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    // Copyright 2018 Developers of the Rand project.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! Low-level API for sampling indices

    #[cfg(feature="alloc")] use core::slice;

    #[cfg(feature="std")] use std::vec;
    #[cfg(all(feature="alloc", not(feature="std")))] use crate::alloc::vec::{self, Vec};
    // BTreeMap is not as fast in tests, but better than nothing.
    #[cfg(feature="std")] use std::collections::{HashSet};
    #[cfg(all(feature="alloc", not(feature="std")))] use crate::alloc::collections::BTreeSet;

    #[cfg(feature="alloc")] use crate::distributions::{Distribution, Uniform, uniform::SampleUniform};
    use crate::Rng;

    /// A vector of indices.
    ///
    /// Multiple internal representations are possible.
    #[derive(Clone, Debug)]
    pub enum IndexVec {
        #[doc(hidden)] U32(Vec<u32>),
        #[doc(hidden)] USize(Vec<usize>),
    }

    impl IndexVec {
        /// Returns the number of indices
        pub fn len(&self) -> usize {
            match self {
                &IndexVec::U32(ref v) => v.len(),
                &IndexVec::USize(ref v) => v.len(),
            }
        }

        /// Return the value at the given `index`.
        ///
        /// (Note: we cannot implement [`std::ops::Index`] because of lifetime
        /// restrictions.)
        pub fn index(&self, index: usize) -> usize {
            match self {
                &IndexVec::U32(ref v) => v[index] as usize,
                &IndexVec::USize(ref v) => v[index],
            }
        }

        /// Return result as a `Vec<usize>`. Conversion may or may not be trivial.
        pub fn into_vec(self) -> Vec<usize> {
            match self {
                IndexVec::U32(v) => v.into_iter().map(|i| i as usize).collect(),
                IndexVec::USize(v) => v,
            }
        }

        /// Iterate over the indices as a sequence of `usize` values
        pub fn iter<'a>(&'a self) -> IndexVecIter<'a> {
            match self {
                &IndexVec::U32(ref v) => IndexVecIter::U32(v.iter()),
                &IndexVec::USize(ref v) => IndexVecIter::USize(v.iter()),
            }
        }

        /// Convert into an iterator over the indices as a sequence of `usize` values
        pub fn into_iter(self) -> IndexVecIntoIter {
            match self {
                IndexVec::U32(v) => IndexVecIntoIter::U32(v.into_iter()),
                IndexVec::USize(v) => IndexVecIntoIter::USize(v.into_iter()),
            }
        }
    }

    impl PartialEq for IndexVec {
        fn eq(&self, other: &IndexVec) -> bool {
            use self::IndexVec::*;
            match (self, other) {
                (&U32(ref v1), &U32(ref v2)) => v1 == v2,
                (&USize(ref v1), &USize(ref v2)) => v1 == v2,
                (&U32(ref v1), &USize(ref v2)) => (v1.len() == v2.len())
                    && (v1.iter().zip(v2.iter()).all(|(x, y)| *x as usize == *y)),
                (&USize(ref v1), &U32(ref v2)) => (v1.len() == v2.len())
                    && (v1.iter().zip(v2.iter()).all(|(x, y)| *x == *y as usize)),
            }
        }
    }

    impl From<Vec<u32>> for IndexVec {
        fn from(v: Vec<u32>) -> Self {
            IndexVec::U32(v)
        }
    }

    impl From<Vec<usize>> for IndexVec {
        fn from(v: Vec<usize>) -> Self {
            IndexVec::USize(v)
        }
    }

    /// Return type of `IndexVec::iter`.
    #[derive(Debug)]
    pub enum IndexVecIter<'a> {
        #[doc(hidden)] U32(slice::Iter<'a, u32>),
        #[doc(hidden)] USize(slice::Iter<'a, usize>),
    }

    impl<'a> Iterator for IndexVecIter<'a> {
        type Item = usize;
        fn next(&mut self) -> Option<usize> {
            use self::IndexVecIter::*;
            match self {
                &mut U32(ref mut iter) => iter.next().map(|i| *i as usize),
                &mut USize(ref mut iter) => iter.next().cloned(),
            }
        }

        fn size_hint(&self) -> (usize, Option<usize>) {
            match self {
                &IndexVecIter::U32(ref v) => v.size_hint(),
                &IndexVecIter::USize(ref v) => v.size_hint(),
            }
        }
    }

    impl<'a> ExactSizeIterator for IndexVecIter<'a> {}

    /// Return type of `IndexVec::into_iter`.
    #[derive(Clone, Debug)]
    pub enum IndexVecIntoIter {
        #[doc(hidden)] U32(vec::IntoIter<u32>),
        #[doc(hidden)] USize(vec::IntoIter<usize>),
    }

    impl Iterator for IndexVecIntoIter {
        type Item = usize;

        fn next(&mut self) -> Option<Self::Item> {
            use self::IndexVecIntoIter::*;
            match self {
                &mut U32(ref mut v) => v.next().map(|i| i as usize),
                &mut USize(ref mut v) => v.next(),
            }
        }

        fn size_hint(&self) -> (usize, Option<usize>) {
            use self::IndexVecIntoIter::*;
            match self {
                &U32(ref v) => v.size_hint(),
                &USize(ref v) => v.size_hint(),
            }
        }
    }

    impl ExactSizeIterator for IndexVecIntoIter {}

    /// Randomly sample exactly `amount` distinct indices from `0..length`, and
    /// return them in random order (fully shuffled).
    ///
    /// This method is used internally by the slice sampling methods, but it can
    /// sometimes be useful to have the indices themselves so this is provided as
    /// an alternative.
    ///
    /// The implementation used is not specified; we automatically select the
    /// fastest available algorithm for the `length` and `amount` parameters
    /// (based on detailed profiling on an Intel Haswell CPU). Roughly speaking,
    /// complexity is `O(amount)`, except that when `amount` is small, performance
    /// is closer to `O(amount^2)`, and when `length` is close to `amount` then
    /// `O(length)`.
    ///
    /// Note that performance is significantly better over `u32` indices than over
    /// `u64` indices. Because of this we hide the underlying type behind an
    /// abstraction, `IndexVec`.
    ///
    /// If an allocation-free `no_std` function is required, it is suggested
    /// to adapt the internal `sample_floyd` implementation.
    ///
    /// Panics if `amount > length`.
    pub fn sample<R>(rng: &mut R, length: usize, amount: usize) -> IndexVec
    where R: Rng + ?Sized {
        if amount > length {
            panic!("`amount` of samples must be less than or equal to `length`");
        }
        if length > (::core::u32::MAX as usize) {
            // We never want to use inplace here, but could use floyd's alg
            // Lazy version: always use the cache alg.
            return sample_rejection(rng, length, amount);
        }
        let amount = amount as u32;
        let length = length as u32;

        // Choice of algorithm here depends on both length and amount. See:
        // https://github.com/rust-random/rand/pull/479
        // We do some calculations with f32. Accuracy is not very important.

        if amount < 163 {
            const C: [[f32; 2]; 2] = [[1.6, 8.0/45.0], [10.0, 70.0/9.0]];
            let j = if length < 500_000 { 0 } else { 1 };
            let amount_fp = amount as f32;
            let m4 = C[0][j] * amount_fp;
            // Short-cut: when amount < 12, floyd's is always faster
            if amount > 11 && (length as f32) < (C[1][j] + m4) * amount_fp {
                sample_inplace(rng, length, amount)
            } else {
                sample_floyd(rng, length, amount)
            }
        } else {
            const C: [f32; 2] = [270.0, 330.0/9.0];
            let j = if length < 500_000 { 0 } else { 1 };
            if (length as f32) < C[j] * (amount as f32) {
                sample_inplace(rng, length, amount)
            } else {
                sample_rejection(rng, length, amount)
            }
        }
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using Floyd's
    /// combination algorithm.
    ///
    /// The output values are fully shuffled. (Overhead is under 50%.)
    ///
    /// This implementation uses `O(amount)` memory and `O(amount^2)` time.
    fn sample_floyd<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
    where R: Rng + ?Sized {
        // For small amount we use Floyd's fully-shuffled variant. For larger
        // amounts this is slow due to Vec::insert performance, so we shuffle
        // afterwards. Benchmarks show little overhead from extra logic.
        let floyd_shuffle = amount < 50;

        debug_assert!(amount <= length);
        let mut indices = Vec::with_capacity(amount as usize);
        for j in length - amount .. length {
            let t = rng.gen_range(0, j + 1);
            if floyd_shuffle {
                if let Some(pos) = indices.iter().position(|&x| x == t) {
                    indices.insert(pos, j);
                    continue;
                }
            } else {
                if indices.contains(&t) {
                    indices.push(j);
                    continue;
                }
            }
            indices.push(t);
        }
        if !floyd_shuffle {
            // Reimplement SliceRandom::shuffle with smaller indices
            for i in (1..amount).rev() {
                // invariant: elements with index > i have been locked in place.
                indices.swap(i as usize, rng.gen_range(0, i + 1) as usize);
            }
        }
        IndexVec::from(indices)
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using an inplace
    /// partial Fisher-Yates method.
    /// Sample an amount of indices using an inplace partial fisher yates method.
    ///
    /// This allocates the entire `length` of indices and randomizes only the first `amount`.
    /// It then truncates to `amount` and returns.
    ///
    /// This method is not appropriate for large `length` and potentially uses a lot
    /// of memory; because of this we only implement for `u32` index (which improves
    /// performance in all cases).
    ///
    /// Set-up is `O(length)` time and memory and shuffling is `O(amount)` time.
    fn sample_inplace<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
    where R: Rng + ?Sized {
        debug_assert!(amount <= length);
        let mut indices: Vec<u32> = Vec::with_capacity(length as usize);
        indices.extend(0..length);
        for i in 0..amount {
            let j: u32 = rng.gen_range(i, length);
            indices.swap(i as usize, j as usize);
        }
        indices.truncate(amount as usize);
        debug_assert_eq!(indices.len(), amount as usize);
        IndexVec::from(indices)
    }

    trait UInt: Copy + PartialOrd + Ord + PartialEq + Eq + SampleUniform + core::hash::Hash {
        fn zero() -> Self;
        fn as_usize(self) -> usize;
    }
    impl UInt for u32 {
        #[inline] fn zero() -> Self { 0 }
        #[inline] fn as_usize(self) -> usize { self as usize }
    }
    impl UInt for usize {
        #[inline] fn zero() -> Self { 0 }
        #[inline] fn as_usize(self) -> usize { self }
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using rejection
    /// sampling.
    ///
    /// Since `amount <<< length` there is a low chance of a random sample in
    /// `0..length` being a duplicate. We test for duplicates and resample where
    /// necessary. The algorithm is `O(amount)` time and memory.
    ///
    /// This function  is generic over X primarily so that results are value-stable
    /// over 32-bit and 64-bit platforms.
    fn sample_rejection<X: UInt, R>(rng: &mut R, length: X, amount: X) -> IndexVec
    where R: Rng + ?Sized, IndexVec: From<Vec<X>> {
        debug_assert!(amount < length);
        #[cfg(feature="std")] let mut cache = HashSet::with_capacity(amount.as_usize());
        #[cfg(not(feature="std"))] let mut cache = BTreeSet::new();
        let distr = Uniform::new(X::zero(), length);
        let mut indices = Vec::with_capacity(amount.as_usize());
        for _ in 0..amount.as_usize() {
            let mut pos = distr.sample(rng);
            while !cache.insert(pos) {
                pos = distr.sample(rng);
            }
            indices.push(pos);
        }

        debug_assert_eq!(indices.len(), amount.as_usize());
        IndexVec::from(indices)
    }

    #[cfg(test)]
    mod test {
        #[cfg(feature="std")] use std::vec;
        #[cfg(all(feature="alloc", not(feature="std")))] use crate::alloc::vec;
        use super::*;

        #[test]
        fn test_sample_boundaries() {
            let mut r = crate::test::rng(404);

            assert_eq!(sample_inplace(&mut r, 0, 0).len(), 0);
            assert_eq!(sample_inplace(&mut r, 1, 0).len(), 0);
            assert_eq!(sample_inplace(&mut r, 1, 1).into_vec(), vec![0]);

            assert_eq!(sample_rejection(&mut r, 1u32, 0).len(), 0);

            assert_eq!(sample_floyd(&mut r, 0, 0).len(), 0);
            assert_eq!(sample_floyd(&mut r, 1, 0).len(), 0);
            assert_eq!(sample_floyd(&mut r, 1, 1).into_vec(), vec![0]);

            // These algorithms should be fast with big numbers. Test average.
            let sum: usize = sample_rejection(&mut r, 1 << 25, 10u32)
                    .into_iter().sum();
            assert!(1 << 25 < sum && sum < (1 << 25) * 25);

            let sum: usize = sample_floyd(&mut r, 1 << 25, 10)
                    .into_iter().sum();
            assert!(1 << 25 < sum && sum < (1 << 25) * 25);
        }

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_sample_alg() {
            let seed_rng = crate::test::rng;

            // We can't test which algorithm is used directly, but Floyd's alg
            // should produce different results from the others. (Also, `inplace`
            // and `cached` currently use different sizes thus produce different results.)

            // A small length and relatively large amount should use inplace
            let (length, amount): (usize, usize) = (100, 50);
            let v1 = sample(&mut seed_rng(420), length, amount);
            let v2 = sample_inplace(&mut seed_rng(420), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);

            // Test Floyd's alg does produce different results
            let v3 = sample_floyd(&mut seed_rng(420), length as u32, amount as u32);
            assert!(v1 != v3);

            // A large length and small amount should use Floyd
            let (length, amount): (usize, usize) = (1<<20, 50);
            let v1 = sample(&mut seed_rng(421), length, amount);
            let v2 = sample_floyd(&mut seed_rng(421), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);

            // A large length and larger amount should use cache
            let (length, amount): (usize, usize) = (1<<20, 600);
            let v1 = sample(&mut seed_rng(422), length, amount);
            let v2 = sample_rejection(&mut seed_rng(422), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);
        }
    }

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