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* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var floor = require( '@stdlib/math/base/special/floor' );
// MAIN //
/**
* Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first array using heapsort.
*
* ## Notes
*
* - This implementation uses an in-place algorithm derived from the work of Floyd (1964).
*
* ## References
*
* - Williams, John William Joseph. 1964. "Algorithm 232: Heapsort." _Communications of the ACM_ 7 (6). New York, NY, USA: Association for Computing Machinery: 347–49. doi:[10.1145/512274.512284](https://doi.org/10.1145/512274.512284).
* - Floyd, Robert W. 1964. "Algorithm 245: Treesort." _Communications of the ACM_ 7 (12). New York, NY, USA: Association for Computing Machinery: 701. doi:[10.1145/355588.365103](https://doi.org/10.1145/355588.365103).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {number} order - sort order
* @param {Float64Array} x - first input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} y - second input array
* @param {integer} strideY - stride length for `y`
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @returns {Float64Array} `x`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
* var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
*
* dsort2hp( x.length, 1.0, x, 1, 0, y, 1, 0 );
*
* console.log( x );
* // => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ]
*
* console.log( y );
* // => <Float64Array>[ 3.0, 1.0, 0.0, 2.0 ]
*/
function dsort2hp( N, order, x, strideX, offsetX, y, strideY, offsetY ) {
var parent;
var child;
var v1;
var v2;
var tx;
var ty;
var ix;
var iy;
var n;
var j;
var k;
if ( N <= 0 || order === 0.0 ) {
return x;
}
// For a positive stride, sorting in decreasing order is equivalent to providing a negative stride and sorting in increasing order, and, for a negative stride, sorting in decreasing order is equivalent to providing a positive stride and sorting in increasing order...
if ( order < 0.0 ) {
strideX *= -1;
strideY *= -1;
offsetX -= (N-1) * strideX;
offsetY -= (N-1) * strideY;
}
// Set the initial heap size:
n = N;
// Specify an initial "parent" index for building the heap:
parent = floor( N / 2 );
// Continue looping until the array is sorted...
while ( true ) {
if ( parent > 0 ) {
// We need to build the heap...
parent -= 1;
tx = x[ offsetX+(parent*strideX) ];
ty = y[ offsetY+(parent*strideY) ];
} else {
// Reduce the heap size:
n -= 1;
// Check if the heap is empty, and, if so, we are finished sorting...
if ( n === 0 ) {
return x;
}
// Store the last heap value in a temporary variable in order to make room for the heap root being placed into its sorted position:
ix = offsetX + (n*strideX);
tx = x[ ix ];
iy = offsetY + (n*strideY);
ty = y[ iy ];
// Move the heap root to its sorted position:
x[ ix ] = x[ offsetX ];
y[ iy ] = y[ offsetY ];
}
// We need to "sift down", pushing `t` down the heap to in order to replace the parent and satisfy the heap property...
// Start at the parent index:
j = parent;
// Get the "left" child index:
child = (j*2) + 1;
while ( child < n ) {
// Find the largest child...
k = child + 1;
if ( k < n ) {
v1 = x[ offsetX+(k*strideX) ];
v2 = x[ offsetX+(child*strideX) ];
// Check if a "right" child exists and is "bigger"...
if ( v1 > v2 || isnan( v1 ) || (v1 === v2 && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
child += 1;
}
}
// Check if the largest child is bigger than `t`...
v1 = x[ offsetX+(child*strideX) ];
if ( v1 > tx || isnan( v1 ) || ( v1 === tx && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
// Insert the larger child value:
x[ offsetX+(j*strideX) ] = v1;
y[ offsetY+(j*strideY) ] = y[ offsetY+(child*strideY) ];
// Update `j` to point to the child index:
j = child;
// Get the "left" child index and repeat...
child = (j*2) + 1;
} else {
// We've found `t`'s place in the heap...
break;
}
}
// Insert `t` into the heap:
x[ offsetX+(j*strideX) ] = tx;
y[ offsetY+(j*strideY) ] = ty;
}
}
// EXPORTS //
module.exports = dsort2hp;
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