Segment Tree

Basic implementation of segment tree in Go

Read more about segment tree: https://en.wikipedia.org/wiki/Segment_tree

All operations (see below) are O(log(n)) where n is the size of the array on which queries are performed.

Basic Usage

package main

import "github.com/ideahitme/segment"

func main() {
	tree, err := segment.NewTree([]int{1,2,3,4,5}, segment.MinFunc{})
	if err != nil { 
		//handle error, only happens when empty slice is passed
	}

	// minimum value in range [0:4]
	fmt.Println(tree.RQ(0, 4)) // 1, <nil>

	// increase values in range [1:4] by -5
	err := tree.Add(-5, 1, 4)
	if err != nil { 
		//handle error, only happens when ranges are incorrect
	}

	// so now we have array of [1, -3, -2, -1, 0]
	fmt.Println(tree.RQ(0, 2)) // -3, <nil>
}

NOTE: Slice passed to the tree is internally copied, therefore can be safely modified

API

`NewTree(x []int, TreeFunc)`

	import "github.com/ideahitme/segment" 

	...

	// supports range minimum queries
	minTree, _ := segment.NewTree([]int{124,123, 1, -10000, 412}, segment.MinFunc{})
	// supports range maximum queries
	maxTree, _ := segment.NewTree([]int{124,123, 1, -10000, 412}, segment.MaxFunc{})

`RQ(l, r)`: range queries on range `[l:r]`

	x := []int{1, 20, 3, 40, 5, 60, 7, -100} // our original array
	tree, _ := segment.NewTree(x, segment.MaxFunc{}) // segment tree which supports Range Maximum Queries

	fmt.Println(tree.RQ(0, 0))
	fmt.Println(tree.RQ(0, 3))
	fmt.Println(tree.RQ(3, 5))
	fmt.Println(tree.RQ(6, 7))
	fmt.Println(tree.RQ(7, 7))

	//Output:
	//1 <nil>
	//40 <nil>
	//60 <nil>
	//7 <nil>
	//-100 <nil>

`Add(x, l, r)`: add value `x` to all numbers in range `[l:r]`

	x := []int{1, 20, 3, 40, 5, 60, 7, -100} // our original array
	tree, _ := segment.NewTree(x, segment.MaxFunc{}) // segment tree which supports Range Maximum Queries

	fmt.Println(tree.RQ(0, 3))
	tree.Add(5, 2, 4) //increase elements in [2:4] by 5
	fmt.Println(tree.RQ(2, 4))
	tree.Add(13, 2, 2) // increase element at 2 by 13
	fmt.Println(tree.RQ(0, 2))
	tree.Add(10000, 0, 7) // increase all by 10000
	fmt.Println(tree.RQ(0, 7))

	//Output:
	//40 <nil>
	//45 <nil>
	//21 <nil>
	//10060 <nil>

More functionalities and their examples coming soon...

Benchmark

Naive approach vs Segment Tree

BenchmarkNaive2-4                   5000            370691 ns/op
BenchmarkNaive100-4                 2000            959208 ns/op
BenchmarkNaive10000-4                 20          90091228 ns/op
BenchmarkNaive100000-4                 1        1003322923 ns/op
BenchmarkTree2-4                    2000            828003 ns/op
BenchmarkTree100-4                   300           4318972 ns/op
BenchmarkTree10000-4                 100          12195815 ns/op
BenchmarkTree100000-4                100          15319705 ns/op

TODOs

Make it work for other types, at least in64 and float64
More/better Benchmarks

ideahitme/segment