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-------------------------------------------------------------------------------- 1 | # go-loser 2 | Loser Tree data structure, for fast k-way merge 3 | 4 | I will be speaking about this at [GopherCon](https://www.gophercon.com/agenda/session/1160355) on 27th Sept 2023. 5 | 6 | There are currently two versions of the code on two Git branches: [main](https://github.com/bboreham/go-loser/tree/main), which works for built-in types like `int` and `string`, and [any](https://github.com/bboreham/go-loser/tree/any) which works on any type but requires you to pass in a function pointer to do `less` comparisons. 7 | 8 | See https://en.wikipedia.org/wiki/K-way_merge_algorithm#Tournament_Tree for more details on the algorithm. 9 | -------------------------------------------------------------------------------- /go.mod: -------------------------------------------------------------------------------- 1 | module github.com/bboreham/go-loser 2 | 3 | go 1.20 4 | 5 | require golang.org/x/exp v0.0.0-20230713183714-613f0c0eb8a1 6 | -------------------------------------------------------------------------------- /go.sum: -------------------------------------------------------------------------------- 1 | golang.org/x/exp v0.0.0-20230713183714-613f0c0eb8a1 h1:MGwJjxBy0HJshjDNfLsYO8xppfqWlA5ZT9OhtUUhTNw= 2 | golang.org/x/exp v0.0.0-20230713183714-613f0c0eb8a1/go.mod h1:FXUEEKJgO7OQYeo8N01OfiKP8RXMtf6e8aTskBGqWdc= 3 | -------------------------------------------------------------------------------- /tree.go: -------------------------------------------------------------------------------- 1 | // Loser tree, from https://en.wikipedia.org/wiki/K-way_merge_algorithm#Tournament_Tree 2 | 3 | package loser 4 | 5 | import "golang.org/x/exp/constraints" 6 | 7 | type Value constraints.Ordered 8 | 9 | type Sequence[E Value] interface { 10 | At() E // Returns the current value. 11 | Next() bool // Advances and returns true if there is a value at this new position. 12 | } 13 | 14 | func New[E Value, S Sequence[E]](sequences []S, maxVal E) *Tree[E, S] { 15 | nSequences := len(sequences) 16 | t := Tree[E, S]{ 17 | maxVal: maxVal, 18 | nodes: make([]node[E, S], nSequences*2), 19 | } 20 | for i, s := range sequences { 21 | t.nodes[i+nSequences].items = s 22 | t.moveNext(i + nSequences) // Must call Next on each item so that At() has a value. 23 | } 24 | if nSequences > 0 { 25 | t.nodes[0].index = -1 // flag to be initialized on first call to Next(). 26 | } 27 | return &t 28 | } 29 | 30 | // Call the close function on all sequences that are still open. 31 | func (t *Tree[E, S]) Close() { 32 | for _, e := range t.nodes[len(t.nodes)/2 : len(t.nodes)] { 33 | if e.index == -1 { 34 | continue 35 | } 36 | } 37 | } 38 | 39 | // A loser tree is a binary tree laid out such that nodes N and N+1 have parent N/2. 40 | // We store M leaf nodes in positions M...2M-1, and M-1 internal nodes in positions 1..M-1. 41 | // Node 0 is a special node, containing the winner of the contest. 42 | type Tree[E Value, S Sequence[E]] struct { 43 | maxVal E 44 | nodes []node[E, S] 45 | } 46 | 47 | type node[E Value, S Sequence[E]] struct { 48 | index int // This is the loser for all nodes except the 0th, where it is the winner. 49 | value E // Value copied from the loser node, or winner for node 0. 50 | items S // Only populated for leaf nodes. 51 | } 52 | 53 | func (t *Tree[E, S]) moveNext(index int) bool { 54 | n := &t.nodes[index] 55 | if n.items.Next() { 56 | n.value = n.items.At() 57 | return true 58 | } 59 | n.value = t.maxVal 60 | n.index = -1 61 | return false 62 | } 63 | 64 | func (t *Tree[E, S]) Winner() S { 65 | return t.nodes[t.nodes[0].index].items 66 | } 67 | 68 | func (t *Tree[E, S]) At() E { 69 | return t.nodes[0].value 70 | } 71 | 72 | func (t *Tree[E, S]) Next() bool { 73 | nodes := t.nodes 74 | if len(nodes) == 0 { 75 | return false 76 | } 77 | if nodes[0].index == -1 { // If tree has not been initialized yet, do that. 78 | t.initialize() 79 | return nodes[nodes[0].index].index != -1 80 | } 81 | if nodes[nodes[0].index].index == -1 { // already exhausted 82 | return false 83 | } 84 | t.moveNext(nodes[0].index) 85 | t.replayGames(nodes[0].index) 86 | return nodes[nodes[0].index].index != -1 87 | } 88 | 89 | // Current winner has been advanced independently; fix up the loser tree. 90 | func (t *Tree[E, S]) Fix(closed bool) { 91 | nodes := t.nodes 92 | cur := &nodes[nodes[0].index] 93 | if closed { 94 | cur.value = t.maxVal 95 | cur.index = -1 96 | } else { 97 | cur.value = cur.items.At() 98 | } 99 | t.replayGames(nodes[0].index) 100 | } 101 | 102 | func (t *Tree[E, S]) IsEmpty() bool { 103 | nodes := t.nodes 104 | if nodes[0].index == -1 { // If tree has not been initialized yet, do that. 105 | t.initialize() 106 | } 107 | return nodes[nodes[0].index].index == -1 108 | } 109 | 110 | func (t *Tree[E, S]) initialize() { 111 | winner := t.playGame(1) 112 | t.nodes[0].index = winner 113 | t.nodes[0].value = t.nodes[winner].value 114 | } 115 | 116 | // Find the winner at position pos; if it is a non-leaf node, store the loser. 117 | // pos must be >= 1 and < len(t.nodes) 118 | func (t *Tree[E, S]) playGame(pos int) int { 119 | nodes := t.nodes 120 | if pos >= len(nodes)/2 { 121 | return pos 122 | } 123 | left := t.playGame(pos * 2) 124 | right := t.playGame(pos*2 + 1) 125 | var loser, winner int 126 | if nodes[left].value < nodes[right].value { 127 | loser, winner = right, left 128 | } else { 129 | loser, winner = left, right 130 | } 131 | nodes[pos].index = loser 132 | nodes[pos].value = nodes[loser].value 133 | return winner 134 | } 135 | 136 | // Starting at pos, which is a winner, re-consider all values up to the root. 137 | func (t *Tree[E, S]) replayGames(pos int) { 138 | nodes := t.nodes 139 | winningValue := nodes[pos].value 140 | for n := parent(pos); n != 0; n = parent(n) { 141 | node := &nodes[n] 142 | if node.value < winningValue { 143 | // Record pos as the loser here, and the old loser is the new winner. 144 | node.index, pos = pos, node.index 145 | node.value, winningValue = winningValue, node.value 146 | } 147 | } 148 | // pos is now the winner; store it in node 0. 149 | nodes[0].index = pos 150 | nodes[0].value = winningValue 151 | } 152 | 153 | func parent(i int) int { return i >> 1 } 154 | -------------------------------------------------------------------------------- /tree_test.go: -------------------------------------------------------------------------------- 1 | package loser_test 2 | 3 | import ( 4 | "math" 5 | "testing" 6 | 7 | "github.com/bboreham/go-loser" 8 | ) 9 | 10 | type List struct { 11 | list []uint64 12 | cur uint64 13 | } 14 | 15 | func NewList(list ...uint64) *List { 16 | return &List{list: list} 17 | } 18 | 19 | func (it *List) At() uint64 { 20 | return it.cur 21 | } 22 | 23 | func (it *List) Next() bool { 24 | if len(it.list) > 0 { 25 | it.cur = it.list[0] 26 | it.list = it.list[1:] 27 | return true 28 | } 29 | it.cur = 0 30 | return false 31 | } 32 | 33 | func (it *List) Seek(val uint64) bool { 34 | for it.cur < val && len(it.list) > 0 { 35 | it.cur = it.list[0] 36 | it.list = it.list[1:] 37 | } 38 | return len(it.list) > 0 39 | } 40 | 41 | func checkIterablesEqual[E loser.Value, S1 loser.Sequence[E], S2 loser.Sequence[E]](t *testing.T, a S1, b S2, less func(E, E) bool) { 42 | t.Helper() 43 | count := 0 44 | for a.Next() { 45 | count++ 46 | if !b.Next() { 47 | t.Fatalf("b ended before a after %d elements", count) 48 | } 49 | if less(a.At(), b.At()) || less(b.At(), a.At()) { 50 | t.Fatalf("position %d: %v != %v", count, a.At(), b.At()) 51 | } 52 | } 53 | if b.Next() { 54 | t.Fatalf("a ended before b after %d elements", count) 55 | } 56 | } 57 | 58 | func TestMerge(t *testing.T) { 59 | tests := []struct { 60 | name string 61 | args []*List 62 | want *List 63 | }{ 64 | { 65 | name: "empty input", 66 | want: NewList(), 67 | }, 68 | { 69 | name: "one list", 70 | args: []*List{NewList(1, 2, 3, 4)}, 71 | want: NewList(1, 2, 3, 4), 72 | }, 73 | { 74 | name: "two lists", 75 | args: []*List{NewList(3, 4, 5), NewList(1, 2)}, 76 | want: NewList(1, 2, 3, 4, 5), 77 | }, 78 | { 79 | name: "two lists, first empty", 80 | args: []*List{NewList(), NewList(1, 2)}, 81 | want: NewList(1, 2), 82 | }, 83 | { 84 | name: "two lists, second empty", 85 | args: []*List{NewList(1, 2), NewList()}, 86 | want: NewList(1, 2), 87 | }, 88 | { 89 | name: "two lists b", 90 | args: []*List{NewList(1, 2), NewList(3, 4, 5)}, 91 | want: NewList(1, 2, 3, 4, 5), 92 | }, 93 | { 94 | name: "two lists c", 95 | args: []*List{NewList(1, 3), NewList(2, 4, 5)}, 96 | want: NewList(1, 2, 3, 4, 5), 97 | }, 98 | { 99 | name: "three lists", 100 | args: []*List{NewList(1, 3), NewList(2, 4), NewList(5)}, 101 | want: NewList(1, 2, 3, 4, 5), 102 | }, 103 | } 104 | for _, tt := range tests { 105 | t.Run(tt.name, func(t *testing.T) { 106 | less := func(a, b uint64) bool { return a < b } 107 | lt := loser.New[uint64](tt.args, math.MaxUint64) 108 | checkIterablesEqual(t, tt.want, lt, less) 109 | }) 110 | } 111 | } 112 | --------------------------------------------------------------------------------