mirror of
https://github.moeyy.xyz/https://github.com/trekhleb/javascript-algorithms.git
synced 2024-12-26 23:21:18 +08:00
Refactor segment tree implementation.
This commit is contained in:
Oleksii Trekhleb
parent
5784a4a95b
commit
434a5649cb
@ -32,6 +32,7 @@ the data.
|
||||
* [Binary Search Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
|
||||
* [AVL Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
|
||||
* [Red-Black Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/red-black-tree)
|
||||
* [Segment Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/segment-tree) - with min/max/sum range queries examples
|
||||
* [Graph](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (both directed and undirected)
|
||||
* [Disjoint Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/disjoint-set)
|
||||
|
||||
|
||||
@ -1,41 +1,23 @@
|
||||
# Segment Tree
|
||||
|
||||
A segment tree is a data structure designed to perform
|
||||
certain array operations efficiently - especially those
|
||||
involving range queries.
|
||||
In computer science, a segment tree also known as a statistic tree
|
||||
is a tree data structure used for storing information about intervals,
|
||||
or segments. It allows querying which of the stored segments contain
|
||||
a given point. It is, in principle, a static structure; that is,
|
||||
it's a structure that cannot be modified once it's built. A similar
|
||||
data structure is the interval tree.
|
||||
|
||||
A common application is the [Range Minimum Query](https://en.wikipedia.org/wiki/Range_minimum_query) (RMQ) problem,
|
||||
where we are given an array of numbers and need to
|
||||
support operations of updating values of the array and
|
||||
finding the minimum of a contiguous subarray.
|
||||
A segment tree implementation for the RMQ problem
|
||||
takes `O(n)` to initialize, and `O(log n)` per query or
|
||||
update. The "minimum" operation can be replaced by any
|
||||
array operation (such as sum).
|
||||
|
||||
A segment tree is a binary tree with contiguous
|
||||
sub-arrays as nodes. The root of the tree represents the
|
||||
A segment tree is a binary tree. The root of the tree represents the
|
||||
whole array. The two children of the root represent the
|
||||
first and second halves of the array. Similarly, the
|
||||
children of each node corresponds to the two halves of
|
||||
the array corresponding to the node. If the array has
|
||||
size `n`, we can prove that the segment tree has size at
|
||||
most `4n`. Each node stores the minimum of its
|
||||
corresponding sub-array.
|
||||
|
||||
In the implementation, we do not explicitly store this
|
||||
tree structure, but represent it using a `4n` sized array.
|
||||
The left child of node i is `2i+1` and the right child
|
||||
is `2i+2`. This is a standard way to represent segment
|
||||
trees, and lends itself to an efficient implementation.
|
||||
the array corresponding to the node.
|
||||
|
||||
We build the tree bottom up, with the value of each node
|
||||
being the minimum of its children's values. This will
|
||||
take time `O(n)`, with one operation for each node. Updates
|
||||
are also done bottom up, with values being recomputed
|
||||
starting from the leaf, and up to the root. The number
|
||||
being the "minimum" (or any other function) of its children's values. This will
|
||||
take `O(n log n)` time. The number
|
||||
of operations done is the height of the tree, which
|
||||
is `O(log n)`. To answer queries, each node splits the
|
||||
is `O(log n)`. To do range queries, each node splits the
|
||||
query into two parts, one sub-query for each child.
|
||||
If a query contains the whole subarray of a node, we
|
||||
can use the precomputed value at the node. Using this
|
||||
@ -44,6 +26,21 @@ operations are done.
|
||||
|
||||
|
||||
|
||||
## Application
|
||||
|
||||
A segment tree is a data structure designed to perform
|
||||
certain array operations efficiently - especially those
|
||||
involving range queries.
|
||||
|
||||
Applications of the segment tree are in the areas of computational geometry,
|
||||
and geographic information systems.
|
||||
|
||||
Current implementation of Segment Tree implies that you may
|
||||
pass any binary (with two input params) function to it and
|
||||
thus you're able to do range query for variety of functions.
|
||||
In tests you may fins examples of doing `min`, `max` and `sam` range
|
||||
queries on SegmentTree.
|
||||
|
||||
## References
|
||||
|
||||
- [Wikipedia](https://en.wikipedia.org/wiki/Segment_tree)
|
||||
|
||||
@ -1,149 +1,168 @@
|
||||
/**
|
||||
* Segment Tree implementation for Range Query data structure
|
||||
* Tracks a array of numbers. 0 indexed
|
||||
* operation is a binary function (eg sum, min) - needs to be associative
|
||||
* identity is the identity of the operation
|
||||
* i.e, operation(x, identity) = x (eg 0 for sum, Infinity for min)
|
||||
* Supports methods
|
||||
* update(index, val) - set value of index
|
||||
* query(l, r) - finds operation(values in range [l, r]) (both inclusive)
|
||||
*
|
||||
* As is customary, we store the tree implicitly with i being the parent of 2i, 2i+1.
|
||||
*/
|
||||
import isPowerOfTwo from '../../../algorithms/math/is-power-of-two/isPowerOfTwo';
|
||||
|
||||
export default class SegmentTree {
|
||||
/**
|
||||
* array initialises the numbers
|
||||
* @param {number[]} array
|
||||
* @param {number[]} inputArray
|
||||
* @param {function} operation - binary function (i.e. sum, min)
|
||||
* @param {number} operationFallback - operation fallback value (i.e. 0 for sum, Infinity for min)
|
||||
*/
|
||||
constructor(array, operation, identity) {
|
||||
this.n = array.length;
|
||||
this.array = array;
|
||||
this.tree = new Array(4 * this.n);
|
||||
|
||||
constructor(inputArray, operation, operationFallback) {
|
||||
this.inputArray = inputArray;
|
||||
this.operation = operation;
|
||||
this.identity = identity;
|
||||
this.operationFallback = operationFallback;
|
||||
|
||||
// use Range Min Query by default
|
||||
if (this.operation === undefined) {
|
||||
this.operation = Math.min;
|
||||
this.identity = Infinity;
|
||||
}
|
||||
// Init array representation of segment tree.
|
||||
this.segmentTree = this.initSegmentTree(this.inputArray);
|
||||
|
||||
|
||||
this.build();
|
||||
this.buildSegmentTree();
|
||||
}
|
||||
|
||||
/**
|
||||
* Stub for recursive call
|
||||
* @param {number[]} inputArray
|
||||
* @return {number[]}
|
||||
*/
|
||||
build() {
|
||||
this.buildRec(1, 0, this.n - 1);
|
||||
}
|
||||
initSegmentTree(inputArray) {
|
||||
let segmentTreeArrayLength;
|
||||
const inputArrayLength = inputArray.length;
|
||||
|
||||
/**
|
||||
* Left child index
|
||||
* @param {number} root
|
||||
*/
|
||||
left(root) {
|
||||
return 2 * root;
|
||||
}
|
||||
|
||||
/**
|
||||
* Right child index
|
||||
* @param {number} root
|
||||
*/
|
||||
right(root) {
|
||||
return (2 * root) + 1;
|
||||
}
|
||||
|
||||
/**
|
||||
* root is the index in the tree, [l,r] (inclusive) is the current array segment being built
|
||||
* @param {number} root
|
||||
* @param {number} l
|
||||
* @param {number} r
|
||||
*/
|
||||
buildRec(root, l, r) {
|
||||
if (l === r) {
|
||||
this.tree[root] = this.array[l];
|
||||
if (isPowerOfTwo(inputArrayLength)) {
|
||||
// If original array length is a power of two.
|
||||
segmentTreeArrayLength = (2 * inputArrayLength) - 1;
|
||||
} else {
|
||||
const mid = Math.floor((l + r) / 2);
|
||||
// build left and right nodes
|
||||
this.buildRec(this.left(root), l, mid);
|
||||
this.buildRec(this.right(root), mid + 1, r);
|
||||
this.tree[root] = this.operation(this.tree[this.left(root)], this.tree[this.right(root)]);
|
||||
// If original array length is not a power of two then we need to find
|
||||
// next number that is a power of two and use it to calculate
|
||||
// tree array size. This is happens because we need to fill empty children
|
||||
// in perfect binary tree with nulls.And those nulls need extra space.
|
||||
const currentPower = Math.floor(Math.log2(inputArrayLength));
|
||||
const nextPower = currentPower + 1;
|
||||
const nextPowerOfTwoNumber = 2 ** nextPower;
|
||||
segmentTreeArrayLength = (2 * nextPowerOfTwoNumber) - 1;
|
||||
}
|
||||
|
||||
return new Array(segmentTreeArrayLength).fill(null);
|
||||
}
|
||||
|
||||
/**
|
||||
* Stub for recursive call
|
||||
* @param {number} lindex
|
||||
* @param {number} rindex
|
||||
* Build segment tree.
|
||||
*/
|
||||
query(lindex, rindex) {
|
||||
return this.queryRec(1, lindex, rindex, 0, this.n - 1);
|
||||
buildSegmentTree() {
|
||||
const leftIndex = 0;
|
||||
const rightIndex = this.inputArray.length - 1;
|
||||
const position = 0;
|
||||
this.buildTreeRecursively(leftIndex, rightIndex, position);
|
||||
}
|
||||
|
||||
/**
|
||||
* [lindex, rindex] is the query region
|
||||
* [l,r] is the current region being processed
|
||||
* Guaranteed that [lindex,rindex] contained in [l,r]
|
||||
* @param {number} root
|
||||
* @param {number} lindex
|
||||
* @param {number} rindex
|
||||
* @param {number} l
|
||||
* @param {number} r
|
||||
* Build segment tree recursively.
|
||||
*
|
||||
* @param {number} leftInputIndex
|
||||
* @param {number} rightInputIndex
|
||||
* @param {number} position
|
||||
*/
|
||||
queryRec(root, lindex, rindex, l, r) {
|
||||
// console.log(root, lindex, rindex, l, r);
|
||||
if (lindex > rindex) {
|
||||
// happens when mid+1 > r - no segment
|
||||
return this.identity;
|
||||
buildTreeRecursively(leftInputIndex, rightInputIndex, position) {
|
||||
// If low input index and high input index are equal that would mean
|
||||
// the we have finished splitting and we are already came to the leaf
|
||||
// of the segment tree. We need to copy this leaf value from input
|
||||
// array to segment tree.
|
||||
if (leftInputIndex === rightInputIndex) {
|
||||
this.segmentTree[position] = this.inputArray[leftInputIndex];
|
||||
return;
|
||||
}
|
||||
if (l === lindex && r === rindex) {
|
||||
// query region matches current region - use tree value
|
||||
return this.tree[root];
|
||||
}
|
||||
const mid = Math.floor((l + r) / 2);
|
||||
// get left and right results and combine
|
||||
const leftResult = this.queryRec(this.left(root), lindex, Math.min(rindex, mid), l, mid);
|
||||
const rightResult = this.queryRec(
|
||||
this.right(root), Math.max(mid + 1, lindex), rindex,
|
||||
mid + 1, r,
|
||||
|
||||
// Split input array on two halves and process them recursively.
|
||||
const middleIndex = Math.floor((leftInputIndex + rightInputIndex) / 2);
|
||||
// Process left half of the input array.
|
||||
this.buildTreeRecursively(leftInputIndex, middleIndex, this.getLeftChildIndex(position));
|
||||
// Process right half of the input array.
|
||||
this.buildTreeRecursively(middleIndex + 1, rightInputIndex, this.getRightChildIndex(position));
|
||||
|
||||
// Once every tree leaf is not empty we're able to build tree bottom up using
|
||||
// provided operation function.
|
||||
this.segmentTree[position] = this.operation(
|
||||
this.segmentTree[this.getLeftChildIndex(position)],
|
||||
this.segmentTree[this.getRightChildIndex(position)],
|
||||
);
|
||||
return this.operation(leftResult, rightResult);
|
||||
}
|
||||
|
||||
/**
|
||||
* Set array[index] to value
|
||||
* @param {number} index
|
||||
* @param {number} value
|
||||
* Do range query on segment tree in context of this.operation function.
|
||||
*
|
||||
* @param {number} queryLeftIndex
|
||||
* @param {number} queryRightIndex
|
||||
* @return {number}
|
||||
*/
|
||||
update(index, value) {
|
||||
this.array[index] = value;
|
||||
this.updateRec(1, index, value, 0, this.n - 1);
|
||||
rangeQuery(queryLeftIndex, queryRightIndex) {
|
||||
const leftIndex = 0;
|
||||
const rightIndex = this.inputArray.length - 1;
|
||||
const position = 0;
|
||||
|
||||
return this.rangeQueryRecursive(
|
||||
queryLeftIndex,
|
||||
queryRightIndex,
|
||||
leftIndex,
|
||||
rightIndex,
|
||||
position,
|
||||
);
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {number} root
|
||||
* @param {number} index
|
||||
* @param {number} value
|
||||
* @param {number} l
|
||||
* @param {number} r
|
||||
* Do range query on segment tree recursively in context of this.operation function.
|
||||
*
|
||||
* @param {number} queryLeftIndex - left index of the query
|
||||
* @param {number} queryRightIndex - right index of the query
|
||||
* @param {number} leftIndex - left index of input array segment
|
||||
* @param {number} rightIndex - right index of input array segment
|
||||
* @param {number} position - root position in binary tree
|
||||
* @return {number}
|
||||
*/
|
||||
updateRec(root, index, value, l, r) {
|
||||
if (l === r) {
|
||||
// we are at tree node containing array[index]
|
||||
this.tree[root] = value;
|
||||
} else {
|
||||
const mid = Math.floor((l + r) / 2);
|
||||
// update whichever child index is in, update this.tree[root]
|
||||
if (index <= mid) {
|
||||
this.updateRec(this.left(root), index, value, l, mid);
|
||||
} else {
|
||||
this.updateRec(this.right(root), index, value, mid + 1, r);
|
||||
}
|
||||
this.tree[root] = this.operation(this.tree[this.left(root)], this.tree[this.right(root)]);
|
||||
rangeQueryRecursive(queryLeftIndex, queryRightIndex, leftIndex, rightIndex, position) {
|
||||
if (queryLeftIndex <= leftIndex && queryRightIndex >= rightIndex) {
|
||||
// Total overlap.
|
||||
return this.segmentTree[position];
|
||||
}
|
||||
|
||||
if (queryLeftIndex > rightIndex || queryRightIndex < leftIndex) {
|
||||
// No overlap.
|
||||
return this.operationFallback;
|
||||
}
|
||||
|
||||
// Partial overlap.
|
||||
const middleIndex = Math.floor((leftIndex + rightIndex) / 2);
|
||||
|
||||
const leftOperationResult = this.rangeQueryRecursive(
|
||||
queryLeftIndex,
|
||||
queryRightIndex,
|
||||
leftIndex,
|
||||
middleIndex,
|
||||
this.getLeftChildIndex(position),
|
||||
);
|
||||
|
||||
const rightOperationResult = this.rangeQueryRecursive(
|
||||
queryLeftIndex,
|
||||
queryRightIndex,
|
||||
middleIndex + 1,
|
||||
rightIndex,
|
||||
this.getRightChildIndex(position),
|
||||
);
|
||||
|
||||
return this.operation(leftOperationResult, rightOperationResult);
|
||||
}
|
||||
|
||||
/**
|
||||
* Left child index.
|
||||
* @param {number} parentIndex
|
||||
* @return {number}
|
||||
*/
|
||||
getLeftChildIndex(parentIndex) {
|
||||
return (2 * parentIndex) + 1;
|
||||
}
|
||||
|
||||
/**
|
||||
* Right child index.
|
||||
* @param {number} parentIndex
|
||||
* @return {number}
|
||||
*/
|
||||
getRightChildIndex(parentIndex) {
|
||||
return (2 * parentIndex) + 2;
|
||||
}
|
||||
}
|
||||
|
||||
@ -1,136 +1,101 @@
|
||||
import SegmentTree from '../SegmentTree';
|
||||
|
||||
describe('SegmentTree', () => {
|
||||
it('create RMQ SegmentTree', () => {
|
||||
const array = [1, 2, 5, 3, 4, 6, 2];
|
||||
const segTree = new SegmentTree(array, Math.min, Infinity);
|
||||
it('should build tree for input array #0 with length of power of two', () => {
|
||||
const array = [-1, 2];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
expect(segTree.array.sort()).toEqual(array.sort());
|
||||
expect(segTree.n).toBe(7);
|
||||
expect(segmentTree.segmentTree).toEqual([-1, -1, 2]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * array.length) - 1);
|
||||
});
|
||||
|
||||
it('check specific tree indices', () => {
|
||||
const array = [1, 2, 5, 3, 4, 6, 2];
|
||||
const segTree = new SegmentTree(array, Math.min, Infinity);
|
||||
it('should build tree for input array #1 with length of power of two', () => {
|
||||
const array = [-1, 2, 4, 0];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
// 1 - [0,6]
|
||||
// 2 - [0,3] 3 - [4,6]
|
||||
// 4 - [0,1] 5 - [2,3] 6 - [4,5] 7 - [6,6]
|
||||
// 8 - [0,0] 9 - [1,1] 10 - [2,2] 11 - [3,3] 12 - [4,4] 13 - [5,5]
|
||||
expect(segTree.tree.slice(8, 14)).toEqual(array.slice(0, 6));
|
||||
expect(segTree.tree[7]).toBe(array[6]);
|
||||
expect(segTree.tree[1]).toBe(Math.min(...array));
|
||||
expect(segTree.tree[2]).toBe(Math.min(...array.slice(0, 4)));
|
||||
expect(segTree.tree[6]).toBe(Math.min(...array.slice(4, 6)));
|
||||
expect(segmentTree.segmentTree).toEqual([-1, -1, 0, -1, 2, 4, 0]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * array.length) - 1);
|
||||
});
|
||||
|
||||
it('check another tree for n=8', () => {
|
||||
const array = [5, 4, 2, 1, 4, 1, 3, 1];
|
||||
const segTree = new SegmentTree(array, Math.min, Infinity);
|
||||
it('should build tree for input array #0 with length not of power of two', () => {
|
||||
const array = [0, 1, 2];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
// 1 - [0,7]
|
||||
// 2 - [0,3] 3 - [4,7]
|
||||
// 4 - [0,1] 5 - [2,3] 6 - [4,5] 7 - [6,7]
|
||||
// 8 - [0,0] 9 - [1,1] 10 - [2,2] 11 - [3,3] 12 - [4,4] 13 - [5,5] 14 - [6,6] 15 - [7,7]
|
||||
expect(segTree.tree.slice(8, 16)).toEqual(array.slice(0, 8));
|
||||
expect(segTree.tree[7]).toBe(Math.min(...array.slice(6, 8)));
|
||||
expect(segTree.tree[1]).toBe(Math.min(...array));
|
||||
expect(segTree.tree[2]).toBe(Math.min(...array.slice(0, 4)));
|
||||
expect(segTree.tree[6]).toBe(Math.min(...array.slice(4, 6)));
|
||||
expect(segmentTree.segmentTree).toEqual([0, 0, 2, 0, 1, null, null]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * 4) - 1);
|
||||
});
|
||||
|
||||
it('check query', () => {
|
||||
const array = [1, 2, 5, 3, 4, 6, 2];
|
||||
const segTree = new SegmentTree(array, Math.min, Infinity);
|
||||
it('should build tree for input array #1 with length not of power of two', () => {
|
||||
const array = [-1, 3, 4, 0, 2, 1];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
const testRanges = [[0, 6], [0, 4], [2, 6], [3, 3], [4, 5], [6, 6], [1, 5], [1, 4]];
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
expect(segTree.query(0, 0)).toBe(1);
|
||||
expect(segmentTree.segmentTree).toEqual([
|
||||
-1, -1, 0, -1, 4, 0, 1, -1, 3, null, null, 0, 2, null, null,
|
||||
]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * 8) - 1);
|
||||
});
|
||||
|
||||
it('check update using queries', () => {
|
||||
const array = [1, 2, 5, 3, 4, 6, 2];
|
||||
const segTree = new SegmentTree(array, Math.min, Infinity);
|
||||
it('should build max array', () => {
|
||||
const array = [-1, 2, 4, 0];
|
||||
const segmentTree = new SegmentTree(array, Math.max, -Infinity);
|
||||
|
||||
const testRanges = [[0, 6], [0, 4], [2, 6], [3, 3], [4, 5], [6, 6], [1, 5], [1, 4]];
|
||||
|
||||
expect(segTree.array[0]).toBe(1);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
|
||||
segTree.update(0, 3);
|
||||
array[0] = 3;
|
||||
|
||||
expect(segTree.array[0]).toBe(3);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
|
||||
segTree.update(2, 2);
|
||||
array[2] = 2;
|
||||
|
||||
expect(segTree.array[2]).toBe(2);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
expect(segmentTree.segmentTree).toEqual([4, 2, 4, -1, 2, 4, 0]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * array.length) - 1);
|
||||
});
|
||||
|
||||
it('check range sum query SegmentTree', () => {
|
||||
const array = [1, 2, 5, 3, 4, 6, 2];
|
||||
const sum = (a, b) => a + b;
|
||||
const segTree = new SegmentTree(array, sum, 0);
|
||||
it('should build sum array', () => {
|
||||
const array = [-1, 2, 4, 0];
|
||||
const segmentTree = new SegmentTree(array, (a, b) => (a + b), 0);
|
||||
|
||||
const testRanges = [[0, 6], [0, 4], [2, 6], [3, 3], [4, 5], [6, 6], [1, 5], [1, 4]];
|
||||
|
||||
expect(segTree.array[0]).toBe(1);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(array.slice(range[0], range[1] + 1).reduce(sum));
|
||||
}
|
||||
|
||||
segTree.update(0, 3);
|
||||
array[0] = 3;
|
||||
|
||||
expect(segTree.array[0]).toBe(3);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(array.slice(range[0], range[1] + 1).reduce(sum));
|
||||
}
|
||||
expect(segmentTree.segmentTree).toEqual([5, 1, 4, -1, 2, 4, 0]);
|
||||
expect(segmentTree.segmentTree.length).toBe((2 * array.length) - 1);
|
||||
});
|
||||
|
||||
it('check default is rmq', () => {
|
||||
const array = [3, 7, 2, 5, 4, 3, 8, 1];
|
||||
const segTree = new SegmentTree(array);
|
||||
it('should do min range query on power of two length array', () => {
|
||||
const array = [-1, 3, 4, 0, 2, 1];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
const testRanges = [[0, 7], [3, 7], [2, 5], [4, 4]];
|
||||
expect(segmentTree.rangeQuery(0, 5)).toBe(-1);
|
||||
expect(segmentTree.rangeQuery(0, 2)).toBe(-1);
|
||||
expect(segmentTree.rangeQuery(1, 3)).toBe(0);
|
||||
expect(segmentTree.rangeQuery(2, 4)).toBe(0);
|
||||
expect(segmentTree.rangeQuery(4, 5)).toBe(1);
|
||||
expect(segmentTree.rangeQuery(2, 2)).toBe(4);
|
||||
});
|
||||
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
it('should do min range query on not power of two length array', () => {
|
||||
const array = [-1, 2, 4, 0];
|
||||
const segmentTree = new SegmentTree(array, Math.min, Infinity);
|
||||
|
||||
segTree.update(0, 1);
|
||||
array[0] = 1;
|
||||
expect(segmentTree.rangeQuery(0, 4)).toBe(-1);
|
||||
expect(segmentTree.rangeQuery(0, 1)).toBe(-1);
|
||||
expect(segmentTree.rangeQuery(1, 3)).toBe(0);
|
||||
expect(segmentTree.rangeQuery(1, 2)).toBe(2);
|
||||
expect(segmentTree.rangeQuery(2, 3)).toBe(0);
|
||||
expect(segmentTree.rangeQuery(2, 2)).toBe(4);
|
||||
});
|
||||
|
||||
expect(segTree.array[0]).toBe(1);
|
||||
for (let i = 0; i < testRanges.length; i += 1) {
|
||||
const range = testRanges[i];
|
||||
expect(segTree.query(range[0], range[1]))
|
||||
.toBe(Math.min(...array.slice(range[0], range[1] + 1)));
|
||||
}
|
||||
it('should do max range query', () => {
|
||||
const array = [-1, 3, 4, 0, 2, 1];
|
||||
const segmentTree = new SegmentTree(array, Math.max, -Infinity);
|
||||
|
||||
expect(segmentTree.rangeQuery(0, 5)).toBe(4);
|
||||
expect(segmentTree.rangeQuery(0, 1)).toBe(3);
|
||||
expect(segmentTree.rangeQuery(1, 3)).toBe(4);
|
||||
expect(segmentTree.rangeQuery(2, 4)).toBe(4);
|
||||
expect(segmentTree.rangeQuery(4, 5)).toBe(2);
|
||||
expect(segmentTree.rangeQuery(3, 3)).toBe(0);
|
||||
});
|
||||
|
||||
it('should do sum range query', () => {
|
||||
const array = [-1, 3, 4, 0, 2, 1];
|
||||
const segmentTree = new SegmentTree(array, (a, b) => (a + b), 0);
|
||||
|
||||
expect(segmentTree.rangeQuery(0, 5)).toBe(9);
|
||||
expect(segmentTree.rangeQuery(0, 1)).toBe(2);
|
||||
expect(segmentTree.rangeQuery(1, 3)).toBe(7);
|
||||
expect(segmentTree.rangeQuery(2, 4)).toBe(6);
|
||||
expect(segmentTree.rangeQuery(4, 5)).toBe(3);
|
||||
expect(segmentTree.rangeQuery(3, 3)).toBe(0);
|
||||
});
|
||||
});
|
||||
|
||||
Loading…
Reference in New Issue
Block a user