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quicksort.js
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quicksort.js
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// Algorithm designed by Vladimir Yaroslavskiy.
// Implementation based on the Dart project; see lib/dart/LICENSE for details.
var quicksort = crossfilter.quicksort = quicksort_by(crossfilter_identity);
quicksort.by = quicksort_by;
function quicksort_by(f) {
var insertionsort = insertionsort_by(f);
function sort(a, lo, hi) {
return (hi - lo < quicksort_sizeThreshold
? insertionsort
: quicksort)(a, lo, hi);
}
function quicksort(a, lo, hi) {
// Compute the two pivots by looking at 5 elements.
var sixth = (hi - lo) / 6 | 0,
i1 = lo + sixth,
i5 = hi - 1 - sixth,
i3 = lo + hi - 1 >> 1, // The midpoint.
i2 = i3 - sixth,
i4 = i3 + sixth;
var e1 = a[i1], x1 = f(e1),
e2 = a[i2], x2 = f(e2),
e3 = a[i3], x3 = f(e3),
e4 = a[i4], x4 = f(e4),
e5 = a[i5], x5 = f(e5);
// Sort the selected 5 elements using a sorting network.
if (x1 > x2) t = e1, e1 = e2, e2 = t, t = x1, x1 = x2, x2 = t;
if (x4 > x5) t = e4, e4 = e5, e5 = t, t = x4, x4 = x5, x5 = t;
if (x1 > x3) t = e1, e1 = e3, e3 = t, t = x1, x1 = x3, x3 = t;
if (x2 > x3) t = e2, e2 = e3, e3 = t, t = x2, x2 = x3, x3 = t;
if (x1 > x4) t = e1, e1 = e4, e4 = t, t = x1, x1 = x4, x4 = t;
if (x3 > x4) t = e3, e3 = e4, e4 = t, t = x3, x3 = x4, x4 = t;
if (x2 > x5) t = e2, e2 = e5, e5 = t, t = x2, x2 = x5, x5 = t;
if (x2 > x3) t = e2, e2 = e3, e3 = t, t = x2, x2 = x3, x3 = t;
if (x4 > x5) t = e4, e4 = e5, e5 = t, t = x4, x4 = x5, x5 = t;
var pivot1 = e2, pivotValue1 = x2,
pivot2 = e4, pivotValue2 = x4;
// e2 and e4 have been saved in the pivot variables. They will be written
// back, once the partitioning is finished.
a[i1] = e1;
a[i2] = a[lo];
a[i3] = e3;
a[i4] = a[hi - 1];
a[i5] = e5;
var less = lo + 1, // First element in the middle partition.
great = hi - 2; // Last element in the middle partition.
// Note that for value comparison, <, <=, >= and > coerce to a primitive via
// Object.prototype.valueOf; == and === do not, so in order to be consistent
// with natural order (such as for Date objects), we must do two compares.
var pivotsEqual = pivotValue1 <= pivotValue2 && pivotValue1 >= pivotValue2;
if (pivotsEqual) {
// Degenerated case where the partitioning becomes a dutch national flag
// problem.
//
// [ | < pivot | == pivot | unpartitioned | > pivot | ]
// ^ ^ ^ ^ ^
// left less k great right
//
// a[left] and a[right] are undefined and are filled after the
// partitioning.
//
// Invariants:
// 1) for x in ]left, less[ : x < pivot.
// 2) for x in [less, k[ : x == pivot.
// 3) for x in ]great, right[ : x > pivot.
for (var k = less; k <= great; ++k) {
var ek = a[k], xk = f(ek);
if (xk < pivotValue1) {
if (k !== less) {
a[k] = a[less];
a[less] = ek;
}
++less;
} else if (xk > pivotValue1) {
// Find the first element <= pivot in the range [k - 1, great] and
// put [:ek:] there. We know that such an element must exist:
// When k == less, then el3 (which is equal to pivot) lies in the
// interval. Otherwise a[k - 1] == pivot and the search stops at k-1.
// Note that in the latter case invariant 2 will be violated for a
// short amount of time. The invariant will be restored when the
// pivots are put into their final positions.
while (true) {
var greatValue = f(a[great]);
if (greatValue > pivotValue1) {
great--;
// This is the only location in the while-loop where a new
// iteration is started.
continue;
} else if (greatValue < pivotValue1) {
// Triple exchange.
a[k] = a[less];
a[less++] = a[great];
a[great--] = ek;
break;
} else {
a[k] = a[great];
a[great--] = ek;
// Note: if great < k then we will exit the outer loop and fix
// invariant 2 (which we just violated).
break;
}
}
}
}
} else {
// We partition the list into three parts:
// 1. < pivot1
// 2. >= pivot1 && <= pivot2
// 3. > pivot2
//
// During the loop we have:
// [ | < pivot1 | >= pivot1 && <= pivot2 | unpartitioned | > pivot2 | ]
// ^ ^ ^ ^ ^
// left less k great right
//
// a[left] and a[right] are undefined and are filled after the
// partitioning.
//
// Invariants:
// 1. for x in ]left, less[ : x < pivot1
// 2. for x in [less, k[ : pivot1 <= x && x <= pivot2
// 3. for x in ]great, right[ : x > pivot2
for (var k = less; k <= great; k++) {
var ek = a[k], xk = f(ek);
if (xk < pivotValue1) {
if (k !== less) {
a[k] = a[less];
a[less] = ek;
}
++less;
} else {
if (xk > pivotValue2) {
while (true) {
var greatValue = f(a[great]);
if (greatValue > pivotValue2) {
great--;
if (great < k) break;
// This is the only location inside the loop where a new
// iteration is started.
continue;
} else {
// a[great] <= pivot2.
if (greatValue < pivotValue1) {
// Triple exchange.
a[k] = a[less];
a[less++] = a[great];
a[great--] = ek;
} else {
// a[great] >= pivot1.
a[k] = a[great];
a[great--] = ek;
}
break;
}
}
}
}
}
}
// Move pivots into their final positions.
// We shrunk the list from both sides (a[left] and a[right] have
// meaningless values in them) and now we move elements from the first
// and third partition into these locations so that we can store the
// pivots.
a[lo] = a[less - 1];
a[less - 1] = pivot1;
a[hi - 1] = a[great + 1];
a[great + 1] = pivot2;
// The list is now partitioned into three partitions:
// [ < pivot1 | >= pivot1 && <= pivot2 | > pivot2 ]
// ^ ^ ^ ^
// left less great right
// Recursive descent. (Don't include the pivot values.)
sort(a, lo, less - 1);
sort(a, great + 2, hi);
if (pivotsEqual) {
// All elements in the second partition are equal to the pivot. No
// need to sort them.
return a;
}
// In theory it should be enough to call _doSort recursively on the second
// partition.
// The Android source however removes the pivot elements from the recursive
// call if the second partition is too large (more than 2/3 of the list).
if (less < i1 && great > i5) {
var lessValue, greatValue;
while ((lessValue = f(a[less])) <= pivotValue1 && lessValue >= pivotValue1) ++less;
while ((greatValue = f(a[great])) <= pivotValue2 && greatValue >= pivotValue2) --great;
// Copy paste of the previous 3-way partitioning with adaptions.
//
// We partition the list into three parts:
// 1. == pivot1
// 2. > pivot1 && < pivot2
// 3. == pivot2
//
// During the loop we have:
// [ == pivot1 | > pivot1 && < pivot2 | unpartitioned | == pivot2 ]
// ^ ^ ^
// less k great
//
// Invariants:
// 1. for x in [ *, less[ : x == pivot1
// 2. for x in [less, k[ : pivot1 < x && x < pivot2
// 3. for x in ]great, * ] : x == pivot2
for (var k = less; k <= great; k++) {
var ek = a[k], xk = f(ek);
if (xk <= pivotValue1 && xk >= pivotValue1) {
if (k !== less) {
a[k] = a[less];
a[less] = ek;
}
less++;
} else {
if (xk <= pivotValue2 && xk >= pivotValue2) {
while (true) {
var greatValue = f(a[great]);
if (greatValue <= pivotValue2 && greatValue >= pivotValue2) {
great--;
if (great < k) break;
// This is the only location inside the loop where a new
// iteration is started.
continue;
} else {
// a[great] < pivot2.
if (greatValue < pivotValue1) {
// Triple exchange.
a[k] = a[less];
a[less++] = a[great];
a[great--] = ek;
} else {
// a[great] == pivot1.
a[k] = a[great];
a[great--] = ek;
}
break;
}
}
}
}
}
}
// The second partition has now been cleared of pivot elements and looks
// as follows:
// [ * | > pivot1 && < pivot2 | * ]
// ^ ^
// less great
// Sort the second partition using recursive descent.
// The second partition looks as follows:
// [ * | >= pivot1 && <= pivot2 | * ]
// ^ ^
// less great
// Simply sort it by recursive descent.
return sort(a, less, great + 1);
}
return sort;
}
var quicksort_sizeThreshold = 32;