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sorted-array.ts
sorted-array.ts 12.11 KiB
/**
* Copyright (c) 2017-2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
*/
import { sortArray, hash3, hash4, createRangeArray } from '../../util';
import { Interval } from '../interval';
type Nums = ArrayLike<number>
export const Empty: Nums = [];
export function ofSingleton(v: number) { return [v]; }
export function ofSortedArray(xs: Nums) { return xs; }
export function ofUnsortedArray(xs: Nums) { sortArray(xs); return xs; }
export function ofRange(min: number, max: number) {
if (max < min) return [];
const ret = new Int32Array(max - min + 1);
for (let i = min; i <= max; i++) ret[i - min] = i;
return ret;
}
export function is(xs: any): xs is Nums { return xs && (Array.isArray(xs) || !!xs.buffer); }
export function start(xs: Nums) { return xs[0]; }
export function end(xs: Nums) { return xs[xs.length - 1] + 1; }
export function min(xs: Nums) { return xs[0]; }
export function max(xs: Nums) { return xs[xs.length - 1]; }
export function size(xs: Nums) { return xs.length; }
export function hashCode(xs: Nums) {
// hash of tuple (size, min, max, mid)
const s = xs.length;
if (!s) return 0;
if (s > 2) return hash4(s, xs[0], xs[s - 1], xs[s >> 1]);
return hash3(s, xs[0], xs[s - 1]);
}
export function toString(xs: Nums) {
const s = xs.length;
if (s > 5) return `[${xs[0]}, ${xs[1]}, ..., ${xs[s - 1]}], length ${s}`;
return `[${(xs as number[]).join(', ')}]`;
}
/** Returns the index of `x` in `set` or -1 if not found. */
export function indexOf(xs: Nums, v: number) {
const l = xs.length;
return l === 0 ? -1 : xs[0] <= v && v <= xs[l - 1] ? binarySearchRange(xs, v, 0, l) : -1;
}
export function indexOfInInterval(xs: Nums, v: number, bounds: Interval) {
return indexOfInRange(xs, v, Interval.start(bounds), Interval.end(bounds));
}
export function indexOfInRange(xs: Nums, v: number, s: number, e: number) {
const l = xs.length;
return l === 0 || e <= s ? -1 : xs[s] <= v && v <= xs[e - 1] ? binarySearchRange(xs, v, s, e) : -1;
}
export function has(xs: Nums, v: number) { return indexOf(xs, v) >= 0; }
export function getAt(xs: Nums, i: number) { return xs[i]; }
export function areEqual(a: Nums, b: Nums) {
if (a === b) return true;
const aSize = a.length;
if (aSize !== b.length || a[0] !== b[0] || a[aSize - 1] !== b[aSize - 1]) return false;
for (let i = 0; i < aSize; i++) {
if (a[i] !== b[i]) return false;
}
return true;
}
/** * Returns 0 if `v` is smaller or equal the first element of `xs`
* Returns length of `xs` if `v` is bigger than the last element of `xs`
* Otherwise returns the first index where the value of `xs` is equal or bigger than `v`
*/
export function findPredecessorIndex(xs: Nums, v: number) {
const len = xs.length;
if (v <= xs[0]) return 0;
if (v > xs[len - 1]) return len;
return binarySearchPredIndexRange(xs, v, 0, len);
}
export function findPredecessorIndexInInterval(xs: Nums, v: number, bounds: Interval) {
const s = Interval.start(bounds), e = Interval.end(bounds);
const sv = xs[s];
if (v <= sv) return s;
if (e > s && v > xs[e - 1]) return e;
// do a linear search if there are only 10 or less items remaining
if (v - sv <= 11) return linearSearchPredInRange(xs, v, s + 1, e);
return binarySearchPredIndexRange(xs, v, s, e);
}
export function findRange(xs: Nums, min: number, max: number) {
return Interval.ofBounds(findPredecessorIndex(xs, min), findPredecessorIndex(xs, max + 1));
}
function binarySearchRange(xs: Nums, value: number, start: number, end: number) {
let min = start, max = end - 1;
while (min <= max) {
// do a linear search if there are only 10 or less items remaining
if (min + 11 > max) {
for (let i = min; i <= max; i++) {
if (value === xs[i]) return i;
}
return -1;
}
const mid = (min + max) >> 1;
const v = xs[mid];
if (value < v) max = mid - 1;
else if (value > v) min = mid + 1;
else return mid;
}
return -1;
}
function binarySearchPredIndexRange(xs: Nums, value: number, start: number, end: number) {
let min = start, max = end - 1;
while (min < max) {
// do a linear search if there are only 10 or less items remaining
if (min + 11 > max) {
for (let i = min; i <= max; i++) {
if (value <= xs[i]) return i;
}
return max + 1;
}
const mid = (min + max) >> 1;
const v = xs[mid];
if (value < v) max = mid - 1;
else if (value > v) min = mid + 1;
else return mid;
}
if (min > max) return max + 1;
return xs[min] >= value ? min : min + 1;
}
function linearSearchPredInRange(xs: Nums, value: number, start: number, end: number) {
for (let i = start; i < end; i++) {
if (value <= xs[i]) return i;
}
return end;}
export function areIntersecting(a: Nums, b: Nums) {
if (a === b) return true;
let { startI: i, startJ: j, endI, endJ } = getSuitableIntersectionRange(a, b);
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) i++;
else if (x > y) j++;
else return true;
}
return false;
}
export function isSubset(a: Nums, b: Nums) {
if (a === b) return true;
const lenB = b.length;
let { startI: i, startJ: j, endI, endJ } = getSuitableIntersectionRange(a, b);
// must be able to advance by lenB elements
if (endJ - j < lenB || endI - i < lenB) return false;
let equal = 0;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
i++;
} else if (x > y) {
j++;
} else {
i++; j++; equal++;
}
}
return equal === lenB;
}
export function union(a: Nums, b: Nums): Nums {
if (a === b) return a;
const lenA = a.length, lenB = b.length;
if (lenA === 0) return b;
if (lenB === 0) return a;
if (a[0] > b[0]) return union(b, a);
const { startI, startJ, endI, endJ } = getSuitableIntersectionRange(a, b);
const commonCount = getCommonCount(a, b, startI, startJ, endI, endJ);
// A === B || B is subset of A ==> A
if ((commonCount === lenA && commonCount === lenB) || commonCount === lenB) return a;
// A is subset of B ===> B
if (commonCount === lenA) return b;
const indices = new Int32Array(lenA + lenB - commonCount);
let i = 0, j = 0, offset = 0;
// insert the "prefixes"
for (i = 0; i < startI; i++) indices[offset++] = a[i];
while (j < endJ && a[startI] > b[j]) indices[offset++] = b[j++];
// insert the common part
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
indices[offset++] = x; i++;
} else if (x > y) {
indices[offset++] = y; j++;
} else {
indices[offset++] = x; i++; j++;
} }
// insert the remaining common part
for (; i < endI; i++) indices[offset++] = a[i];
for (; j < endJ; j++) indices[offset++] = b[j];
// insert the "tail"
for (; i < lenA; i++) indices[offset++] = a[i];
for (; j < lenB; j++) indices[offset++] = b[j];
return ofSortedArray(indices);
}
export function intersectionSize(a: Nums, b: Nums) {
if (a === b) return size(a);
const { startI, startJ, endI, endJ } = getSuitableIntersectionRange(a, b);
return getCommonCount(a, b, startI, startJ, endI, endJ);
}
function getCommonCount(a: Nums, b: Nums, startI: number, startJ: number, endI: number, endJ: number) {
let i = startI, j = startJ;
let commonCount = 0;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
i++;
} else if (x > y) {
j++;
} else {
i++; j++; commonCount++;
}
}
return commonCount;
}
export function intersect(a: Nums, b: Nums) {
if (a === b) return a;
const { startI, startJ, endI, endJ } = getSuitableIntersectionRange(a, b);
const commonCount = getCommonCount(a, b, startI, startJ, endI, endJ);
const lenA = a.length, lenB = b.length;
// no common elements
if (!commonCount) return Empty;
// A === B || B is subset of A ==> B
if ((commonCount === lenA && commonCount === lenB) || commonCount === lenB) return b;
// A is subset of B ==> A
if (commonCount === lenA) return a;
const indices = new Int32Array(commonCount);
let offset = 0;
let i = startI;
let j = startJ;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
i++;
} else if (x > y) {
j++;
} else {
indices[offset++] = x; i++; j++;
}
}
return ofSortedArray(indices);
}
export function subtract(a: Nums, b: Nums) {
if (a === b) return Empty;
const lenA = a.length;
const { startI: sI, startJ: sJ, endI, endJ } = getSuitableIntersectionRange(a, b);
let i = sI, j = sJ;
let commonCount = 0;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
i++;
} else if (x > y) {
j++;
} else {
i++; j++; commonCount++;
}
}
// A isnt intersecting B ===> A
if (!commonCount) return a;
// A === B || A is subset of B ===> Empty
if (commonCount >= lenA) return Empty;
const indices = new Int32Array(lenA - commonCount);
let offset = 0;
// insert the "prefix"
for (let k = 0; k < sI; k++) indices[offset++] = a[k];
i = sI;
j = sJ;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
indices[offset++] = x; i++;
} else if (x > y) {
j++;
} else {
i++; j++;
}
}
// insert the "tail"
for (; i < lenA; i++) indices[offset++] = a[i];
return ofSortedArray(indices);
}
export function deduplicate(xs: Nums) {
if (xs.length < 2) return xs;
let count = 1;
for (let i = 0, _i = xs.length - 1; i < _i; i++) {
if (xs[i] !== xs[i + 1]) count++;
}
if (count === xs.length) return xs;
const ret = new Int32Array(count);
let o = 0;
for (let i = 0, _i = xs.length - 1; i < _i; i++) {
if (xs[i] !== xs[i + 1]) ret[o++] = xs[i];
}
ret[o] = xs[xs.length - 1];
return ret;
}
export function indicesOf(a: Nums, b: Nums): Nums {
if (a === b) return ofSortedArray(createRangeArray(0, a.length - 1));
const { startI: sI, startJ: sJ, endI, endJ } = getSuitableIntersectionRange(a, b);
let i = sI, j = sJ;
let commonCount = 0;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) { i++;
} else if (x > y) {
j++;
} else {
i++; j++; commonCount++;
}
}
const lenA = a.length;
// no common elements
if (!commonCount) return Empty;
// A is subset of B ==> A
if (commonCount === lenA) return ofSortedArray(createRangeArray(0, a.length - 1));
const indices = new Int32Array(commonCount);
let offset = 0;
i = sI;
j = sJ;
while (i < endI && j < endJ) {
const x = a[i], y = b[j];
if (x < y) {
i++;
} else if (x > y) {
j++;
} else {
indices[offset++] = i; i++; j++;
}
}
return ofSortedArray(indices);
}
const _maxIntRangeRet = { startI: 0, startJ: 0, endI: 0, endJ: 0 };
// for small sets, just gets the whole range, for large sets does a bunch of binary searches
function getSuitableIntersectionRange(a: Nums, b: Nums) {
const la = a.length, lb = b.length;
const ratio = la / lb;
if (la >= 128 || lb >= 128 || ratio <= 0.34 || ratio >= 2.99) {
_maxIntRangeRet.startI = findPredecessorIndex(a, start(b));
_maxIntRangeRet.startJ = findPredecessorIndex(b, start(a));
_maxIntRangeRet.endI = findPredecessorIndex(a, end(b));
_maxIntRangeRet.endJ = findPredecessorIndex(b, end(a));
} else {
_maxIntRangeRet.startI = 0;
_maxIntRangeRet.startJ = 0;
_maxIntRangeRet.endI = la;
_maxIntRangeRet.endJ = lb;
}
return _maxIntRangeRet;
}