Revert "optimization that does not work, but is maybe not totally bad"

This reverts commit cebc516125e67dd0928a97a577d18564b0db064c.

chatgpt_qs.cpp

@@ -0,0 +1,17 @@
+#include <iostream>
+#include <vector>
+#include <cstdint>
+#include "chatgpt_qs.h"
+
+// Example usage
+int main() {
+    std::vector<uint32_t> arr = {3, 6, 8, 10, 1, 2, 1};
+    std::vector<uint32_t> sorted = gpt_quicksort(arr);
+
+    for (uint32_t num : sorted) {
+        std::cout << num << " ";
+    }
+    std::cout << std::endl;
+
+    return 0;
+}

chatgpt_qs.h

@@ -0,0 +1,37 @@
+#ifndef CHATGPT_QS_H
+#define CHATGPT_QS_H
+
+std::vector<uint32_t> gpt_quicksort(const std::vector<uint32_t> &arr) {
+    if (arr.size() <= 1) {
+        return arr;
+    }
+
+    uint32_t pivot = arr[arr.size() / 2];
+    std::vector<uint32_t> left;
+    std::vector<uint32_t> middle;
+    std::vector<uint32_t> right;
+
+    for (uint32_t x : arr) {
+        if (x < pivot) {
+            left.push_back(x);
+        } else if (x == pivot) {
+            middle.push_back(x);
+        } else {
+            right.push_back(x);
+        }
+    }
+
+    std::vector<uint32_t> sorted_left = gpt_quicksort(left);
+    std::vector<uint32_t> sorted_right = gpt_quicksort(right);
+
+    // Concatenate sorted_left + middle + sorted_right
+    std::vector<uint32_t> result;
+    result.reserve(sorted_left.size() + middle.size() + sorted_right.size());
+    result.insert(result.end(), sorted_left.begin(), sorted_left.end());
+    result.insert(result.end(), middle.begin(), middle.end());
+    result.insert(result.end(), sorted_right.begin(), sorted_right.end());
+
+    return result;
+}
+
+#endif // CHATGPT_QS_H

qs.c

@@ -43,7 +43,7 @@ void qsr() {
   printArray(data, n);
 }
 
-// qs test function
+// zss test function
 void zss() {
   #include "data.inc"
   
@@ -56,9 +56,26 @@ void zss() {
   printArray(data, n);
 }
 
+// qs3 test function
+void qs3() {
+  #include "data.inc"
+  
+  int n = sizeof(data) / sizeof(data[0]);
+
+  // memory junnnk is enough
+  rpivotstate rand;
+  
+  // perform qs3 on data
+  quicksort_rand3(data, 0, n - 1, &rand);
+  
+  printf("(qs3) Sorted array in ascending order: \n");
+  printArray(data, n);
+}
+
 int main() {
 	qs();
 	qsr();
 	zss();
+	qs3();
 	return 0;
 }

qsort.h

@@ -4,10 +4,16 @@
 
 #include <stdint.h>
 
+/* Uncomment for debugging with if(someevent) raise(SIGINT); */
+#include <signal.h>
+
 /* Structure:
  *
- * - BASICS
- * - EXTRAS
+ * - BASICS:	Basic quicksort
+ * - RANDOMPIV:	Randomized pivoting and partitioning by given pivot-indexed element.
+ * - MINMAX:	partitioning while doing min-max over the whole + related extras.
+ * - PMINMAX:	Partitioning with min-max searches in generated partitions + related.
+ * - VALPART:	Partitioning by value - not by random or given pivot index!
  */
 
 /* BASICS */
@@ -28,6 +34,7 @@ static inline void swapit(uint32_t *a, uint32_t *b) {
  * @param array The array to partition
  * @param low From when. (inclusive)
  * @param high Until when. (inclusive too!)
+ * @returns The partition point.
  */
 static inline int partition(uint32_t array[], int low, int high) {
 	/* This is "Lomuto"s unidirectional partitioner - see algorithms book */
@@ -43,7 +50,6 @@ static inline int partition(uint32_t array[], int low, int high) {
 	#pragma GCC unroll 4
 	for (int j = low; j < high; ++j) {
 		if (array[j] <= pivot) {
-				
 			/* if element smaller than pivot is found */
 			/* swap it with the greater element pointed by i */
 			++i;
@@ -73,7 +79,79 @@ static inline void quicksort(uint32_t array[], int low, int high) {
 	}
 }
 
-/* EXTRAS */
+/* THREEWAY */
+
+struct pret3 {
+	int leftend;
+	int rightend;
+};
+typedef struct pret3 pret3;
+
+/**
+ * Partition the array threeway by puutting ALL pivots to the middle and smaller/biggers left-right
+ *
+ * @param array The array to partition
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param pivotval This value is used to partition the array.
+ * @returns The partition points, end of left and right (inclusive)
+ */
+static inline pret3 partition3(uint32_t array[], int low, int high, uint32_t pivotval) {
+	/* select the rightmost element as pivot */
+	uint32_t pivot = pivotval;
+
+	/* index until smaller or eq elements lay */
+	int i = (low - 1);
+	uint32_t pc = 0;
+
+	/* traverse each element of the array */
+	/* compare them with the pivot */
+	#pragma GCC unroll 4
+	for (int j = low; j <= high; ++j) {
+		/* Branchless pivot-count */
+		pc += (array[j] == pivot);
+
+		if(array[j] < pivot) {
+			/* if element smaller than pivot is found */
+			/* swap it with the greater element pointed by i */
+			++i;
+
+			/* swap element at i with element at j */
+			swapit(&array[i], &array[j]);
+		}
+	}
+
+	/* Can spare out the second loop in these cases */
+	if(pc < 2) {
+		pret3 ret;
+		ret.leftend = i;
+		ret.rightend = i + 1;
+		return ret;
+	}
+
+	/* index until smaller or eq elements lay */
+	int i2 = (high + 1);
+
+	#pragma GCC unroll 4
+	for (int j = high; j > i; --j) {
+		if (array[j] > pivot) {
+			/* if element smaller than pivot is found */
+			/* swap it with the greater element pointed by i */
+			--i2;
+
+			/* swap element at i with element at j */
+			swapit(&array[i2], &array[j]);
+		}
+	}
+
+	/* return the partition points */
+	pret3 ret;
+	ret.leftend = i;
+	ret.rightend = i2;
+	return ret;
+}
+
+/* RANDOMPIV */
 
 /**
  * Partition the array and using the pivot index
@@ -85,6 +163,7 @@ static inline void quicksort(uint32_t array[], int low, int high) {
  * @param pi The index of the pivot element to use. 0 or high is what OG quicksorts do.
  * @param low From when. (inclusive)
  * @param high Until when. (inclusive too!)
+ * @returns The partition point.
  */
 static inline int partition_with_pivot(uint32_t array[], int pi, int low, int high) {
 	/*
@@ -129,4 +208,269 @@ static inline void quicksort_rand(uint32_t array[], int low, int high, rpivotsta
 	}
 }
 
+/* THREEWAY_RAND */
+
+/** Randomized pivoting in-place recursive quicksort on array for elements in [low, high] indices */
+static inline void quicksort_rand3(uint32_t array[], int low, int high, rpivotstate *state) {
+	if (low < high) {
+		/* partition threeway by random pivot */
+		int pi = pick_pivot(state, (high + 1) - low) + low;
+		pret3 res = partition3(array, low, high, array[pi]);
+
+		/* recursive call on the left of pivot */
+		quicksort_rand3(array, low, res.leftend, state);
+
+		/* recursive call on the right of pivot */
+		quicksort_rand3(array, res.rightend, high, state);
+	}
+}
+
+/* MINMAX */
+
+/**
+ * Partition the array while doing a min-max search and find the pivot element such that
+ *
+ * - Elements smaller than pivot are on left of pivot
+ * - Elements greater than pivot are on right of pivot
+ *
+ * @param array The array to partition
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param minout OUT: Will be filled with the minimum key
+ * @param maxout OUT: Will be filled with the maximum key
+ * @returns The partition point.
+ */
+static inline int partition_and_minmax(uint32_t array[], int low, int high, uint32_t *minout, uint32_t *maxout) {
+	/* This is "Lomuto"s unidirectional partitioner - see algorithms book */
+	
+	/* select the rightmost element as pivot */
+	uint32_t pivot = array[high];
+	*minout = pivot;
+	*maxout = pivot;
+	
+	/* index until smaller or eq elements lay */
+	int i = (low - 1);
+
+	/* traverse each element of the array */
+	/* compare them with the pivot */
+	#pragma GCC unroll 4
+	for (int j = low; j < high; ++j) {
+		/* Branchless min-max */
+		*minout = array[j] < *minout ? array[j] : *minout;
+		*maxout = array[j] > *maxout ? array[j] : *maxout;
+
+		/* Lomuto partitioning */
+		if (array[j] <= pivot) {
+			/* if element smaller than pivot is found */
+			/* swap it with the greater element pointed by i */
+			++i;
+
+			/* swap element at i with element at j */
+			swapit(&array[i], &array[j]);
+		}
+	}
+
+	/* swap the pivot element with the greater element at i */
+	swapit(&array[i + 1], &array[high]);
+
+	/* return the partition point */
+	return (i + 1);
+}
+
+/**
+ * Partition the array and min-max and using the pivot index
+ *
+ * - Elements smaller than pivot are on left of pivot
+ * - Elements greater than pivot are on right of pivot
+ *
+ * @param array The array to partition
+ * @param pi The index of the pivot element to use. 0 or high is what OG quicksorts do.
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param minout OUT: Will be filled with the minimum key
+ * @param maxout OUT: Will be filled with the maximum key
+ * @returns The partition point.
+ */
+static inline int partition_and_minmax_with_pivot(uint32_t array[], int pi, int low, int high, uint32_t *minout, uint32_t *maxout) {
+	/*
+	 * Rem.: This looks like overhead,
+	 * but after seriously considering
+	 * writing the whole out I can tell
+	 * this is still fastests basically.
+	 */
+
+	/* swap pivot with rightmost */
+	swapit(&array[high], &array[pi]);
+	/* delegate to previous sol. */
+	return partition_and_minmax(array, low, high, minout, maxout);
+}
+
+/* PMINMAX */
+
+/**
+ * Partition the array with partition-based min-max search (4 values: 2 per partition) and find the pivot element such that
+ *
+ * - Elements smaller than pivot are on left of pivot
+ * - Elements greater than pivot are on right of pivot
+ *
+ * (***): The left min-max outputs can return not just the left partition, but left partition ++ pivotpoint region min-max!
+ *        This does not only happen if partition is empty, but also when pivot was already highest and last earlier.
+ *        Would be hard to handle this edge-case and min-max out is generally used as output hints only so I prefer speed..
+ *
+ * @param array The array to partition
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param minout_left OUT: Will be filled with the minimum key of left partition or pivot value when partition empty. Also (***)
+ * @param maxout_left OUT: Will be filled with the maximum key of left partition or pivot value when partition empty. Also (***)
+ * @param minout_right OUT: Will be filled with the minimum key of right partition or pivot value when partition empty
+ * @param maxout_right OUT: Will be filled with the maximum key of right partition or pivot value when partition empty
+ * @returns The partition point.
+ */
+static inline int partition_and_pminmax(
+		uint32_t array[],
+		int low,
+		int high,
+		uint32_t *minout_left,
+		uint32_t *maxout_left,
+		uint32_t *minout_right,
+		uint32_t *maxout_right) {
+	/* This is "Lomuto"s unidirectional partitioner - see algorithms book */
+
+	/* select the rightmost element as pivot */
+	uint32_t pivot = array[high];
+	*minout_left = pivot;
+	*maxout_left = pivot;
+	*minout_right = pivot;
+	*maxout_right = pivot;
+
+	/* index until smaller or eq elements lay */
+	int i = (low - 1);
+
+	/* traverse each element of the array */
+	/* compare them with the pivot */
+	#pragma GCC unroll 4
+	for (int j = low; j < high; ++j) {
+		/* Lomuto partitioning */
+		if (array[j] <= pivot) {
+			/* Branchless min-max */
+			*minout_left = array[j] < *minout_left ? array[j] : *minout_left;
+			*maxout_left = array[j] > *maxout_left ? array[j] : *maxout_left;
+
+			/* if element smaller than pivot is found */
+			/* swap it with the greater element pointed by i */
+			++i;
+
+			/* swap element at i with element at j */
+			swapit(&array[i], &array[j]);
+		} else {
+			/* Branchless min-max */
+			*minout_right = array[j] < *minout_right ? array[j] : *minout_right;
+			*maxout_right = array[j] > *maxout_right ? array[j] : *maxout_right;
+		}
+	}
+
+	/* swap the pivot element with the greater element at i */
+	swapit(&array[i + 1], &array[high]);
+
+	/* return the partition point */
+	return (i + 1);
+}
+
+/**
+ * Partition the array with partition-based min-max search (4 values: 2 per partition) and using the pivot index
+ *
+ * - Elements smaller than pivot are on left of pivot
+ * - Elements greater than pivot are on right of pivot
+ *
+ * @param array The array to partition
+ * @param pi The index of the pivot element to use. 0 or high is what OG quicksorts do.
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param minout OUT: Will be filled with the minimum key
+ * @param maxout OUT: Will be filled with the maximum key
+ * @returns The partition point.
+ */
+static inline int partition_and_pminmax_with_pivot(
+		uint32_t array[],
+		int pi,
+		int low,
+		int high,
+		uint32_t *minout_left,
+		uint32_t *maxout_left,
+		uint32_t *minout_right,
+		uint32_t *maxout_right) {
+	/*
+	 * Rem.: This looks like overhead,
+	 * but after seriously considering
+	 * writing the whole out I can tell
+	 * this is still fastests basically.
+	 */
+
+	/* swap pivot with rightmost */
+	swapit(&array[high], &array[pi]);
+	/* delegate to previous sol. */
+	return partition_and_pminmax(array, low, high, minout_left, maxout_left, minout_right, maxout_right);
+}
+
+/* VALPART */
+
+/**
+ * Partition the array using pivot value - and find pivot closest to that value (and place them at proper pivot index)
+ *
+ * - Elements smaller-eq than pivotval are on left of pivot
+ * - Elements greater than pivotval are on right of pivot
+ * - The "pivot" element we find is the biggest among the ones smaller-eq to the pivot value
+ *   or if there is no such (all is greater) we return first greater-than value index (right[0])
+ *
+ * @param array The array to partition
+ * @param low From when. (inclusive)
+ * @param high Until when. (inclusive too!)
+ * @param pivotval This value is used to partition the array.
+ * @returns The partition point.
+ */
+static inline int partition_with_pivotval(uint32_t array[], int low, int high, uint32_t pivotval) {
+	/* This is "Lomuto"s unidirectional partitioner - see algorithms book */
+
+	/* Select the rightmost element as pivot just because */
+	/* Need some start-value for min(abs(pv - p)) search! */
+	int64_t leftmax = -1;
+	/* Index of currently found pivot value */
+	uint32_t pivoti = low;
+
+	/* index until smaller or eq elements lay */
+	int i = (low - 1);
+
+	/* traverse each element of the array */
+	/* compare them with the pivotval */
+	/* The "<=" is needed for our trickz here too */
+	#pragma GCC unroll 4
+	for (int j = low; j <= high; ++j) {
+		/* This "<=" ensures pivoti must be only searched among "left" values! */
+		if (array[j] <= pivotval) {
+			/* if element smaller than pivot is found */
+			/* swap it with the greater element pointed by i */
+			++i;
+
+			/* swap element at i with element at j */
+			swapit(&array[i], &array[j]);
+
+			/* After this, array[i] can never change - so we can save it as a found pivot-index */
+			/* Max-search on elements by telling which is closest to pivotval by abs difference! */
+			if(array[i] > leftmax) {
+				pivoti = i;
+				leftmax = array[i];
+			}
+		}
+	}
+
+	/* Must check if above loop found elem at all - because its guessing */
+	if(i != (low - 1)) {
+		/* swap the pivot element into its place */
+		swapit(&array[i], &array[pivoti]);
+	}
+
+	/* return the partition point: index of pivot element */
+	return i;
+}
+
 #endif /* MY_QUICKSORT_H */

zssort.h

@@ -1,9 +1,19 @@
 #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) {
@@ -27,6 +37,9 @@ static inline void zssort(uint32_t array[], int low, int high) {
 	}
 }
 
+/* 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;
@@ -50,4 +63,158 @@ static inline void zssort_rand(uint32_t array[], int low, int high, rpivotstate
 	}
 }
 
+/* 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 */