myqsort/zssort.h

#ifndef ZS_SORT_H
#define ZS_SORT_H
/*
 * Structure:
 * - ZSSORT:	The at most log(n) space needing quicksort
 * - RZSSORT:	Randomized pivoting variant at most log(n) space needing quicksort
 * - RZSSORTC:	Added check for fully same value const array (also randomized pivot)
 * - MEANQS:	Randomized pivoting AND pivoting based on min-max range - dual recursive
 */

#include <stdint.h>
#include "qsort.h"

/* ZSSORT */

/** Always at most log(n) space needing quicksort variant */
static inline void zssort(uint32_t array[], int low, int high) {
	/* (*) Loop handles original "other half recursion"! */
	while(low < high) {
		int pi = partition(array, low, high);

		/* If we recurse only the smaller part */
		/* That ensures at most n/2 elements can */
		/* be on any given level of the recursion */
		/* tree: that is we ensure log2(N) memuse! */
		if((pi - low) < (high - pi)) {
			// Left smaller: recurse left of pivot
			zssort(array, low, pi - 1);
			// (*) Update partitioning loop for remaining part
			low = pi + 1;
		} else {
			// Right smaller: recurse right of pivot
			zssort(array, pi + 1, high);
			// (*) Update partitioning loop for remaining part
			high = pi - 1; /* high inclusive! */
		}
	}
}

/* ZSSORTR */

/** Always at most log(n) space needing randomized quicksort variant */
static inline void zssort_rand(uint32_t array[], int low, int high, rpivotstate *state) {
	while (low < high) {
		int pi = pick_pivot(state, (high + 1) - low) + low;

		pi = partition_with_pivot(array, pi, low, high);
		/* If we recurse only the smaller part */
		/* That ensures at most n/2 elements can */
		/* be on any given level of the recursion */
		/* tree: that is we ensure log2(N) memuse! */
		if((pi - low) < (high - pi)) {
			// Left smaller: recurse left of pivot
			zssort_rand(array, low, pi - 1, state);
			// (*) Update partitioning loop for remaining part
			low = pi + 1;
		} else {
			// Right smaller: recurse right of pivot
			zssort_rand(array, pi + 1, high, state);
			// (*) Update partitioning loop for remaining part
			high = pi - 1; /* high inclusive! */
		}
	}
}

/* THREEWAY_ZS */

/** Always at most log(n) space needing randomized quicksort variant */
static inline void zssort_rand3(uint32_t array[], int low, int high, rpivotstate *state) {
	while (low < high) {
		int pi = pick_pivot(state, (high + 1) - low) + low;
		pret3 res = partition3(array, low, high, array[pi]);

		/* If we recurse only the smaller part */
		/* That ensures at most n/2 elements can */
		/* be on any given level of the recursion */
		/* tree: that is we ensure log2(N) memuse! */
		if((res.leftend - low) < (high - res.rightend)) {
			// Left smaller: recurse left of pivot
			zssort_rand3(array, low, res.leftend, state);
			// (*) Update partitioning loop for remaining part
			low = res.rightend;
		} else {
			// Right smaller: recurse right of pivot
			zssort_rand3(array, res.rightend, high, state);
			// (*) Update partitioning loop for remaining part
			high = res.leftend; /* high inclusive! */
		}
	}
}

/* ZSSORTC */

/** Always at most log(n) space needing randomized quicksort variant - with checking for sameconst-arrays */
static inline void zsrc(uint32_t array[], int low, int high, rpivotstate *state) {
	if (low < high) {
		uint32_t min, max;
		int pi = pick_pivot(state, (high + 1) - low) + low;
		pi = partition_and_minmax_with_pivot(array, pi, low, high, &min, &max);
		if(min != max) {
			/* Recursion with zssort_rand ensures logn+1 stack spacen need! */
			zssort_rand(array, low, pi - 1, state);
			zssort_rand(array, pi + 1, high, state);
		}
	}
}

/* MEANQS */

/**
 * Rangsort entry point and outer-recursive function of meanqs.
 *
 * We pick a random pivot, but in the meantime try to quess mean for next level partitioning.
 * This and meanqs_inner is co-recursive (call each other)
 *
 * @param array The array to sort
 * @param low From when. (inclusive)
 * @param high Until when. (inclusive too!)
 * @param state The random pivot picking state
 */
static inline void meanqs(uint32_t array[], int low, int high, rpivotstate *state);

/**
 * Inner-recursive function of meanqs - calls meanqs() as next level recursion.
 *
 * @param array The array to sort
 * @param low From when. (inclusive)
 * @param high Until when. (inclusive too!)
 * @param pivotval We first partition to smaller-eq/bigger than pivotval, later we might pick random though
 * @param state The random pivot picking state
 */
static inline void meanqs_inter(uint32_t array[], int low, int high, uint32_t pivotval, rpivotstate *state) {

	/* First: partition using pivot val + recurse */

	if (low < high) {
		/* For the first level, use the pivotval they provide */
		/* This only helps somewhat, because below loop.... */
		/* ..But code it better if you can do consistently! */
		int pi = partition_with_pivotval(array, low, high, pivotval);

		/* If we recurse only the smaller part */
		/* That ensures at most n/2 elements can */
		/* be on any given level of the recursion */
		/* tree: that is we ensure log2(N) memuse! */
		if((pi - low) < (high - pi)) {
			// Left smaller: recurse left of pivot
			meanqs(array, low, pi - 1, state);
			// (*) Update partitioning loop for remaining part
			low = pi + 1;
		} else {
			// Right smaller: recurse right of pivot
			meanqs(array, pi + 1, high, state);
			// (*) Update partitioning loop for remaining part
			high = pi - 1; /* high inclusive! */
		}
	}

	/* Later: picking random pivot and partition like that */

	/* (*) Rem.: The above if can be understood as different first iteration of this while loop... */
	while (low < high) {
		/* Random picking here - no info anymore about mean */
		int pi = pick_pivot(state, (high + 1) - low) + low;
		pi = partition_with_pivot(array, pi, low, high);

		/* If we recurse only the smaller part */
		/* That ensures at most n/2 elements can */
		/* be on any given level of the recursion */
		/* tree: that is we ensure log2(N) memuse! */
		if((pi - low) < (high - pi)) {
			// Left smaller: recurse left of pivot
			meanqs(array, low, pi - 1, state);
			// (*) Update partitioning loop for remaining part
			low = pi + 1;
		} else {
			// Right smaller: recurse right of pivot
			meanqs(array, pi + 1, high, state);
			// (*) Update partitioning loop for remaining part
			high = pi - 1; /* high inclusive! */
		}
	}
}

/**
 * Rangsort entry point and outer-recursive function of meanqs.
 *
 * We pick a random pivot, but in the meantime try to quess mean for next level partitioning.
 * This and meanqs_inner is co-recursive (call each other)
 *
 * @param array The array to sort
 * @param low From when. (inclusive)
 * @param high Until when. (inclusive too!)
 * @param state The random pivot picking state
 */
static inline void meanqs(uint32_t array[], int low, int high, rpivotstate *state) {
	if (low < high) {
		uint32_t lmin, lmax, rmin, rmax;
		int pi = pick_pivot(state, (high + 1) - low) + low;
		pi = partition_and_pminmax_with_pivot(array, pi, low, high, &lmin, &lmax, &rmin, &rmax);

		/* These also handle constant (always same valued) subarrays */
		if(lmin != lmax) {
			/* Better than (a+b)/2 avg because of overflow possibilities */
			uint32_t lavg = lmin + (lmax - lmin) / 2;
			/* Recursion with inter "ensures" logn stack spacen need! */
			meanqs_inter(array, low, pi - 1, lavg, state);
		}
		if(rmin != rmax) {
			/* Better than (a+b)/2 avg because of overflow possibilities */
			uint32_t ravg = rmin + (rmax - rmin) / 2;
			/* Recursion with inter "ensures" logn stack spacen need! */
			meanqs_inter(array, pi + 1, high, ravg, state);
		}
	}
}

// TODO: Idea: Quadratic time happens when you repeatedly pick pivots close to the maximum or minimum - so why not re-pick near extremals being picked which now can be cheked? I think we should have a treshold - maybe dynamically set by first minmax - and logarithmically divide the treshold by 2 in case its still too close the next randomization time. This handles smallrange badly though.

#endif /* ZS_SORT_H */