treez

A collection of useful data structures

segment tree

implementation: array based

todo: generic type

notes: for static use after initialization

```rust

let mut segments = vec![]; for i in 0..10 { let n = (i5, 5i+5, i); //(leftbound,rightbound,segment_id); inclusive bounds segments.push( n ); }

let t : treez::seg::TreeSeg = treez::seg::TreeSeg::init( segments.asslice() ); let querysegs: HashSet<_> = t.getsegsfrom_bound( (15,20) ).iter().cloned().collect();

let check: HashSet<_> = [ 2, 3, 4 ].iter().cloned().collect(); println!( "query segs: {:?}", querysegs ); assert!( check.intersection(&querysegs).count() == check.len() );

```

red black tree

implementation: array based, threshold compaction, minimal heap allocation

todo: optimize internal representation and operations, generic type

notes: comparable performance to BTreeMap

```rust

let mut t = treez::rb::TreeRb::new(); for i in 0..nums.len() { let r = nums[i]; t.insert( r, i as isize ); }

for i in 0..nums.len() { let r = nums[i]; let v = t.remove( &r ).expect( "remove unsuccessful" ); }

```

reverse automatic gradient differentiation

implementation: array based, scalar variable

todo: add more test coverage, tweek to more ergonomic interface, interval optimization

```rust

let mut c : autograd::Context = Default::default();

//setup variables
let mut buf = {
    let mut x = autograd::init_var( & mut c, &[ 6f64 ] );
    let mut y = autograd::init_var( & mut c, &[ 7f64, 3f64 ] );
    let mut z = autograd::init_op( & mut c, autograd::OpType::Mul, & mut [ & mut x, & mut y ] );
    let mut a = autograd::init_var( & mut c, &[ 3f64, 8f64 ] );
    let mut b = autograd::init_op( & mut c, autograd::OpType::Add, & mut [ & mut z, & mut a ] );
    vec![ x, y, z, a, b ]
};

let var_ids = autograd::fwd_pass( & mut c, & mut buf ).unwrap();

let mut var_map = HashMap::new();
for i in [ "x", "y", "z", "a", "b" ].iter().zip( var_ids ) {
    var_map.insert( i.0, i.1 );
}

//compute gradient of b with respect to every other variable
{
    let mut var_grad = HashMap::new();

    let b_id = *var_map.get(&"b").unwrap();
    for i in var_map.iter() {
        let grad = autograd::compute_grad( & mut c, b_id, *i.1 ).unwrap();
        var_grad.insert( *i.0, grad );
    }

    //var x reshaped?
    assert_eq!( c.get_var(*var_map.get(&"x").unwrap()).unwrap()._val.len(), 2usize );
    assert_eq!( c.get_var(*var_map.get(&"x").unwrap()).unwrap()._grad.len(), 2usize );

    assert_eq!( c.get_var(*var_map.get(&"z").unwrap()).unwrap()._val, &[ 42f64, 18f64 ] );
    assert_eq!( c.get_var(*var_map.get(&"x").unwrap()).unwrap()._val, &[ 6f64,  6f64  ] );
    assert_eq!( c.get_var(*var_map.get(&"y").unwrap()).unwrap()._val, &[ 7f64,  3f64  ] );
    assert_eq!( c.get_var(*var_map.get(&"b").unwrap()).unwrap()._val, &[ 45f64, 26f64 ] );
    assert_eq!( c.get_var(*var_map.get(&"a").unwrap()).unwrap()._val, &[ 3f64,  8f64  ] );


    assert_eq!( var_grad.get(&"z").unwrap(), &[ 1f64, 1f64 ] );
    assert_eq!( var_grad.get(&"x").unwrap(), &[ 7f64, 3f64 ] );
    assert_eq!( var_grad.get(&"y").unwrap(), &[ 6f64, 6f64 ] );
    assert_eq!( var_grad.get(&"b").unwrap(), &[ 1f64, 1f64 ] );
    assert_eq!( var_grad.get(&"a").unwrap(), &[ 1f64, 1f64 ] );
}

//compute gradient of z with respect to a
{
    let z_id = *var_map.get(&"z").unwrap();
    let a_id = *var_map.get(&"a").unwrap();
    let grad = autograd::compute_grad( & mut c, z_id, a_id ).unwrap();
    assert_eq!( &grad[..], &[ 0f64, 0f64 ] );
}

```

prefix sum tree

implementation: array based

todo: support generic commutative operation

```rust

let mut t = treez::prefix::TreePrefix::init(16);
t.set(0, 5);
t.set(1, 7);
t.set(10, 4);
assert_eq!( t.get_interval(0, 16), 16isize );
assert_eq!( t.get_interval(10, 11), 4isize );
assert_eq!( t.get_interval(1, 11), 11isize );

t.set(1, 9);
assert_eq!( t.get_interval(1, 2), 9isize );
assert_eq!( t.get_interval(1, 11), 13isize );
assert_eq!( t.get_interval_start( 2 ), 14isize );
assert_eq!( t.get_interval_start( 11 ), 18isize );

t.add( 0, 1);
assert_eq!( t.get_interval_start( 2 ), 15isize );
assert_eq!( t.get_interval_start( 11 ), 19isize );

```