Question

作为Haskell的新手，我正在尝试添加两个n位二进制整数。

以下是我用C ++编写的内容，用于展示我想要实现的内容。任何人都可以告诉我如何在Haskell中做到这一点吗？

#include <iostream>
#include <vector>
#include <deque>
using namespace std;
int main()
{
    vector<int> lhs{1,1,1,1}, rhs{1,0,1,1};

    //! 3 inputs -> 2 outputs
    deque<int> sum;
    int carry = 0;
    for( auto l = lhs.crbegin(), r = rhs.crbegin(); l != lhs.crend(); ++l, ++r)
    {
        int digit_sum = carry + *l + *r;
        sum.push_front(digit_sum%2);
        carry = digit_sum/2;
    }

    if(carry)
        sum.push_front(carry);

    for(auto b : sum)
        cout << b << " ";

    return 0;
}

输出：

1 1 0 1 0

下面是我在Haskell中停留的地方..

add :: (Int, Int, Int) -> (Int, Int)
add (l,r,c) = (((l+r+c) `mod` 2), ((l+r+c) `div` 2))

bAdd :: [Int] -> [Int] -> ([Int], Int)
bAdd []     []       =  ([fst (add (0,0,0))], snd (add(0,0,0)))
bAdd [l]    [r]      =  ([fst (add (l,r,0))], snd (add(l,r,0)))
bAdd (l:lt) (r:rt)   =  ([fst (add (l,r,add (head)))])

Answer 1

我们先添加一位。

addWithCarry :: Bool -> Bool -> (Bool, Bool)
addWithCarry x y = (x /= y, x && y)
--                  "x+y"   its carry

然后，让我们转到列表：

-- numbers are represented LSB first e.g. 6 is [False,True,True]
addBitsWithCarry :: [Bool] -> [Bool] -> Bool -> [Bool]
-- when we ran out of digits on both args:
addBitsWithCarry []     []     False = []
addBitsWithCarry []     []     True  = [True]
-- when we ran out of digits on one arg, add a zero there:
addBitsWithCarry a      []     c     = addBitsWithCarry a       [False] c
addBitsWithCarry []     b      c     = addBitsWithCarry [False] b       c
-- some digits on both sides
addBitsWithCarry (x:xs) (y:ys) c     = ???
          where (z,c') = addWithCarry ???

你能弄明白在最后几行做什么吗？

如果您可以假设您的数字具有相同的位长度（就像在C ++代码中那样），则可以删除上面添加零的两行。

额外提示：

-- some digits on both sides
addBitsWithCarry (x:xs) (y:ys) c     = lsbOfTheSum : restOfTheSum
          where (z,c') = addWithCarry someBit someOtherBit someCarry
                lsbOfTheSum  = ???  -- what is the first bit (LSB) of the result?
                restOfTheSum = ???  -- how to compute the other bits (think recursively)
                someBit      = ???  -- what bit we should add at this step?
                someOtherBit = ???  -- ... with what other bit?
                someCarry    = ???  -- ... using which carry?

如果您了解二元和的工作原理，并且您对Haskell，模式匹配和递归有基本的了解，那么您应该能够得出结论。

如何在Haskell中添加两个n位二进制整数？

1 个答案: