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- /**
- * Default minimum size of a run.
- */
- const DEFAULT_MIN_MERGE = 32;
- /**
- * Minimum ordered subsequece required to do galloping.
- */
- const DEFAULT_MIN_GALLOPING = 7;
- /**
- * Default tmp storage length. Can increase depending on the size of the
- * smallest run to merge.
- */
- const DEFAULT_TMP_STORAGE_LENGTH = 256;
- /**
- * Pre-computed powers of 10 for efficient lexicographic comparison of
- * small integers.
- */
- const POWERS_OF_TEN = [1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9]
- /**
- * Estimate the logarithm base 10 of a small integer.
- *
- * @param {number} x - The integer to estimate the logarithm of.
- * @return {number} - The estimated logarithm of the integer.
- */
- function log10(x) {
- if (x < 1e5) {
- if (x < 1e2) {
- return x < 1e1 ? 0 : 1;
- }
- if (x < 1e4) {
- return x < 1e3 ? 2 : 3;
- }
- return 4;
- }
- if (x < 1e7) {
- return x < 1e6 ? 5 : 6;
- }
- if (x < 1e9) {
- return x < 1e8 ? 7 : 8;
- }
- return 9;
- }
- /**
- * Default alphabetical comparison of items.
- *
- * @param {string|object|number} a - First element to compare.
- * @param {string|object|number} b - Second element to compare.
- * @return {number} - A positive number if a.toString() > b.toString(), a
- * negative number if .toString() < b.toString(), 0 otherwise.
- */
- function alphabeticalCompare(a, b) {
- if (a === b) {
- return 0;
- }
- if (~~a === a && ~~b === b) {
- if (a === 0 || b === 0) {
- return a < b ? -1 : 1;
- }
- if (a < 0 || b < 0) {
- if (b >= 0) {
- return -1;
- }
- if (a >= 0) {
- return 1;
- }
- a = -a;
- b = -b;
- }
- const al = log10(a);
- const bl = log10(b);
- let t = 0;
- if (al < bl) {
- a *= POWERS_OF_TEN[bl - al - 1];
- b /= 10;
- t = -1;
- } else if (al > bl) {
- b *= POWERS_OF_TEN[al - bl - 1];
- a /= 10;
- t = 1;
- }
- if (a === b) {
- return t;
- }
- return a < b ? -1 : 1;
- }
- let aStr = String(a);
- let bStr = String(b);
- if (aStr === bStr) {
- return 0;
- }
- return aStr < bStr ? -1 : 1;
- }
- /**
- * Compute minimum run length for TimSort
- *
- * @param {number} n - The size of the array to sort.
- */
- function minRunLength(n) {
- let r = 0;
- while (n >= DEFAULT_MIN_MERGE) {
- r |= (n & 1);
- n >>= 1;
- }
- return n + r;
- }
- /**
- * Counts the length of a monotonically ascending or strictly monotonically
- * descending sequence (run) starting at array[lo] in the range [lo, hi). If
- * the run is descending it is made ascending.
- *
- * @param {array} array - The array to reverse.
- * @param {number} lo - First element in the range (inclusive).
- * @param {number} hi - Last element in the range.
- * @param {function} compare - Item comparison function.
- * @return {number} - The length of the run.
- */
- function makeAscendingRun(array, lo, hi, compare) {
- let runHi = lo + 1;
- if (runHi === hi) {
- return 1;
- }
- // Descending
- if (compare(array[runHi++], array[lo]) < 0) {
- while (runHi < hi && compare(array[runHi], array[runHi - 1]) < 0) {
- runHi++;
- }
- reverseRun(array, lo, runHi);
- // Ascending
- } else {
- while (runHi < hi && compare(array[runHi], array[runHi - 1]) >= 0) {
- runHi++;
- }
- }
- return runHi - lo;
- }
- /**
- * Reverse an array in the range [lo, hi).
- *
- * @param {array} array - The array to reverse.
- * @param {number} lo - First element in the range (inclusive).
- * @param {number} hi - Last element in the range.
- */
- function reverseRun(array, lo, hi) {
- hi--;
- while (lo < hi) {
- let t = array[lo];
- array[lo++] = array[hi];
- array[hi--] = t;
- }
- }
- /**
- * Perform the binary sort of the array in the range [lo, hi) where start is
- * the first element possibly out of order.
- *
- * @param {array} array - The array to sort.
- * @param {number} lo - First element in the range (inclusive).
- * @param {number} hi - Last element in the range.
- * @param {number} start - First element possibly out of order.
- * @param {function} compare - Item comparison function.
- */
- function binaryInsertionSort(array, lo, hi, start, compare) {
- if (start === lo) {
- start++;
- }
- for (; start < hi; start++) {
- let pivot = array[start];
- // Ranges of the array where pivot belongs
- let left = lo;
- let right = start;
- /*
- * pivot >= array[i] for i in [lo, left)
- * pivot < array[i] for i in in [right, start)
- */
- while (left < right) {
- let mid = (left + right) >>> 1;
- if (compare(pivot, array[mid]) < 0) {
- right = mid;
- } else {
- left = mid + 1;
- }
- }
- /*
- * Move elements right to make room for the pivot. If there are elements
- * equal to pivot, left points to the first slot after them: this is also
- * a reason for which TimSort is stable
- */
- let n = start - left;
- // Switch is just an optimization for small arrays
- switch (n) {
- case 3:
- array[left + 3] = array[left + 2];
- /* falls through */
- case 2:
- array[left + 2] = array[left + 1];
- /* falls through */
- case 1:
- array[left + 1] = array[left];
- break;
- default:
- while (n > 0) {
- array[left + n] = array[left + n - 1];
- n--;
- }
- }
- array[left] = pivot;
- }
- }
- /**
- * Find the position at which to insert a value in a sorted range. If the range
- * contains elements equal to the value the leftmost element index is returned
- * (for stability).
- *
- * @param {number} value - Value to insert.
- * @param {array} array - The array in which to insert value.
- * @param {number} start - First element in the range.
- * @param {number} length - Length of the range.
- * @param {number} hint - The index at which to begin the search.
- * @param {function} compare - Item comparison function.
- * @return {number} - The index where to insert value.
- */
- function gallopLeft(value, array, start, length, hint, compare) {
- let lastOffset = 0;
- let maxOffset = 0;
- let offset = 1;
- if (compare(value, array[start + hint]) > 0) {
- maxOffset = length - hint;
- while (offset < maxOffset && compare(value, array[start + hint + offset]) > 0) {
- lastOffset = offset;
- offset = (offset << 1) + 1;
- if (offset <= 0) {
- offset = maxOffset;
- }
- }
- if (offset > maxOffset) {
- offset = maxOffset;
- }
- // Make offsets relative to start
- lastOffset += hint;
- offset += hint;
- // value <= array[start + hint]
- } else {
- maxOffset = hint + 1;
- while (offset < maxOffset && compare(value, array[start + hint - offset]) <= 0) {
- lastOffset = offset;
- offset = (offset << 1) + 1;
- if (offset <= 0) {
- offset = maxOffset;
- }
- }
- if (offset > maxOffset) {
- offset = maxOffset;
- }
- // Make offsets relative to start
- let tmp = lastOffset;
- lastOffset = hint - offset;
- offset = hint - tmp;
- }
- /*
- * Now array[start+lastOffset] < value <= array[start+offset], so value
- * belongs somewhere in the range (start + lastOffset, start + offset]. Do a
- * binary search, with invariant array[start + lastOffset - 1] < value <=
- * array[start + offset].
- */
- lastOffset++;
- while (lastOffset < offset) {
- let m = lastOffset + ((offset - lastOffset) >>> 1);
- if (compare(value, array[start + m]) > 0) {
- lastOffset = m + 1;
- } else {
- offset = m;
- }
- }
- return offset;
- }
- /**
- * Find the position at which to insert a value in a sorted range. If the range
- * contains elements equal to the value the rightmost element index is returned
- * (for stability).
- *
- * @param {number} value - Value to insert.
- * @param {array} array - The array in which to insert value.
- * @param {number} start - First element in the range.
- * @param {number} length - Length of the range.
- * @param {number} hint - The index at which to begin the search.
- * @param {function} compare - Item comparison function.
- * @return {number} - The index where to insert value.
- */
- function gallopRight(value, array, start, length, hint, compare) {
- let lastOffset = 0;
- let maxOffset = 0;
- let offset = 1;
- if (compare(value, array[start + hint]) < 0) {
- maxOffset = hint + 1;
- while (offset < maxOffset && compare(value, array[start + hint - offset]) < 0) {
- lastOffset = offset;
- offset = (offset << 1) + 1;
- if (offset <= 0) {
- offset = maxOffset;
- }
- }
- if (offset > maxOffset) {
- offset = maxOffset;
- }
- // Make offsets relative to start
- let tmp = lastOffset;
- lastOffset = hint - offset;
- offset = hint - tmp;
- // value >= array[start + hint]
- } else {
- maxOffset = length - hint;
- while (offset < maxOffset && compare(value, array[start + hint + offset]) >= 0) {
- lastOffset = offset;
- offset = (offset << 1) + 1;
- if (offset <= 0) {
- offset = maxOffset;
- }
- }
- if (offset > maxOffset) {
- offset = maxOffset;
- }
- // Make offsets relative to start
- lastOffset += hint;
- offset += hint;
- }
- /*
- * Now array[start+lastOffset] < value <= array[start+offset], so value
- * belongs somewhere in the range (start + lastOffset, start + offset]. Do a
- * binary search, with invariant array[start + lastOffset - 1] < value <=
- * array[start + offset].
- */
- lastOffset++;
- while (lastOffset < offset) {
- let m = lastOffset + ((offset - lastOffset) >>> 1);
- if (compare(value, array[start + m]) < 0) {
- offset = m;
- } else {
- lastOffset = m + 1;
- }
- }
- return offset;
- }
- class TimSort {
- array = null;
- compare = null;
- minGallop = DEFAULT_MIN_GALLOPING;
- length = 0;
- tmpStorageLength = DEFAULT_TMP_STORAGE_LENGTH;
- stackLength = 0;
- runStart = null;
- runLength = null;
- stackSize = 0;
- constructor(array, compare) {
- this.array = array;
- this.compare = compare;
- this.length = array.length;
- if (this.length < 2 * DEFAULT_TMP_STORAGE_LENGTH) {
- this.tmpStorageLength = this.length >>> 1;
- }
- this.tmp = new Array(this.tmpStorageLength);
- this.stackLength =
- (this.length < 120 ? 5 :
- this.length < 1542 ? 10 :
- this.length < 119151 ? 19 : 40);
- this.runStart = new Array(this.stackLength);
- this.runLength = new Array(this.stackLength);
- }
- /**
- * Push a new run on TimSort's stack.
- *
- * @param {number} runStart - Start index of the run in the original array.
- * @param {number} runLength - Length of the run;
- */
- pushRun(runStart, runLength) {
- this.runStart[this.stackSize] = runStart;
- this.runLength[this.stackSize] = runLength;
- this.stackSize += 1;
- }
- /**
- * Merge runs on TimSort's stack so that the following holds for all i:
- * 1) runLength[i - 3] > runLength[i - 2] + runLength[i - 1]
- * 2) runLength[i - 2] > runLength[i - 1]
- */
- mergeRuns() {
- while (this.stackSize > 1) {
- let n = this.stackSize - 2;
- if ((n >= 1 &&
- this.runLength[n - 1] <= this.runLength[n] + this.runLength[n + 1]) ||
- (n >= 2 &&
- this.runLength[n - 2] <= this.runLength[n] + this.runLength[n - 1])) {
- if (this.runLength[n - 1] < this.runLength[n + 1]) {
- n--;
- }
- } else if (this.runLength[n] > this.runLength[n + 1]) {
- break;
- }
- this.mergeAt(n);
- }
- }
- /**
- * Merge all runs on TimSort's stack until only one remains.
- */
- forceMergeRuns() {
- while (this.stackSize > 1) {
- let n = this.stackSize - 2;
- if (n > 0 && this.runLength[n - 1] < this.runLength[n + 1]) {
- n--;
- }
- this.mergeAt(n);
- }
- }
- /**
- * Merge the runs on the stack at positions i and i+1. Must be always be called
- * with i=stackSize-2 or i=stackSize-3 (that is, we merge on top of the stack).
- *
- * @param {number} i - Index of the run to merge in TimSort's stack.
- */
- mergeAt(i) {
- let compare = this.compare;
- let array = this.array;
- let start1 = this.runStart[i];
- let length1 = this.runLength[i];
- let start2 = this.runStart[i + 1];
- let length2 = this.runLength[i + 1];
- this.runLength[i] = length1 + length2;
- if (i === this.stackSize - 3) {
- this.runStart[i + 1] = this.runStart[i + 2];
- this.runLength[i + 1] = this.runLength[i + 2];
- }
- this.stackSize--;
- /*
- * Find where the first element in the second run goes in run1. Previous
- * elements in run1 are already in place
- */
- let k = gallopRight(array[start2], array, start1, length1, 0, compare);
- start1 += k;
- length1 -= k;
- if (length1 === 0) {
- return;
- }
- /*
- * Find where the last element in the first run goes in run2. Next elements
- * in run2 are already in place
- */
- length2 = gallopLeft(array[start1 + length1 - 1], array, start2, length2, length2 - 1, compare);
- if (length2 === 0) {
- return;
- }
- /*
- * Merge remaining runs. A tmp array with length = min(length1, length2) is
- * used
- */
- if (length1 <= length2) {
- this.mergeLow(start1, length1, start2, length2);
- } else {
- this.mergeHigh(start1, length1, start2, length2);
- }
- }
- /**
- * Merge two adjacent runs in a stable way. The runs must be such that the
- * first element of run1 is bigger than the first element in run2 and the
- * last element of run1 is greater than all the elements in run2.
- * The method should be called when run1.length <= run2.length as it uses
- * TimSort temporary array to store run1. Use mergeHigh if run1.length >
- * run2.length.
- *
- * @param {number} start1 - First element in run1.
- * @param {number} length1 - Length of run1.
- * @param {number} start2 - First element in run2.
- * @param {number} length2 - Length of run2.
- */
- mergeLow(start1, length1, start2, length2) {
- let compare = this.compare;
- let array = this.array;
- let tmp = this.tmp;
- let i = 0;
- for (i = 0; i < length1; i++) {
- tmp[i] = array[start1 + i];
- }
- let cursor1 = 0;
- let cursor2 = start2;
- let dest = start1;
- array[dest++] = array[cursor2++];
- if (--length2 === 0) {
- for (i = 0; i < length1; i++) {
- array[dest + i] = tmp[cursor1 + i];
- }
- return;
- }
- if (length1 === 1) {
- for (i = 0; i < length2; i++) {
- array[dest + i] = array[cursor2 + i];
- }
- array[dest + length2] = tmp[cursor1];
- return;
- }
- let minGallop = this.minGallop;
- while (true) {
- let count1 = 0;
- let count2 = 0;
- let exit = false;
- do {
- if (compare(array[cursor2], tmp[cursor1]) < 0) {
- array[dest++] = array[cursor2++];
- count2++;
- count1 = 0;
- if (--length2 === 0) {
- exit = true;
- break;
- }
- } else {
- array[dest++] = tmp[cursor1++];
- count1++;
- count2 = 0;
- if (--length1 === 1) {
- exit = true;
- break;
- }
- }
- } while ((count1 | count2) < minGallop);
- if (exit) {
- break;
- }
- do {
- count1 = gallopRight(array[cursor2], tmp, cursor1, length1, 0, compare);
- if (count1 !== 0) {
- for (i = 0; i < count1; i++) {
- array[dest + i] = tmp[cursor1 + i];
- }
- dest += count1;
- cursor1 += count1;
- length1 -= count1;
- if (length1 <= 1) {
- exit = true;
- break;
- }
- }
- array[dest++] = array[cursor2++];
- if (--length2 === 0) {
- exit = true;
- break;
- }
- count2 = gallopLeft(tmp[cursor1], array, cursor2, length2, 0, compare);
- if (count2 !== 0) {
- for (i = 0; i < count2; i++) {
- array[dest + i] = array[cursor2 + i];
- }
- dest += count2;
- cursor2 += count2;
- length2 -= count2;
- if (length2 === 0) {
- exit = true;
- break;
- }
- }
- array[dest++] = tmp[cursor1++];
- if (--length1 === 1) {
- exit = true;
- break;
- }
- minGallop--;
- } while (count1 >= DEFAULT_MIN_GALLOPING || count2 >= DEFAULT_MIN_GALLOPING);
- if (exit) {
- break;
- }
- if (minGallop < 0) {
- minGallop = 0;
- }
- minGallop += 2;
- }
- this.minGallop = minGallop;
- if (minGallop < 1) {
- this.minGallop = 1;
- }
- if (length1 === 1) {
- for (i = 0; i < length2; i++) {
- array[dest + i] = array[cursor2 + i];
- }
- array[dest + length2] = tmp[cursor1];
- } else if (length1 === 0) {
- throw new Error('mergeLow preconditions were not respected');
- } else {
- for (i = 0; i < length1; i++) {
- array[dest + i] = tmp[cursor1 + i];
- }
- }
- }
- /**
- * Merge two adjacent runs in a stable way. The runs must be such that the
- * first element of run1 is bigger than the first element in run2 and the
- * last element of run1 is greater than all the elements in run2.
- * The method should be called when run1.length > run2.length as it uses
- * TimSort temporary array to store run2. Use mergeLow if run1.length <=
- * run2.length.
- *
- * @param {number} start1 - First element in run1.
- * @param {number} length1 - Length of run1.
- * @param {number} start2 - First element in run2.
- * @param {number} length2 - Length of run2.
- */
- mergeHigh(start1, length1, start2, length2) {
- let compare = this.compare;
- let array = this.array;
- let tmp = this.tmp;
- let i = 0;
- for (i = 0; i < length2; i++) {
- tmp[i] = array[start2 + i];
- }
- let cursor1 = start1 + length1 - 1;
- let cursor2 = length2 - 1;
- let dest = start2 + length2 - 1;
- let customCursor = 0;
- let customDest = 0;
- array[dest--] = array[cursor1--];
- if (--length1 === 0) {
- customCursor = dest - (length2 - 1);
- for (i = 0; i < length2; i++) {
- array[customCursor + i] = tmp[i];
- }
- return;
- }
- if (length2 === 1) {
- dest -= length1;
- cursor1 -= length1;
- customDest = dest + 1;
- customCursor = cursor1 + 1;
- for (i = length1 - 1; i >= 0; i--) {
- array[customDest + i] = array[customCursor + i];
- }
- array[dest] = tmp[cursor2];
- return;
- }
- let minGallop = this.minGallop;
- while (true) {
- let count1 = 0;
- let count2 = 0;
- let exit = false;
- do {
- if (compare(tmp[cursor2], array[cursor1]) < 0) {
- array[dest--] = array[cursor1--];
- count1++;
- count2 = 0;
- if (--length1 === 0) {
- exit = true;
- break;
- }
- } else {
- array[dest--] = tmp[cursor2--];
- count2++;
- count1 = 0;
- if (--length2 === 1) {
- exit = true;
- break;
- }
- }
- } while ((count1 | count2) < minGallop);
- if (exit) {
- break;
- }
- do {
- count1 = length1 - gallopRight(tmp[cursor2], array, start1, length1, length1 - 1, compare);
- if (count1 !== 0) {
- dest -= count1;
- cursor1 -= count1;
- length1 -= count1;
- customDest = dest + 1;
- customCursor = cursor1 + 1;
- for (i = count1 - 1; i >= 0; i--) {
- array[customDest + i] = array[customCursor + i];
- }
- if (length1 === 0) {
- exit = true;
- break;
- }
- }
- array[dest--] = tmp[cursor2--];
- if (--length2 === 1) {
- exit = true;
- break;
- }
- count2 = length2 - gallopLeft(array[cursor1], tmp, 0, length2, length2 - 1, compare);
- if (count2 !== 0) {
- dest -= count2;
- cursor2 -= count2;
- length2 -= count2;
- customDest = dest + 1;
- customCursor = cursor2 + 1;
- for (i = 0; i < count2; i++) {
- array[customDest + i] = tmp[customCursor + i];
- }
- if (length2 <= 1) {
- exit = true;
- break;
- }
- }
- array[dest--] = array[cursor1--];
- if (--length1 === 0) {
- exit = true;
- break;
- }
- minGallop--;
- } while (count1 >= DEFAULT_MIN_GALLOPING || count2 >= DEFAULT_MIN_GALLOPING);
- if (exit) {
- break;
- }
- if (minGallop < 0) {
- minGallop = 0;
- }
- minGallop += 2;
- }
- this.minGallop = minGallop;
- if (minGallop < 1) {
- this.minGallop = 1;
- }
- if (length2 === 1) {
- dest -= length1;
- cursor1 -= length1;
- customDest = dest + 1;
- customCursor = cursor1 + 1;
- for (i = length1 - 1; i >= 0; i--) {
- array[customDest + i] = array[customCursor + i];
- }
- array[dest] = tmp[cursor2];
- } else if (length2 === 0) {
- throw new Error('mergeHigh preconditions were not respected');
- } else {
- customCursor = dest - (length2 - 1);
- for (i = 0; i < length2; i++) {
- array[customCursor + i] = tmp[i];
- }
- }
- }
- }
- /**
- * Sort an array in the range [lo, hi) using TimSort.
- *
- * @param {array} array - The array to sort.
- * @param {function=} compare - Item comparison function. Default is
- * alphabetical
- * @param {number} lo - First element in the range (inclusive).
- * @param {number} hi - Last element in the range.
- * comparator.
- */
- export function sort(array, compare, lo, hi) {
- if (!Array.isArray(array)) {
- throw new TypeError('Can only sort arrays');
- }
- /*
- * Handle the case where a comparison function is not provided. We do
- * lexicographic sorting
- */
- if (!compare) {
- compare = alphabeticalCompare;
- } else if (typeof compare !== 'function') {
- hi = lo;
- lo = compare;
- compare = alphabeticalCompare;
- }
- if (!lo) {
- lo = 0;
- }
- if (!hi) {
- hi = array.length;
- }
- let remaining = hi - lo;
- // The array is already sorted
- if (remaining < 2) {
- return;
- }
- let runLength = 0;
- // On small arrays binary sort can be used directly
- if (remaining < DEFAULT_MIN_MERGE) {
- runLength = makeAscendingRun(array, lo, hi, compare);
- binaryInsertionSort(array, lo, hi, lo + runLength, compare);
- return;
- }
- let ts = new TimSort(array, compare);
- let minRun = minRunLength(remaining);
- do {
- runLength = makeAscendingRun(array, lo, hi, compare);
- if (runLength < minRun) {
- let force = remaining;
- if (force > minRun) {
- force = minRun;
- }
- binaryInsertionSort(array, lo, lo + force, lo + runLength, compare);
- runLength = force;
- }
- // Push new run and merge if necessary
- ts.pushRun(lo, runLength);
- ts.mergeRuns();
- // Go find next run
- remaining -= runLength;
- lo += runLength;
- } while (remaining !== 0);
- // Force merging of remaining runs
- ts.forceMergeRuns();
- }
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