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Segment Tree implementation (#45)

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* added segment tree implementation - supports custom operation

* added readme for segment tree
This commit is contained in:
Vignesh Manoharan
2018-06-04 09:02:34 +05:30
committed by Oleksii Trekhleb
parent beb8501aca
commit 2e5fd8d583
3 changed files with 294 additions and 0 deletions
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src/data-structures/tree/segment-tree/__test__/SegmentTree.test.js Normal file
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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);
expect(segTree.array.sort()).toEqual(array.sort());
expect(segTree.n).toBe(7);
});
it('check specific tree indices', () => {
const array = [1, 2, 5, 3, 4, 6, 2];
const segTree = 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)));
});
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);
// 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)));
});
it('check query', () => {
const array = [1, 2, 5, 3, 4, 6, 2];
const segTree = 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);
});
it('check update using queries', () => {
const array = [1, 2, 5, 3, 4, 6, 2];
const segTree = new SegmentTree(array, Math.min, 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)));
}
});
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);
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));
}
});
it('check default is rmq', () => {
const array = [3, 7, 2, 5, 4, 3, 8, 1];
const segTree = new SegmentTree(array);
const testRanges = [[0, 7], [3, 7], [2, 5], [4, 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)));
}
segTree.update(0, 1);
array[0] = 1;
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)));
}
});
});