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# reverse_iter_fold

### Synopsis

    template<
          typename Sequence
        , typename State
        , typename BackwardOp
        , typename ForwardOp = _1
        >
    struct reverse_iter_fold
    {
        typedef unspecified  type;
    };

### Description

Returns the result of the successive application of binary `BackwardOp` to the result of the previous `BackwardOp` invocation (`State` if it's the first call) and each iterator in the range [`begin<Sequence>::type`, `end<Sequence>::type`) in reverse order. If `ForwardOp` is provided, then it's applied on forward traversal to form the result which is passed to the first `BackwardOp` call.

### Header

    #include <boost/mpl/reverse_iter_fold.hpp>

### Parameters

Parameter | Requirement | Description
--- | --- | ---
`Sequence` | Forward Sequence | A sequence to iterate.
`State` | Any type | The initial state for the first `BackwardOp` / `ForwardOp` application.
`BackwardOp` | Binary Lambda Expression | The operation to be executed on backward traversal.
`ForwardOp` | Binary Lambda Expression | The operation to be executed on forward traversal.

### Expression semantics

For any Forward Sequence `s`, binary Lambda Expression `backward_op` and `forward_op`, and arbitrary type `state`:

    typedef reverse_iter_fold< s,state,backward_op >::type t;

Return type: | A type.
Semantics: | Equivalent to
    typedef begin<s>::type i1;
    typedef next<i1>::type i2;
    ...
    typedef next<in>::type last;
    typedef apply<backward_op,state,in>::type staten;
    typedef apply<backward_op,staten,in-1>::type staten-1;
    ...
    typedef apply<backward_op,state2,i1>::type state1;
    typedef state1 t;
where `n == size<s>::value` and `last` is identical to `end<s>::type`; equivalent to `typedef state t;` if `empty<s>::value == true`.

    typedef reverse_iter_fold< s,state,backward_op,forward_op >::type t;

Return type: | A type.
Semantics: | Equivalent to
    typedef reverse_iter_fold<
          Sequence
        , iter_fold<s,state,forward_op>::type
        , backward_op
        >::type t;

### Complexity

Linear. Exactly `size<s>::value` applications of `backward_op` and `forward_op`.

### Example

Build a list of iterators to the negative elements in a sequence.

    typedef vector_c<int,5,-1,0,-7,-2,0,-5,4> numbers;
    typedef list_c<int,-1,-7,-2,-5> negatives;
    typedef reverse_iter_fold<
          numbers
        , list<>
        , if_< less< deref<_2>,int_<0> >, push_front<_1,_2>, _1 >
        >::type iters;

    BOOST_MPL_ASSERT(( equal<
          negatives
        , transform_view< iters,deref<_1> >
        > ));

### See also

Algorithms, iter_fold, reverse_fold, fold