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// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package bzip2

import "sort"

// A huffmanTree is a binary tree which is navigated, bit-by-bit to reach a
// symbol.
type huffmanTree struct {
        // nodes contains all the non-leaf nodes in the tree. nodes[0] is the
        // root of the tree and nextNode contains the index of the next element
        // of nodes to use when the tree is being constructed.
        nodes    []huffmanNode
        nextNode int
}

// A huffmanNode is a node in the tree. left and right contain indexes into the
// nodes slice of the tree. If left or right is invalidNodeValue then the child
// is a left node and its value is in leftValue/rightValue.
//
// The symbols are uint16s because bzip2 encodes not only MTF indexes in the
// tree, but also two magic values for run-length encoding and an EOF symbol.
// Thus there are more than 256 possible symbols.
type huffmanNode struct {
        left, right           uint16
        leftValue, rightValue uint16
}

// invalidNodeValue is an invalid index which marks a leaf node in the tree.
const invalidNodeValue = 0xffff

// Decode reads bits from the given bitReader and navigates the tree until a
// symbol is found.
func (t huffmanTree) Decode(br *bitReader) (v uint16) {
        nodeIndex := uint16(0) // node 0 is the root of the tree.

        for {
                node := &t.nodes[nodeIndex]
                bit := br.ReadBit()
                // bzip2 encodes left as a true bit.
                if bit {
                        // left
                        if node.left == invalidNodeValue {
                                return node.leftValue
                        }
                        nodeIndex = node.left
                } else {
                        // right
                        if node.right == invalidNodeValue {
                                return node.rightValue
                        }
                        nodeIndex = node.right
                }
        }

        panic("unreachable")
}

// newHuffmanTree builds a Huffman tree from a slice containing the code
// lengths of each symbol. The maximum code length is 32 bits.
func newHuffmanTree(lengths []uint8) (huffmanTree, error) {
        // There are many possible trees that assign the same code length to
        // each symbol (consider reflecting a tree down the middle, for
        // example). Since the code length assignments determine the
        // efficiency of the tree, each of these trees is equally good. In
        // order to minimize the amount of information needed to build a tree
        // bzip2 uses a canonical tree so that it can be reconstructed given
        // only the code length assignments.

        if len(lengths) < 2 {
                panic("newHuffmanTree: too few symbols")
        }

        var t huffmanTree

        // First we sort the code length assignments by ascending code length,
        // using the symbol value to break ties.
        pairs := huffmanSymbolLengthPairs(make([]huffmanSymbolLengthPair, len(lengths)))
        for i, length := range lengths {
                pairs[i].value = uint16(i)
                pairs[i].length = length
        }

        sort.Sort(pairs)

        // Now we assign codes to the symbols, starting with the longest code.
        // We keep the codes packed into a uint32, at the most-significant end.
        // So branches are taken from the MSB downwards. This makes it easy to
        // sort them later.
        code := uint32(0)
        length := uint8(32)

        codes := huffmanCodes(make([]huffmanCode, len(lengths)))
        for i := len(pairs) - 1; i >= 0; i-- {
                if length > pairs[i].length {
                        // If the code length decreases we shift in order to
                        // zero any bits beyond the end of the code.
                        length >>= 32 - pairs[i].length
                        length <<= 32 - pairs[i].length
                        length = pairs[i].length
                }
                codes[i].code = code
                codes[i].codeLen = length
                codes[i].value = pairs[i].value
                // We need to 'increment' the code, which means treating |code|
                // like a |length| bit number.
                code += 1 << (32 - length)
        }

        // Now we can sort by the code so that the left half of each branch are
        // grouped together, recursively.
        sort.Sort(codes)

        t.nodes = make([]huffmanNode, len(codes))
        _, err := buildHuffmanNode(&t, codes, 0)
        return t, err
}

// huffmanSymbolLengthPair contains a symbol and its code length.
type huffmanSymbolLengthPair struct {
        value  uint16
        length uint8
}

// huffmanSymbolLengthPair is used to provide an interface for sorting.
type huffmanSymbolLengthPairs []huffmanSymbolLengthPair

func (h huffmanSymbolLengthPairs) Len() int {
        return len(h)
}

func (h huffmanSymbolLengthPairs) Less(i, j int) bool {
        if h[i].length < h[j].length {
                return true
        }
        if h[i].length > h[j].length {
                return false
        }
        if h[i].value < h[j].value {
                return true
        }
        return false
}

func (h huffmanSymbolLengthPairs) Swap(i, j int) {
        h[i], h[j] = h[j], h[i]
}

// huffmanCode contains a symbol, its code and code length.
type huffmanCode struct {
        code    uint32
        codeLen uint8
        value   uint16
}

// huffmanCodes is used to provide an interface for sorting.
type huffmanCodes []huffmanCode

func (n huffmanCodes) Len() int {
        return len(n)
}

func (n huffmanCodes) Less(i, j int) bool {
        return n[i].code < n[j].code
}

func (n huffmanCodes) Swap(i, j int) {
        n[i], n[j] = n[j], n[i]
}

// buildHuffmanNode takes a slice of sorted huffmanCodes and builds a node in
// the Huffman tree at the given level. It returns the index of the newly
// constructed node.
func buildHuffmanNode(t *huffmanTree, codes []huffmanCode, level uint32) (nodeIndex uint16, err error) {
        test := uint32(1) << (31 - level)

        // We have to search the list of codes to find the divide between the left and right sides.
        firstRightIndex := len(codes)
        for i, code := range codes {
                if code.code&test != 0 {
                        firstRightIndex = i
                        break
                }
        }

        left := codes[:firstRightIndex]
        right := codes[firstRightIndex:]

        if len(left) == 0 || len(right) == 0 {
                return 0, StructuralError("superfluous level in Huffman tree")
        }

        nodeIndex = uint16(t.nextNode)
        node := &t.nodes[t.nextNode]
        t.nextNode++

        if len(left) == 1 {
                // leaf node
                node.left = invalidNodeValue
                node.leftValue = left[0].value
        } else {
                node.left, err = buildHuffmanNode(t, left, level+1)
        }

        if err != nil {
                return
        }

        if len(right) == 1 {
                // leaf node
                node.right = invalidNodeValue
                node.rightValue = right[0].value
        } else {
                node.right, err = buildHuffmanNode(t, right, level+1)
        }

        return
}