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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.

    //! Weighted index sampling
    //!
    //! This module provides two implementations for sampling indices:
    //!
    //! *   [`WeightedIndex`] allows `O(log N)` sampling
    //! *   [`alias_method::WeightedIndex`] allows `O(1)` sampling, but with
    //!      much greater set-up cost
    //!
    //! [`alias_method::WeightedIndex`]: alias_method/struct.WeightedIndex.html

    pub mod alias_method;

    use crate::Rng;
    use crate::distributions::Distribution;
    use crate::distributions::uniform::{UniformSampler, SampleUniform, SampleBorrow};
    use core::cmp::PartialOrd;
    use core::fmt;

    // Note that this whole module is only imported if feature="alloc" is enabled.
    #[cfg(not(feature="std"))] use crate::alloc::vec::Vec;

    /// A distribution using weighted sampling to pick a discretely selected
    /// item.
    ///
    /// Sampling a `WeightedIndex` distribution returns the index of a randomly
    /// selected element from the iterator used when the `WeightedIndex` was
    /// created. The chance of a given element being picked is proportional to the
    /// value of the element. The weights can use any type `X` for which an
    /// implementation of [`Uniform<X>`] exists.
    ///
    /// # Performance
    ///
    /// A `WeightedIndex<X>` contains a `Vec<X>` and a [`Uniform<X>`] and so its
    /// size is the sum of the size of those objects, possibly plus some alignment.
    ///
    /// Creating a `WeightedIndex<X>` will allocate enough space to hold `N - 1`
    /// weights of type `X`, where `N` is the number of weights. However, since
    /// `Vec` doesn't guarantee a particular growth strategy, additional memory
    /// might be allocated but not used. Since the `WeightedIndex` object also
    /// contains, this might cause additional allocations, though for primitive
    /// types, ['Uniform<X>`] doesn't allocate any memory.
    ///
    /// Time complexity of sampling from `WeightedIndex` is `O(log N)` where
    /// `N` is the number of weights.
    ///
    /// Sampling from `WeightedIndex` will result in a single call to
    /// `Uniform<X>::sample` (method of the [`Distribution`] trait), which typically
    /// will request a single value from the underlying [`RngCore`], though the
    /// exact number depends on the implementaiton of `Uniform<X>::sample`.
    ///
    /// # Example
    ///
    /// ```
    /// use rand::prelude::*;
    /// use rand::distributions::WeightedIndex;
    ///
    /// let choices = ['a', 'b', 'c'];
    /// let weights = [2,   1,   1];
    /// let dist = WeightedIndex::new(&weights).unwrap();
    /// let mut rng = thread_rng();
    /// for _ in 0..100 {
    ///     // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
    ///     println!("{}", choices[dist.sample(&mut rng)]);
    /// }
    ///
    /// let items = [('a', 0), ('b', 3), ('c', 7)];
    /// let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap();
    /// for _ in 0..100 {
    ///     // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
    ///     println!("{}", items[dist2.sample(&mut rng)].0);
    /// }
    /// ```
    ///
    /// [`Uniform<X>`]: crate::distributions::uniform::Uniform
    /// [`RngCore`]: crate::RngCore
    #[derive(Debug, Clone)]
    pub struct WeightedIndex<X: SampleUniform + PartialOrd> {
        cumulative_weights: Vec<X>,
        weight_distribution: X::Sampler,
    }

    impl<X: SampleUniform + PartialOrd> WeightedIndex<X> {
        /// Creates a new a `WeightedIndex` [`Distribution`] using the values
        /// in `weights`. The weights can use any type `X` for which an
        /// implementation of [`Uniform<X>`] exists.
        ///
        /// Returns an error if the iterator is empty, if any weight is `< 0`, or
        /// if its total value is 0.
        ///
        /// [`Uniform<X>`]: crate::distributions::uniform::Uniform
        pub fn new<I>(weights: I) -> Result<WeightedIndex<X>, WeightedError>
            where I: IntoIterator,
                  I::Item: SampleBorrow<X>,
                  X: for<'a> ::core::ops::AddAssign<&'a X> +
                     Clone +
                     Default {
            let mut iter = weights.into_iter();
            let mut total_weight: X = iter.next()
                                          .ok_or(WeightedError::NoItem)?
                                          .borrow()
                                          .clone();

            let zero = <X as Default>::default();
            if total_weight < zero {
                return Err(WeightedError::InvalidWeight);
            }

            let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
            for w in iter {
                if *w.borrow() < zero {
                    return Err(WeightedError::InvalidWeight);
                }
                weights.push(total_weight.clone());
                total_weight += w.borrow();
            }

            if total_weight == zero {
                return Err(WeightedError::AllWeightsZero);
            }
            let distr = X::Sampler::new(zero, total_weight);

            Ok(WeightedIndex { cumulative_weights: weights, weight_distribution: distr })
        }
    }

    impl<X> Distribution<usize> for WeightedIndex<X> where
        X: SampleUniform + PartialOrd {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
            use ::core::cmp::Ordering;
            let chosen_weight = self.weight_distribution.sample(rng);
            // Find the first item which has a weight *higher* than the chosen weight.
            self.cumulative_weights.binary_search_by(
                |w| if *w <= chosen_weight { Ordering::Less } else { Ordering::Greater }).unwrap_err()
        }
    }

    #[cfg(test)]
    mod test {
        use super::*;

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weightedindex() {
            let mut r = crate::test::rng(700);
            const N_REPS: u32 = 5000;
            let weights = [1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7];
            let total_weight = weights.iter().sum::<u32>() as f32;

            let verify = |result: [i32; 14]| {
                for (i, count) in result.iter().enumerate() {
                    let exp = (weights[i] * N_REPS) as f32 / total_weight;
                    let mut err = (*count as f32 - exp).abs();
                    if err != 0.0 {
                        err /= exp;
                    }
                    assert!(err <= 0.25);
                }
            };

            // WeightedIndex from vec
            let mut chosen = [0i32; 14];
            let distr = WeightedIndex::new(weights.to_vec()).unwrap();
            for _ in 0..N_REPS {
                chosen[distr.sample(&mut r)] += 1;
            }
            verify(chosen);

            // WeightedIndex from slice
            chosen = [0i32; 14];
            let distr = WeightedIndex::new(&weights[..]).unwrap();
            for _ in 0..N_REPS {
                chosen[distr.sample(&mut r)] += 1;
            }
            verify(chosen);

            // WeightedIndex from iterator
            chosen = [0i32; 14];
            let distr = WeightedIndex::new(weights.iter()).unwrap();
            for _ in 0..N_REPS {
                chosen[distr.sample(&mut r)] += 1;
            }
            verify(chosen);

            for _ in 0..5 {
                assert_eq!(WeightedIndex::new(&[0, 1]).unwrap().sample(&mut r), 1);
                assert_eq!(WeightedIndex::new(&[1, 0]).unwrap().sample(&mut r), 0);
                assert_eq!(WeightedIndex::new(&[0, 0, 0, 0, 10, 0]).unwrap().sample(&mut r), 4);
            }

            assert_eq!(WeightedIndex::new(&[10][0..0]).unwrap_err(), WeightedError::NoItem);
            assert_eq!(WeightedIndex::new(&[0]).unwrap_err(), WeightedError::AllWeightsZero);
            assert_eq!(WeightedIndex::new(&[10, 20, -1, 30]).unwrap_err(), WeightedError::InvalidWeight);
            assert_eq!(WeightedIndex::new(&[-10, 20, 1, 30]).unwrap_err(), WeightedError::InvalidWeight);
            assert_eq!(WeightedIndex::new(&[-10]).unwrap_err(), WeightedError::InvalidWeight);
        }
    }

    /// Error type returned from `WeightedIndex::new`.
    #[derive(Debug, Clone, Copy, PartialEq, Eq)]
    pub enum WeightedError {
        /// The provided weight collection contains no items.
        NoItem,

        /// A weight is either less than zero, greater than the supported maximum or
        /// otherwise invalid.
        InvalidWeight,

        /// All items in the provided weight collection are zero.
        AllWeightsZero,

        /// Too many weights are provided (length greater than `u32::MAX`)
        TooMany,
    }

    impl WeightedError {
        fn msg(&self) -> &str {
            match *self {
                WeightedError::NoItem => "No weights provided.",
                WeightedError::InvalidWeight => "A weight is invalid.",
                WeightedError::AllWeightsZero => "All weights are zero.",
                WeightedError::TooMany => "Too many weights (hit u32::MAX)",
            }
        }
    }

    #[cfg(feature="std")]
    impl ::std::error::Error for WeightedError {
        fn description(&self) -> &str {
            self.msg()
        }
        fn cause(&self) -> Option<&dyn (::std::error::Error)> {
            None
        }
    }

    impl fmt::Display for WeightedError {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            write!(f, "{}", self.msg())
        }
    }

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