shyamlibakale1001-alt · Nov 11, 2026
diff --git a/src/main/java/com/thealgorithms/datastructures/heaps/HeapElement.java b/src/main/java/com/thealgorithms/datastructures/heaps/HeapElement.java
@@ -20,6 +20,16 @@
  * methods to retrieve the key and additional information.
  * </p>
  *
+ * <p>
+ * Complexity: for {@code N} constructed and queried {@code HeapElement} instances, every
+ * constructor, {@link #getKey()}, and {@link #getInfo()} executes in {@code O(1)} worst-case
+ * time and space per element ({@code O(N)} total work across {@code N} elements, performing a
+ * constant number of field accesses per element); observed wall-clock per-element times may vary
+ * across {@code N} due to JVM JIT warmup and allocation/GC behavior rather than algorithmic
+ * work. {@link #toString()}, {@link #equals(Object)}, and {@link #hashCode()} add {@code O(1)}
+ * key work plus the cost of {@code additionalInfo}'s corresponding method.
+ * </p>
+ *
  * @author Nicolas Renard
  */
 public class HeapElement {

diff --git a/src/test/java/com/thealgorithms/datastructures/heaps/HeapElementScalingTest.java b/src/test/java/com/thealgorithms/datastructures/heaps/HeapElementScalingTest.java
@@ -0,0 +1,134 @@
+package com.thealgorithms.datastructures.heaps;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertNotEquals;
+import static org.junit.jupiter.api.Assertions.assertNull;
+
+import java.util.Arrays;
+import java.util.Random;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Correctness and scaling checks for {@link HeapElement}.
+ *
+ * <p>Source preconditions ({@code HeapElement.java}):
+ * <ul>
+ * <li>lines 37-38: immutable fields {@code final double key} and
+ * {@code final Object additionalInfo}</li>
+ * <li>lines 47-50: {@code HeapElement(double, Object)} performs 2 constant-time field
+ * assignments</li>
+ * <li>lines 100-103: {@code HeapElement(int)} initializes {@code additionalInfo = null}</li>
+ * <li>lines 131-142: {@code getInfo()} and {@code getKey()} are constant-time field reads</li>
+ * <li>lines 151-178: {@code toString()}, {@code equals(Object)}, and {@code hashCode()} compare
+ * {@code key} and delegate to {@code additionalInfo} when non-null</li>
+ * </ul>
+ */
+public class HeapElementScalingTest {
+
+    private static final long FIXED_SEED = 20261111L;
+    private static final int REPETITIONS = 5;
+    private static final int[] SIZES = {1_000, 10_000, 100_000};
+
+    private static void logRecord(String tag, String detail) {
+        System.out.println("[" + tag + "] " + detail);
+    }
+
+    /**
+     * Smallest valid input ({@code new HeapElement(0.0, null)} and {@code new HeapElement(0)})
+     * and ordinary input ({@code new HeapElement(5.0, "Info")}) with independently calculated
+     * literal expected outputs:
+     * {@code "Info".hashCode() = ((73*31 + 110)*31 + 102)*31 + 111 = 2283726};
+     * {@code 31 * 5 + 2283726 = 2283881}.
+     */
+    @Test
+    public void smallestAndOrdinaryInputsMatchLiteralExpectedOutputs() {
+        HeapElement smallest = new HeapElement(0.0, null);
+        logRecord("R45-T019", "smallest-double-null | input=(0.0, null) | expected=0.0/null/0"
+            + " | actual=" + smallest.getKey() + "/" + smallest.getInfo() + "/" + smallest.hashCode());
+        assertEquals(0.0, smallest.getKey());
+        assertNull(smallest.getInfo());
+        assertEquals("Key: 0.0 - No additional info", smallest.toString());
+        assertEquals(0, smallest.hashCode());
+        assertEquals(new HeapElement(0), smallest);
+
+        HeapElement ordinary = new HeapElement(5.0, "Info");
+        logRecord("R45-T019", "ordinary-double-info | input=(5.0, \"Info\") | expected=5.0/Info/2283881"
+            + " | actual=" + ordinary.getKey() + "/" + ordinary.getInfo() + "/" + ordinary.hashCode());
+        assertEquals(5.0, ordinary.getKey());
+        assertEquals("Info", ordinary.getInfo());
+        assertEquals("Key: 5.0 - Info", ordinary.toString());
+        assertEquals(2283881, ordinary.hashCode());
+        assertEquals(new HeapElement(5, "Info"), ordinary);
+        assertNotEquals(new HeapElement(5.0, "Other"), ordinary);
+        assertNotEquals(new HeapElement(6.0, "Info"), ordinary);
+    }
+
+    /**
+     * Scaling experiment over {@code N in {1000, 10000, 100000}} with fixed seed and 5 repetitions
+     * per size. Fresh inputs are prepared before the timed interval, only {@code HeapElement}
+     * construction and {@code getKey()}/{@code getInfo()} lookups are timed, and all {@code N}
+     * outputs plus exact operation counts ({@code 3 * N}) are verified outside the timed interval.
+     */
+    @Test
+    public void scalingAcrossThreeSizesPreservesCorrectnessAndLinearOperationCount() {
+        Random rng = new Random(FIXED_SEED);
+
+        // Warmup outside reported repetitions to reduce JIT compilation skew.
+        for (int i = 0; i < 200; i++) {
+            HeapElement w = new HeapElement((double) i, "w");
+            assertEquals((double) i, w.getKey());
+        }
+
+        for (int n : SIZES) {
+            long[] elapsedNanos = new long[REPETITIONS];
+            long totalOpsPerRep = 0;
+
+            for (int rep = 0; rep < REPETITIONS; rep++) {
+                double[] keys = new double[n];
+                String[] infos = new String[n];
+                for (int i = 0; i < n; i++) {
+                    keys[i] = rng.nextInt(10_000);
+                    infos[i] = "item-" + (i & 63);
+                }
+
+                HeapElement[] elements = new HeapElement[n];
+                double[] observedKeys = new double[n];
+                Object[] observedInfos = new Object[n];
+
+                long ops = 0;
+                long start = System.nanoTime();
+                for (int i = 0; i < n; i++) {
+                    HeapElement el = new HeapElement(keys[i], infos[i]);
+                    elements[i] = el;
+                    observedKeys[i] = el.getKey();
+                    observedInfos[i] = el.getInfo();
+                    ops += 3; // 1 construction + 1 getKey + 1 getInfo
+                }
+                long duration = System.nanoTime() - start;
+                elapsedNanos[rep] = duration;
+                totalOpsPerRep = ops;
+
+                // Verify every constructed element outside the timed interval.
+                assertEquals(3L * n, ops);
+                for (int i = 0; i < n; i++) {
+                    assertEquals(keys[i], observedKeys[i]);
+                    assertEquals(infos[i], observedInfos[i]);
+                }
+            }
+
+            long[] sorted = Arrays.copyOf(elapsedNanos, elapsedNanos.length);
+            Arrays.sort(sorted);
+            long medianNs = sorted[REPETITIONS / 2];
+            long minNs = sorted[0];
+            long maxNs = sorted[REPETITIONS - 1];
+            double medianNsPerElement = (double) medianNs / n;
+
+            logRecord("R45-T019", "scaling-n-" + n + " | input=N=" + n + ",reps=" + REPETITIONS
+                + ",seed=" + FIXED_SEED + " | expected=ops=" + (3L * n)
+                + ",all_correct=true | actual=ops=" + totalOpsPerRep + ",all_correct=true");
+            logRecord("R45-T019-TIMING", String.format(
+                "N=%d | ops=%d | median_ns=%d | min_ns=%d | max_ns=%d | range_ns=%d | median_ns_per_elem=%.2f",
+                n, totalOpsPerRep, medianNs, minNs, maxNs, maxNs - minNs, medianNsPerElement));
+        }
+    }
+}
diff --git a/src/test/java/com/thealgorithms/datastructures/heaps/HeapElementTest.java b/src/test/java/com/thealgorithms/datastructures/heaps/HeapElementTest.java
@@ -53,4 +53,19 @@ void testHashCode() {
         assertEquals(element1.hashCode(), element2.hashCode()); // Same key and info
         assertNotEquals(element1.hashCode(), element3.hashCode()); // Different info
     }
+
+    @Test
+    void testSmallestAndOrdinaryContractAndHashCode() {
+        HeapElement smallest = new HeapElement(0.0, null);
+        assertEquals(0.0, smallest.getKey());
+        assertNull(smallest.getInfo());
+        assertEquals("Key: 0.0 - No additional info", smallest.toString());
+        assertEquals(0, smallest.hashCode());
+
+        HeapElement ordinary = new HeapElement(5.0, "Info");
+        assertEquals(5.0, ordinary.getKey());
+        assertEquals("Info", ordinary.getInfo());
+        assertEquals("Key: 5.0 - Info", ordinary.toString());
+        assertEquals(2283881, ordinary.hashCode());
+    }
 }
diff --git a/work/R45-T019/check.py b/work/R45-T019/check.py
@@ -0,0 +1,80 @@
+#!/usr/bin/env python3
+"""Runner for task R45-T019: scaling and correctness checks for HeapElement.
+
+Runs the focused JUnit test through Maven, requires a nonzero test count,
+saves inputs, expected versus actual results, median/range timings, and tool versions
+into work/R45-T019/, and exits non-zero on any failure.
+"""
+import glob
+import subprocess
+import sys
+import xml.etree.ElementTree as ET
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+REPO = HERE.parent.parent
+TEST_CLASS = "HeapElementScalingTest"
+CMD = ["mvn", "-B", "test", f"-Dtest={TEST_CLASS}", "-Dsurefire.failIfNoSpecifiedTests=false"]
+
+
+def tool_version(cmd):
+    try:
+        out = subprocess.run(cmd, capture_output=True, text=True, cwd=REPO)
+        return "\n".join(l for l in (out.stdout + out.stderr).splitlines()
+                         if not l.startswith("Picked up")).strip()
+    except FileNotFoundError:
+        return f"{cmd[0]}: not found"
+
+
+def main():
+    (HERE / "tool_versions.txt").write_text(
+        "java:\n" + tool_version(["java", "-version"]) + "\n\nmvn:\n"
+        + tool_version(["mvn", "-v"]) + "\n\npython:\n" + sys.version + "\n")
+
+    print("Running:", " ".join(CMD))
+    proc = subprocess.run(CMD, capture_output=True, text=True, cwd=REPO)
+    combined_output = proc.stdout + proc.stderr
+    (HERE / "mvn_output.txt").write_text(combined_output)
+
+    comparisons = [line.strip() for line in combined_output.splitlines()
+                   if line.strip().startswith("[R45-T019]")]
+    timings = [line.strip() for line in combined_output.splitlines()
+               if line.strip().startswith("[R45-T019-TIMING]")]
+    (HERE / "comparisons.txt").write_text(
+        ("\n".join(comparisons) + "\n") if comparisons else "No comparison records captured.\n")
+    (HERE / "timings.txt").write_text(
+        ("\n".join(timings) + "\n") if timings else "No timing records captured.\n")
+
+    reports = glob.glob(str(REPO / "target/surefire-reports" / f"TEST-*{TEST_CLASS}.xml"))
+    if not reports:
+        (HERE / "result.txt").write_text(
+            f"command: {' '.join(CMD)}\nFAIL: no surefire report found\n")
+        print("FAIL: no surefire report found")
+        return 1
+
+    suite = ET.parse(reports[0]).getroot()
+    tests = int(suite.get("tests", 0))
+    failures = int(suite.get("failures", 0)) + int(suite.get("errors", 0))
+    skipped = int(suite.get("skipped", 0))
+    passed = (
+        proc.returncode == 0
+        and failures == 0
+        and tests > 0
+        and len(comparisons) > 0
+        and len(timings) == 3
+    )
+    status = "PASS" if passed else "FAIL"
+    summary = (
+        f"command: {' '.join(CMD)}\n"
+        f"tests={tests} failures/errors={failures} skipped={skipped} "
+        f"comparisons={len(comparisons)} timings={len(timings)} mvn_exit={proc.returncode}\n"
+        f"status={status}\n"
+    )
+    (HERE / "result.txt").write_text(summary)
+    print(summary)
+
+    return 0 if passed else 1
+
+
+if __name__ == "__main__":
+    sys.exit(main())
diff --git a/work/R45-T019/comparisons.txt b/work/R45-T019/comparisons.txt
@@ -0,0 +1,5 @@
+[R45-T019] smallest-double-null | input=(0.0, null) | expected=0.0/null/0 | actual=0.0/null/0
+[R45-T019] ordinary-double-info | input=(5.0, "Info") | expected=5.0/Info/2283881 | actual=5.0/Info/2283881
+[R45-T019] scaling-n-1000 | input=N=1000,reps=5,seed=20261111 | expected=ops=3000,all_correct=true | actual=ops=3000,all_correct=true
+[R45-T019] scaling-n-10000 | input=N=10000,reps=5,seed=20261111 | expected=ops=30000,all_correct=true | actual=ops=30000,all_correct=true
+[R45-T019] scaling-n-100000 | input=N=100000,reps=5,seed=20261111 | expected=ops=300000,all_correct=true | actual=ops=300000,all_correct=true
diff --git a/work/R45-T019/mvn_output.txt b/work/R45-T019/mvn_output.txt
@@ -0,0 +1,57 @@
+[INFO] Scanning for projects...
+[INFO] Loaded 24447 auto-discovered prefixes for remote repository central (prefixes-central.txt)
+[INFO] 
+[INFO] -----------------------< com.thealgorithms:Java >-----------------------
+[INFO] Building Java 1.0-SNAPSHOT
+[INFO]   from pom.xml
+[INFO] --------------------------------[ jar ]---------------------------------
+[INFO] 
+[INFO] --- jacoco:0.8.16:prepare-agent (default) @ Java ---
+[INFO] Loaded 64 auto-discovered prefixes for remote repository apache.snapshots (prefixes-apache.snapshots.txt)
+[INFO] argLine set to -javaagent:/Users/shyamlibakale/.m2/repository/org/jacoco/org.jacoco.agent/0.8.16/org.jacoco.agent-0.8.16-runtime.jar=destfile=/Users/shyamlibakale/TheAlgorithms-Java/TheAlgorithms-Java/target/jacoco.exec
+[INFO] 
+[INFO] --- resources:3.5.0:resources (default-resources) @ Java ---
+[INFO] skip non existing resourceDirectory /Users/shyamlibakale/TheAlgorithms-Java/TheAlgorithms-Java/src/main/resources
+[INFO] 
+[INFO] --- compiler:3.16.0:compile (default-compile) @ Java ---
+[INFO] Recompiling the module because of changed source code.
+[INFO] Compiling 848 source files with javac [debug release 21] to target/classes
+[INFO] 
+[INFO] --- resources:3.5.0:testResources (default-testResources) @ Java ---
+[INFO] skip non existing resourceDirectory /Users/shyamlibakale/TheAlgorithms-Java/TheAlgorithms-Java/src/test/resources
+[INFO] 
+[INFO] --- compiler:3.16.0:testCompile (default-testCompile) @ Java ---
+[INFO] Recompiling the module because of changed dependency.
+[INFO] Compiling 797 source files with javac [debug release 21] to target/test-classes
+[INFO] 
+[INFO] --- surefire:3.6.0:test (default-test) @ Java ---
+[INFO] Using auto detected provider org.apache.maven.surefire.junitplatform.JUnitPlatformProvider
+[INFO] 
+[INFO] -------------------------------------------------------
+[INFO]  T E S T S
+[INFO] -------------------------------------------------------
+[INFO] Running com.thealgorithms.datastructures.heaps.HeapElementScalingTest
+[R45-T019] smallest-double-null | input=(0.0, null) | expected=0.0/null/0 | actual=0.0/null/0
+[R45-T019] ordinary-double-info | input=(5.0, "Info") | expected=5.0/Info/2283881 | actual=5.0/Info/2283881
+[R45-T019] scaling-n-1000 | input=N=1000,reps=5,seed=20261111 | expected=ops=3000,all_correct=true | actual=ops=3000,all_correct=true
+[R45-T019-TIMING] N=1000 | ops=3000 | median_ns=46083 | min_ns=45583 | max_ns=86167 | range_ns=40584 | median_ns_per_elem=46.08
+[R45-T019] scaling-n-10000 | input=N=10000,reps=5,seed=20261111 | expected=ops=30000,all_correct=true | actual=ops=30000,all_correct=true
+[R45-T019-TIMING] N=10000 | ops=30000 | median_ns=447333 | min_ns=113541 | max_ns=479292 | range_ns=365751 | median_ns_per_elem=44.73
+[R45-T019] scaling-n-100000 | input=N=100000,reps=5,seed=20261111 | expected=ops=300000,all_correct=true | actual=ops=300000,all_correct=true
+[R45-T019-TIMING] N=100000 | ops=300000 | median_ns=1108875 | min_ns=1104500 | max_ns=1221667 | range_ns=117167 | median_ns_per_elem=11.09
+[INFO] Tests run: 2, Failures: 0, Errors: 0, Skipped: 0, Time elapsed: 0.074 s -- in com.thealgorithms.datastructures.heaps.HeapElementScalingTest
+[INFO] 
+[INFO] Results:
+[INFO] 
+[INFO] Tests run: 2, Failures: 0, Errors: 0, Skipped: 0
+[INFO] 
+[INFO] 
+[INFO] --- jacoco:0.8.16:report (generate-code-coverage-report) @ Java ---
+[INFO] Loading execution data file /Users/shyamlibakale/TheAlgorithms-Java/TheAlgorithms-Java/target/jacoco.exec
+[INFO] Analyzed bundle 'Java' with 1073 classes
+[INFO] ------------------------------------------------------------------------
+[INFO] BUILD SUCCESS
+[INFO] ------------------------------------------------------------------------
+[INFO] Total time:  5.566 s
+[INFO] Finished at: 2026-11-11T19:49:04+05:30
+[INFO] ------------------------------------------------------------------------
diff --git a/work/R45-T019/result.txt b/work/R45-T019/result.txt
@@ -0,0 +1,3 @@
+command: mvn -B test -Dtest=HeapElementScalingTest -Dsurefire.failIfNoSpecifiedTests=false
+tests=2 failures/errors=0 skipped=0 comparisons=5 timings=3 mvn_exit=0
+status=PASS
diff --git a/work/R45-T019/timings.txt b/work/R45-T019/timings.txt
@@ -0,0 +1,3 @@
+[R45-T019-TIMING] N=1000 | ops=3000 | median_ns=46083 | min_ns=45583 | max_ns=86167 | range_ns=40584 | median_ns_per_elem=46.08
+[R45-T019-TIMING] N=10000 | ops=30000 | median_ns=447333 | min_ns=113541 | max_ns=479292 | range_ns=365751 | median_ns_per_elem=44.73
+[R45-T019-TIMING] N=100000 | ops=300000 | median_ns=1108875 | min_ns=1104500 | max_ns=1221667 | range_ns=117167 | median_ns_per_elem=11.09
diff --git a/work/R45-T019/tool_versions.txt b/work/R45-T019/tool_versions.txt
@@ -0,0 +1,14 @@
+java:
+openjdk version "21.0.13" 2026-10-20 LTS
+OpenJDK Runtime Environment Temurin-21.0.13+9 (build 21.0.13+9-LTS)
+OpenJDK 64-Bit Server VM Temurin-21.0.13+9 (build 21.0.13+9-LTS, mixed mode, sharing)
+
+mvn:
+Apache Maven 3.10.0 (c43a36b8d67be7e0805a411bc0898af1a51f5472)
+Maven home: /opt/homebrew/Cellar/maven/3.10.0/libexec
+Java version: 27.0.1.0.3, vendor: Homebrew, runtime: /opt/homebrew/Cellar/openjdk/27.0.1.0.3/libexec/openjdk.jdk/Contents/Home
+Default locale: en_IN, platform encoding: UTF-8, time zone: Asia/Kolkata
+OS name: "mac os x", version: "27.0", arch: "aarch64", family: "mac"
+
+python:
+3.14.7 (v3.14.7:823f0323ee6, Aug  5 2026, 07:07:01) [Clang 21.0.0 (clang-2100.1.1.101)]