 : i32 to i64
    %83 = llvm.getelementptr %77[%78] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %82, %83 : i64, !llvm.ptr
    %84 = arith.constant 1 : i32
    %85 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
    %87 = arith.constant 0 : i32
    %88 = arith.constant 1 : i32
    %89 = arith.constant 0 : i32
    %86 = func.call @idx(%87, %88, %89) : (i32, i32, i32) -> i64
    %90 = arith.extsi %84 : i32 to i64
    %91 = llvm.getelementptr %85[%86] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %90, %91 : i64, !llvm.ptr
    %92 = arith.constant 1 : i32
    %93 = llvm.mlir.constant(1 : i64) : i64
    %94 = llvm.alloca %93 x i32 : (i64) -> !llvm.ptr
    llvm.store %92, %94 : i32, !llvm.ptr
    cf.br ^bb15
    ^bb15:
    %95 = llvm.load %94 : !llvm.ptr -> i32
    %96 = arith.cmpi slt, %95, %59 : i32
    cf.cond_br %96, ^bb16, ^bb17
    ^bb16:
      %98 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
      %99 = arith.constant 0 : i32
      %100 = arith.constant 8 : i32
      %102 = arith.extsi %100 : i32 to i64
      %101 = arith.muli %64, %102 : i64
      func.call @memset(%98, %99, %101) : (!llvm.ptr, i32, i64) -> ()
      %103 = arith.constant 0 : i32
      %104 = llvm.mlir.constant(1 : i64) : i64
      %105 = llvm.alloca %104 x i32 : (i64) -> !llvm.ptr
      llvm.store %103, %105 : i32, !llvm.ptr
      cf.br ^bb18
      ^bb18:
      %106 = llvm.load %105 : !llvm.ptr -> i32
      %107 = arith.cmpi sle, %106, %arg0 : i32
      cf.cond_br %107, ^bb19, ^bb20
      ^bb19:
        %108 = llvm.load %94 : !llvm.ptr -> i32
        %109 = llvm.load %105 : !llvm.ptr -> i32
        %110 = arith.subi %108, %109 : i32
        %111 = arith.constant 0 : i32
        %112 = arith.cmpi slt, %110, %111 : i32
        %113 = scf.if %112 -> (i1) {
          %114 = arith.constant true
          scf.yield %114 : i1
        } else {
          %115 = arith.cmpi sgt, %110, %arg0 : i32
          scf.yield %115 : i1
        }
        cf.cond_br %113, ^bb21, ^bb22
        ^bb21:
          %116 = llvm.load %105 : !llvm.ptr -> i32
          %117 = arith.constant 1 : i32
          %118 = arith.addi %116, %117 : i32
          llvm.store %118, %105 : i32, !llvm.ptr
          cf.br ^bb18
        ^bb22:
          cf.br ^bb23
        ^bb23:
        %119 = arith.constant 0 : i32
        %120 = llvm.mlir.constant(1 : i64) : i64
        %121 = llvm.alloca %120 x i32 : (i64) -> !llvm.ptr
        llvm.store %119, %121 : i32, !llvm.ptr
        cf.br ^bb24
        ^bb24:
        %122 = llvm.load %121 : !llvm.ptr -> i32
        %123 = arith.constant 2 : i32
        %124 = arith.cmpi slt, %122, %123 : i32
        cf.cond_br %124, ^bb25, ^bb26
        ^bb25:
          %125 = arith.constant 0 : i32
          %126 = llvm.mlir.constant(1 : i64) : i64
          %127 = llvm.alloca %126 x i32 : (i64) -> !llvm.ptr
          llvm.store %125, %127 : i32, !llvm.ptr
          cf.br ^bb27
          ^bb27:
          %128 = llvm.load %127 : !llvm.ptr -> i32
          %129 = arith.constant 3 : i32
          %130 = arith.cmpi slt, %128, %129 : i32
          cf.cond_br %130, ^bb28, ^bb29
          ^bb28:
            %132 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
            %134 = llvm.load %105 : !llvm.ptr -> i32
            %135 = llvm.load %121 : !llvm.ptr -> i32
            %136 = llvm.load %127 : !llvm.ptr -> i32
            %133 = func.call @idx(%134, %135, %136) : (i32, i32, i32) -> i64
            %137 = llvm.getelementptr %132[%133] : (!llvm.ptr, i64) -> !llvm.ptr, i64
            %131 = llvm.load %137 : !llvm.ptr -> i64
            %138 = arith.constant 0 : i32
            %140 = arith.extsi %138 : i32 to i64
            %139 = arith.cmpi ne, %131, %140 : i64
            cf.cond_br %139, ^bb30, ^bb31
            ^bb30:
              %141 = llvm.load %127 : !llvm.ptr -> i32
              %142 = arith.constant 1 : i32
              %143 = arith.addi %141, %142 : i32
              %144 = llvm.load %105 : !llvm.ptr -> i32
              %145 = arith.constant 1 : i32
              %146 = arith.addi %144, %145 : i32
              %147 = arith.cmpi sle, %146, %arg0 : i32
              cf.cond_br %147, ^bb33, ^bb34
              ^bb33:
                %148 = llvm.load %121 : !llvm.ptr -> i32
                %149 = arith.constant 0 : i32
                %150 = arith.cmpi eq, %148, %149 : i32
                cf.cond_br %150, ^bb36, ^bb37
                ^bb36:
                  %151 = arith.constant 1 : i32
                  %152 = arith.addi %143, %151 : i32
                  %153 = llvm.mlir.constant(1 : i64) : i64
                  %154 = llvm.alloca %153 x i32 : (i64) -> !llvm.ptr
                  llvm.store %152, %154 : i32, !llvm.ptr
                  %155 = arith.constant 3 : i32
                  %156 = arith.cmpi sge, %143, %155 : i32
                  cf.cond_br %156, ^bb39, ^bb40
                  ^bb39:
                    %157 = arith.constant 3 : i32
                    llvm.store %157, %154 : i32, !llvm.ptr
                    cf.br ^bb41
                  ^bb40:
                    cf.br ^bb41
                  ^bb41:
                  %159 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                  %161 = llvm.load %105 : !llvm.ptr -> i32
                  %162 = arith.constant 1 : i32
                  %163 = arith.addi %161, %162 : i32
                  %164 = arith.constant 0 : i32
                  %165 = llvm.load %154 : !llvm.ptr -> i32
                  %166 = arith.constant 1 : i32
                  %167 = arith.subi %165, %166 : i32
                  %160 = func.call @idx(%163, %164, %167) : (i32, i32, i32) -> i64
                  %168 = llvm.getelementptr %159[%160] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                  %158 = llvm.load %168 : !llvm.ptr -> i64
                  %169 = arith.addi %158, %131 : i64
                  %170 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                  %172 = llvm.load %105 : !llvm.ptr -> i32
                  %173 = arith.constant 1 : i32
                  %174 = arith.addi %172, %173 : i32
                  %175 = arith.constant 0 : i32
                  %176 = llvm.load %154 : !llvm.ptr -> i32
                  %177 = arith.constant 1 : i32
                  %178 = arith.subi %176, %177 : i32
                  %171 = func.call @idx(%174, %175, %178) : (i32, i32, i32) -> i64
                  %179 = llvm.getelementptr %170[%171] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                  llvm.store %169, %179 : i64, !llvm.ptr
                  cf.br ^bb38
                ^bb37:
                  %180 = arith.constant 2 : i32
                  %181 = arith.cmpi ne, %143, %180 : i32
                  cf.cond_br %181, ^bb42, ^bb43
                  ^bb42:
                    %183 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                    %185 = llvm.load %105 : !llvm.ptr -> i32
                    %186 = arith.constant 1 : i32
                    %187 = arith.addi %185, %186 : i32
                    %188 = arith.constant 0 : i32
                    %189 = arith.constant 0 : i32
                    %184 = func.call @idx(%187, %188, %189) : (i32, i32, i32) -> i64
                    %190 = llvm.getelementptr %183[%184] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                    %182 = llvm.load %190 : !llvm.ptr -> i64
                    %191 = arith.addi %182, %131 : i64
                    %192 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                    %194 = llvm.load %105 : !llvm.ptr -> i32
                    %195 = arith.constant 1 : i32
                    %196 = arith.addi %194, %195 : i32
                    %197 = arith.constant 0 : i32
                    %198 = arith.constant 0 : i32
                    %193 = func.call @idx(%196, %197, %198) : (i32, i32, i32) -> i64
                    %199 = llvm.getelementptr %192[%193] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                    llvm.store %191, %199 : i64, !llvm.ptr
                    cf.br ^bb44
                  ^bb43:
                    cf.br ^bb44
                  ^bb44:
                  cf.br ^bb38
                ^bb38:
                cf.br ^bb35
              ^bb34:
                cf.br ^bb35
              ^bb35:
              %200 = arith.constant 1 : i32
              %201 = arith.addi %110, %200 : i32
              %202 = arith.cmpi sle, %201, %arg0 : i32
              cf.cond_br %202, ^bb45, ^bb46
              ^bb45:
                %203 = llvm.load %121 : !llvm.ptr -> i32
                %204 = arith.constant 1 : i32
                %205 = arith.cmpi eq, %203, %204 : i32
                cf.cond_br %205, ^bb48, ^bb49
                ^bb48:
                  %206 = arith.constant 1 : i32
                  %207 = arith.addi %143, %206 : i32
                  %208 = llvm.mlir.constant(1 : i64) : i64
                  %209 = llvm.alloca %208 x i32 : (i64) -> !llvm.ptr
                  llvm.store %207, %209 : i32, !llvm.ptr
                  %210 = arith.constant 3 : i32
                  %211 = arith.cmpi sge, %143, %210 : i32
                  cf.cond_br %211, ^bb51, ^bb52
                  ^bb51:
                    %212 = arith.constant 3 : i32
                    llvm.store %212, %209 : i32, !llvm.ptr
                    cf.br ^bb53
                  ^bb52:
                    cf.br ^bb53
                  ^bb53:
                  %214 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                  %216 = llvm.load %105 : !llvm.ptr -> i32
                  %217 = arith.constant 1 : i32
                  %218 = llvm.load %209 : !llvm.ptr -> i32
                  %219 = arith.constant 1 : i32
                  %220 = arith.subi %218, %219 : i32
                  %215 = func.call @idx(%216, %217, %220) : (i32, i32, i32) -> i64
                  %221 = llvm.getelementptr %214[%215] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                  %213 = llvm.load %221 : !llvm.ptr -> i64
                  %222 = arith.addi %213, %131 : i64
                  %223 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                  %225 = llvm.load %105 : !llvm.ptr -> i32
                  %226 = arith.constant 1 : i32
                  %227 = llvm.load %209 : !llvm.ptr -> i32
                  %228 = arith.constant 1 : i32
                  %229 = arith.subi %227, %228 : i32
                  %224 = func.call @idx(%225, %226, %229) : (i32, i32, i32) -> i64
                  %230 = llvm.getelementptr %223[%224] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                  llvm.store %222, %230 : i64, !llvm.ptr
                  cf.br ^bb50
                ^bb49:
                  %231 = arith.constant 2 : i32
                  %232 = arith.cmpi ne, %143, %231 : i32
                  cf.cond_br %232, ^bb54, ^bb55
                  ^bb54:
                    %234 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                    %236 = llvm.load %105 : !llvm.ptr -> i32
                    %237 = arith.constant 1 : i32
                    %238 = arith.constant 0 : i32
                    %235 = func.call @idx(%236, %237, %238) : (i32, i32, i32) -> i64
                    %239 = llvm.getelementptr %234[%235] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                    %233 = llvm.load %239 : !llvm.ptr -> i64
                    %240 = arith.addi %233, %131 : i64
                    %241 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
                    %243 = llvm.load %105 : !llvm.ptr -> i32
                    %244 = arith.constant 1 : i32
                    %245 = arith.constant 0 : i32
                    %242 = func.call @idx(%243, %244, %245) : (i32, i32, i32) -> i64
                    %246 = llvm.getelementptr %241[%242] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                    llvm.store %240, %246 : i64, !llvm.ptr
                    cf.br ^bb56
                  ^bb55:
                    cf.br ^bb56
                  ^bb56:
                  cf.br ^bb50
                ^bb50:
                cf.br ^bb47
              ^bb46:
                cf.br ^bb47
              ^bb47:
              cf.br ^bb32
            ^bb31:
              cf.br ^bb32
            ^bb32:
            %247 = llvm.load %127 : !llvm.ptr -> i32
            %248 = arith.constant 1 : i32
            %249 = arith.addi %247, %248 : i32
            llvm.store %249, %127 : i32, !llvm.ptr
            cf.br ^bb27
          ^bb29:
          %250 = llvm.load %121 : !llvm.ptr -> i32
          %251 = arith.constant 1 : i32
          %252 = arith.addi %250, %251 : i32
          llvm.store %252, %121 : i32, !llvm.ptr
          cf.br ^bb24
        ^bb26:
        %253 = llvm.load %105 : !llvm.ptr -> i32
        %254 = arith.constant 1 : i32
        %255 = arith.addi %253, %254 : i32
        llvm.store %255, %105 : i32, !llvm.ptr
        cf.br ^bb18
      ^bb20:
      %256 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
      %257 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
      llvm.store %257, %70 : !llvm.ptr, !llvm.ptr
      llvm.store %256, %75 : !llvm.ptr, !llvm.ptr
      %258 = llvm.load %94 : !llvm.ptr -> i32
      %259 = arith.constant 1 : i32
      %260 = arith.addi %258, %259 : i32
      llvm.store %260, %94 : i32, !llvm.ptr
      cf.br ^bb15
    ^bb17:
    %261 = arith.constant 0 : i32
    %262 = arith.extsi %261 : i32 to i64
    %263 = llvm.mlir.constant(1 : i64) : i64
    %264 = llvm.alloca %263 x i64 : (i64) -> !llvm.ptr
    llvm.store %262, %264 : i64, !llvm.ptr
    %265 = arith.constant 0 : i32
    %266 = llvm.mlir.constant(1 : i64) : i64
    %267 = llvm.alloca %266 x i32 : (i64) -> !llvm.ptr
    llvm.store %265, %267 : i32, !llvm.ptr
    cf.br ^bb57
    ^bb57:
    %268 = llvm.load %267 : !llvm.ptr -> i32
    %269 = arith.constant 2 : i32
    %270 = arith.cmpi slt, %268, %269 : i32
    cf.cond_br %270, ^bb58, ^bb59
    ^bb58:
      %271 = llvm.load %264 : !llvm.ptr -> i64
      %273 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
      %275 = llvm.load %267 : !llvm.ptr -> i32
      %276 = arith.constant 0 : i32
      %274 = func.call @idx(%arg0, %275, %276) : (i32, i32, i32) -> i64
      %277 = llvm.getelementptr %273[%274] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %272 = llvm.load %277 : !llvm.ptr -> i64
      %278 = arith.addi %271, %272 : i64
      llvm.store %278, %264 : i64, !llvm.ptr
      %279 = llvm.load %264 : !llvm.ptr -> i64
      %281 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
      %283 = llvm.load %267 : !llvm.ptr -> i32
      %284 = arith.constant 2 : i32
      %282 = func.call @idx(%arg0, %283, %284) : (i32, i32, i32) -> i64
      %285 = llvm.getelementptr %281[%282] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %280 = llvm.load %285 : !llvm.ptr -> i64
      %286 = arith.addi %279, %280 : i64
      llvm.store %286, %264 : i64, !llvm.ptr
      %287 = llvm.load %267 : !llvm.ptr -> i32
      %288 = arith.constant 1 : i32
      %289 = arith.addi %287, %288 : i32
      llvm.store %289, %267 : i32, !llvm.ptr
      cf.br ^bb57
    ^bb59:
    %291 = llvm.load %70 : !llvm.ptr -> !llvm.ptr
    func.call @free(%291) : (!llvm.ptr) -> ()
    %293 = llvm.load %75 : !llvm.ptr -> !llvm.ptr
    func.call @free(%293) : (!llvm.ptr) -> ()
    %294 = llvm.load %264 : !llvm.ptr -> i64
    func.return %294 : i64
  }
  func.func @main() -> i32 {
    %295 = arith.constant 26 : i32
    %297 = arith.constant 2 : i32
    %298 = arith.muli %297, %295 : i32
    %296 = func.call @comb(%298, %295) : (i32, i32) -> i64
    %299 = func.call @count_balanced_no_run2(%295) : (i32) -> i64
    %300 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %301 = arith.subi %296, %299 : i64
    %302 = llvm.call @printf(%300, %301) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %303 = arith.constant 0 : i32
    func.return %303 : i32
  }
}