From 9ffaaa873e607444ba218fb37662d9b66664b17a Mon Sep 17 00:00:00 2001
From: Petr Chmel <petr@chmel.net>
Date: Mon, 10 Mar 2025 19:39:42 +0100
Subject: [PATCH] Publish splay experiment
---
03-splay_experiment/cpp/Makefile | 22 ++
03-splay_experiment/cpp/random.h | 61 +++++
03-splay_experiment/cpp/splay_experiment.cpp | 208 ++++++++++++++++++
03-splay_experiment/python/Makefile | 15 ++
.../python/splay_experiment.py | 127 +++++++++++
03-splay_experiment/task.md | 87 ++++++++
6 files changed, 520 insertions(+)
create mode 100644 03-splay_experiment/cpp/Makefile
create mode 100644 03-splay_experiment/cpp/random.h
create mode 100644 03-splay_experiment/cpp/splay_experiment.cpp
create mode 100644 03-splay_experiment/python/Makefile
create mode 100644 03-splay_experiment/python/splay_experiment.py
create mode 100644 03-splay_experiment/task.md
diff --git a/03-splay_experiment/cpp/Makefile b/03-splay_experiment/cpp/Makefile
new file mode 100644
index 0000000..f97bee9
--- /dev/null
+++ b/03-splay_experiment/cpp/Makefile
@@ -0,0 +1,22 @@
+STUDENT_ID ?= PLEASE_SET_STUDENT_ID
+
+.PHONY: test
+test: splay_experiment
+ @rm -rf out && mkdir out
+ @for test in sequential random subset ; do \
+ for mode in std naive ; do \
+ echo t-$$test-$$mode ; \
+ ./splay_experiment $$test $(STUDENT_ID) $$mode >out/t-$$test-$$mode ; \
+ done ; \
+ done
+
+INCLUDE ?= .
+CXXFLAGS=-std=c++23 -O2 -Wall -Wextra -g -Wno-sign-compare -I$(INCLUDE)
+
+splay_experiment: splay_operation.h splay_experiment.cpp $(INCLUDE)/random.h
+ $(CXX) $(CPPFLAGS) $(CXXFLAGS) $^ -o $@
+
+.PHONY: clean
+clean::
+ rm -f splay_experiment
+ rm -rf out
diff --git a/03-splay_experiment/cpp/random.h b/03-splay_experiment/cpp/random.h
new file mode 100644
index 0000000..5ef10ae
--- /dev/null
+++ b/03-splay_experiment/cpp/random.h
@@ -0,0 +1,61 @@
+#ifndef DS1_RANDOM_H
+#define DS1_RANDOM_H
+
+#include <cstdint>
+
+/*
+ * This is the xoroshiro128+ random generator, designed in 2016 by David Blackman
+ * and Sebastiano Vigna, distributed under the CC-0 license. For more details,
+ * see http://vigna.di.unimi.it/xorshift/.
+ *
+ * Rewritten to C++ by Martin Mares, also placed under CC-0.
+ */
+
+class RandomGen {
+ uint64_t state[2];
+
+ uint64_t rotl(uint64_t x, int k)
+ {
+ return (x << k) | (x >> (64 - k));
+ }
+
+ public:
+ // Initialize the generator, set its seed and warm it up.
+ RandomGen(unsigned int seed)
+ {
+ state[0] = seed * 0xdeadbeef;
+ state[1] = seed ^ 0xc0de1234;
+ for (int i=0; i<100; i++)
+ next_u64();
+ }
+
+ // Generate a random 64-bit number.
+ uint64_t next_u64(void)
+ {
+ uint64_t s0 = state[0], s1 = state[1];
+ uint64_t result = s0 + s1;
+ s1 ^= s0;
+ state[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14);
+ state[1] = rotl(s1, 36);
+ return result;
+ }
+
+ // Generate a random 32-bit number.
+ uint32_t next_u32(void)
+ {
+ return next_u64() >> 11;
+ }
+
+ // Generate a number between 0 and range-1.
+ unsigned int next_range(unsigned int range)
+ {
+ /*
+ * This is not perfectly uniform, unless the range is a power of two.
+ * However, for 64-bit random values and 32-bit ranges, the bias is
+ * insignificant.
+ */
+ return next_u64() % range;
+ }
+};
+
+#endif
diff --git a/03-splay_experiment/cpp/splay_experiment.cpp b/03-splay_experiment/cpp/splay_experiment.cpp
new file mode 100644
index 0000000..a47da8b
--- /dev/null
+++ b/03-splay_experiment/cpp/splay_experiment.cpp
@@ -0,0 +1,208 @@
+#include <algorithm>
+#include <functional>
+#include <string>
+#include <utility>
+#include <vector>
+#include <iostream>
+#include <cmath>
+
+#include "splay_operation.h"
+#include "random.h"
+
+using namespace std;
+
+/*
+ * A modified Splay tree for benchmarking.
+ *
+ * We inherit the implementation of operations from the Tree class
+ * and extend it by keeping statistics on the number of splay operations
+ * and the total number of rotations. Also, if naive is turned on,
+ * splay uses only single rotations.
+ *
+ * Please make sure that your Tree class defines the rotate() and splay()
+ * methods as virtual.
+ */
+
+class BenchmarkingTree : public Tree {
+public:
+ int num_operations;
+ int num_rotations;
+ bool do_naive;
+
+ BenchmarkingTree(bool naive=false)
+ {
+ do_naive = naive;
+ reset();
+ }
+
+ void reset()
+ {
+ num_operations = 0;
+ num_rotations = 0;
+ }
+
+ void rotate(Node *node) override
+ {
+ num_rotations++;
+ Tree::rotate(node);
+ }
+
+ void splay(Node *node) override
+ {
+ num_operations++;
+ if (do_naive) {
+ while (node->parent)
+ rotate(node);
+ } else {
+ Tree::splay(node);
+ }
+ }
+
+ // Return the average number of rotations per operation.
+ double rot_per_op()
+ {
+ if (num_operations > 0)
+ return (double) num_rotations / num_operations;
+ else
+ return 0;
+ }
+};
+
+bool naive; // Use of naive rotations requested
+RandomGen *rng; // Random generator object
+
+void test_sequential()
+{
+ for (int n=100; n<=3000; n+=100) {
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+
+ for (int x=0; x<n; x++)
+ tree.insert(x);
+
+ for (int i=0; i<5; i++)
+ for (int x=0; x<n; x++)
+ tree.lookup(x);
+
+ cout << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+// An auxiliary function for generating a random permutation.
+vector<int> random_permutation(int n)
+{
+ vector<int> perm;
+ for (int i=0; i<n; i++)
+ perm.push_back(i);
+ for (int i=0; i<n-1; i++)
+ swap(perm[i], perm[i + rng->next_range(n-i)]);
+ return perm;
+}
+
+void test_random()
+{
+ for (int e=32; e<=64; e++) {
+ int n = (int) pow(2, e/4.);
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+
+ vector<int> perm = random_permutation(n);
+ for (int x : perm)
+ tree.insert(x);
+
+ for (int i=0; i<5*n; i++)
+ tree.lookup(rng->next_range(n));
+
+ cout << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+/*
+ * An auxiliary function for constructing arithmetic progressions.
+ * The vector seq will be modified to contain an arithmetic progression
+ * of elements in interval [A,B] starting from position s with step inc.
+ */
+void make_progression(vector<int> &seq, int A, int B, int s, int inc)
+{
+ for (int i=0; i<seq.size(); i++)
+ while (seq[i] >= A && seq[i] <= B && s + inc*(seq[i]-A) != i)
+ swap(seq[i], seq[s + inc*(seq[i] - A)]);
+}
+
+void test_subset_s(int sub)
+{
+ for (int e=32; e<=64; e++) {
+ int n = (int) pow(2, e/4.);
+ if (n < sub)
+ continue;
+
+ // We will insert elements in order, which contain several
+ // arithmetic progressions interspersed with random elements.
+ vector<int> seq = random_permutation(n);
+ make_progression(seq, n/4, n/4 + n/20, n/10, 1);
+ make_progression(seq, n/2, n/2 + n/20, n/10, -1);
+ make_progression(seq, 3*n/4, 3*n/4 + n/20, n/2, -4);
+ make_progression(seq, 17*n/20, 17*n/20 + n/20, 2*n/5, 5);
+
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+ for (int x : seq)
+ tree.insert(x);
+ tree.reset();
+
+ for (int i=0; i<10000; i++)
+ tree.lookup(seq[rng->next_range(sub)]);
+
+ cout << sub << " " << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+void test_subset()
+{
+ test_subset_s(10);
+ test_subset_s(100);
+ test_subset_s(1000);
+}
+
+vector<pair<string, function<void()>>> tests = {
+ { "sequential", test_sequential },
+ { "random", test_random },
+ { "subset", test_subset },
+};
+
+int main(int argc, char **argv)
+{
+ if (argc != 4) {
+ cerr << "Usage: " << argv[0] << " <test> <student-id> (std|naive)" << endl;
+ return 1;
+ }
+
+ string which_test = argv[1];
+ string id_str = argv[2];
+ string mode = argv[3];
+
+ try {
+ rng = new RandomGen(stoi(id_str));
+ } catch (...) {
+ cerr << "Invalid student ID" << endl;
+ return 1;
+ }
+
+ if (mode == "std")
+ naive = false;
+ else if (mode == "naive")
+ naive = true;
+ else
+ {
+ cerr << "Last argument must be either 'std' or 'naive'" << endl;
+ return 1;
+ }
+
+ for (const auto& test : tests) {
+ if (test.first == which_test)
+ {
+ cout.precision(12);
+ test.second();
+ return 0;
+ }
+ }
+ cerr << "Unknown test " << which_test << endl;
+ return 1;
+}
diff --git a/03-splay_experiment/python/Makefile b/03-splay_experiment/python/Makefile
new file mode 100644
index 0000000..4a5efbf
--- /dev/null
+++ b/03-splay_experiment/python/Makefile
@@ -0,0 +1,15 @@
+STUDENT_ID ?= PLEASE_SET_STUDENT_ID
+
+.PHONY: test
+test: splay_experiment.py splay_operation.py
+ @rm -rf out && mkdir out
+ @for test in sequential random subset ; do \
+ for mode in std naive ; do \
+ echo t-$$test-$$mode ; \
+ ./splay_experiment.py $$test $(STUDENT_ID) $$mode >out/t-$$test-$$mode ; \
+ done ; \
+ done
+
+.PHONY: clean
+clean::
+ rm -rf out __pycache__
diff --git a/03-splay_experiment/python/splay_experiment.py b/03-splay_experiment/python/splay_experiment.py
new file mode 100644
index 0000000..8cf3d6d
--- /dev/null
+++ b/03-splay_experiment/python/splay_experiment.py
@@ -0,0 +1,127 @@
+#!/usr/bin/env python3
+
+import sys
+import random
+
+from splay_operation import Tree
+
+class BenchmarkingTree(Tree):
+ """ A modified Splay tree for benchmarking.
+
+ We inherit the implementation of operations from the Tree class
+ and extend it by keeping statistics on the number of splay operations
+ and the total number of rotations. Also, if naive is turned on,
+ splay uses only single rotations.
+ """
+
+ def __init__(self, naive=False):
+ Tree.__init__(self)
+ self.do_naive = naive
+ self.reset()
+
+ def reset(self):
+ """Reset statistics."""
+ self.num_rotations = 0;
+ self.num_operations = 0;
+
+ def rotate(self, node):
+ self.num_rotations += 1
+ Tree.rotate(self, node)
+
+ def splay(self, node):
+ self.num_operations += 1
+ if self.do_naive:
+ while node.parent is not None:
+ self.rotate(node)
+ else:
+ Tree.splay(self, node)
+
+ def rot_per_op(self):
+ """Return the average number of rotations per operation."""
+ if self.num_operations > 0:
+ return self.num_rotations / self.num_operations
+ else:
+ return 0
+
+def test_sequential():
+ for n in range(100, 3001, 100):
+ tree = BenchmarkingTree(naive)
+ for elem in range(n):
+ tree.insert(elem)
+
+ for _ in range(5):
+ for elem in range(n):
+ tree.lookup(elem)
+
+ print(n, tree.rot_per_op())
+
+def test_random():
+ for exp in range(32, 64):
+ n = int(2**(exp/4))
+ tree = BenchmarkingTree(naive)
+
+ for elem in random.sample(range(n), n):
+ tree.insert(elem)
+
+ for _ in range(5*n):
+ tree.lookup(random.randrange(n))
+
+ print(n, tree.rot_per_op())
+
+def make_progression(seq, A, B, s, inc):
+ """An auxiliary function for constructing arithmetic progressions.
+
+ The array seq will be modified to contain an arithmetic progression
+ of elements in interval [A,B] starting from position s with step inc.
+ """
+ for i in range(len(seq)):
+ while seq[i] >= A and seq[i] <= B and s + inc*(seq[i]-A) != i:
+ pos = s + inc*(seq[i]-A)
+ seq[i], seq[pos] = seq[pos], seq[i]
+
+def test_subset():
+ for sub in [10, 100, 1000]:
+ for exp in range(32,64):
+ n = int(2**(exp/4))
+ if n < sub:
+ continue
+
+ # We will insert elements in order, which contain several
+ # arithmetic progressions interspersed with random elements.
+ seq = random.sample(range(n), n)
+ make_progression(seq, n//4, n//4 + n//20, n//10, 1)
+ make_progression(seq, n//2, n//2 + n//20, n//10, -1)
+ make_progression(seq, 3*n//4, 3*n//4 + n//20, n//2, -4)
+ make_progression(seq, 17*n//20, 17*n//20 + n//20, 2*n//5, 5)
+
+ tree = BenchmarkingTree(naive)
+ for elem in seq:
+ tree.insert(elem)
+ tree.reset()
+
+ for _ in range(10000):
+ tree.lookup(seq[random.randrange(sub)])
+
+ print(sub, n, tree.rot_per_op())
+
+tests = {
+ "sequential": test_sequential,
+ "random": test_random,
+ "subset": test_subset,
+}
+
+if len(sys.argv) == 4:
+ test, student_id = sys.argv[1], sys.argv[2]
+ if sys.argv[3] == "std":
+ naive = False
+ elif sys.argv[3] == "naive":
+ naive = True
+ else:
+ raise ValueError("Last argument must be either 'std' or 'naive'")
+ random.seed(student_id)
+ if test in tests:
+ tests[test]()
+ else:
+ raise ValueError("Unknown test {}".format(test))
+else:
+ raise ValueError("Usage: {} <test> <student-id> (std|naive)".format(sys.argv[0]))
diff --git a/03-splay_experiment/task.md b/03-splay_experiment/task.md
new file mode 100644
index 0000000..0d96811
--- /dev/null
+++ b/03-splay_experiment/task.md
@@ -0,0 +1,87 @@
+## Goal
+
+The goal of this assignment is to evaluate your implementation of Splay trees
+experimentally and to compare it with a "naive" implementation which splays
+using single rotations only.
+
+You are given a test program (`splay_experiment`) which calls your
+implementation from the previous assignment to perform the following
+experiments:
+
+- _Sequential test:_ Insert _n_ elements sequentially and then repeatedly
+ find them all in sequential order.
+- _Random test:_ Insert _n_ elements in random order and then find _5n_
+ random elements.
+- _Subset test:_ Insert a sequence of _n_ elements, which contains arithmetic
+ progressions interspersed with random elements. Then repeatedly access
+ a small subset of these elements in random order. Try this with subsets of
+ different cardinalities.
+
+The program tries each experiment with different values of _n_. In each try,
+it prints the average number of rotations per splay operation.
+
+You should perform these experiments and write a report, which contains the following
+plots of the measured data. Each plot should show the dependence of the average
+number of rotations on the set size _n_.
+
+- The sequential test: one curve for the standard implementation, one for the naive one.
+- The random test: one curve for the standard implementation, one for the naive one.
+- The subset test: three curves for the standard implementation with different sizes
+ of the subset, three for the naive implementation with the same sizes.
+
+The report should discuss the experimental results and try to explain the observed
+behavior using theory from the lectures. (If you want, you can carry out further
+experiments to gain better understanding of the data structure and include these
+in the report. This is strictly optional.)
+
+You should submit a PDF file with the report (and no source code).
+You will get 1 temporary point upon submission if the file is syntantically correct;
+proper points will be assigned later.
+
+## Test program
+
+The test program is given three arguments:
+- The name of the test (`sequential`, `random`, `subset`).
+- The random seed: you should use the last 2 digits of your student ID (you can find
+ it in the Study Information System – just click on the Personal data icon). Please
+ include the random seed in your report.
+- The implementation to test (`std` or `naive`).
+
+The output of the program contains one line per experiment, which consists of:
+- For the sequential and random test: the set size and the average number of rotations.
+- For the subset test: the subset size, the set size, and the average number of rotations
+ per find. The initial insertions of the full set are not counted.
+
+## Your implementation
+
+Please use your implementation from the previous exercise. Methods `splay()`
+and `rotate()` will be augmented by the test program. If you are performing
+a double rotation directly instead of composing it from single rotations, you
+need to adjust the `BenchmarkingTree` class accordingly.
+
+## Hints
+
+The following tools can be useful for producing nice plots:
+- [pandas](https://pandas.pydata.org/)
+- [matplotlib](https://matplotlib.org/)
+- [gnuplot](http://www.gnuplot.info/)
+
+A quick checklist for plots:
+- Is there a caption explaining what is plotted?
+- Are the axes clearly labelled? Do they have value ranges and units?
+- Have you mentioned that this axis has logarithmic scale? (Logarithmic graphs
+ are more fitting in some cases, but you should tell.)
+- Is it clear which curve means what?
+- Is it clear what are the measured points and what is an interpolated
+ curve between them?
+- Are there any overlaps? (E.g., the most interesting part of the curve
+ hidden underneath a label?)
+
+In your discussion, please distinguish the following kinds of claims.
+It should be always clear which is which:
+- Experimental results (i.e., the raw data you obtained from the experiments)
+- Theoretical facts (i.e., claims we have proved mathematically)
+- Your hypotheses (e.g., when you claim that the graph looks like something is true,
+ but you are not able to prove rigorously that it always holds)
+
+Source code templates can be found in [git](https://gitlab.kam.mff.cuni.cz/datovky/assignments/-/tree/master).
--
GitLab