shyamlibakale1001-alt · Nov 11, 2026
diff --git a/src/main/java/com/thealgorithms/maths/ComplexNumberMultiply.java b/src/main/java/com/thealgorithms/maths/ComplexNumberMultiply.java
@@ -20,6 +20,22 @@ private static int[] parse(String num) {
         return new int[] {real, imaginary};
     }
 
+    /**
+     * Multiplies two complex numbers formatted as {@code "a+bi"}.
+     *
+     * <p>Input contract: both {@code num1} and {@code num2} must be non-null strings matching
+     * {@code -?\d+\+-?\d+i} with integer components (for example {@code "0+0i"} or
+     * {@code "1+-2i"}); otherwise {@link IllegalArgumentException} is thrown.
+     *
+     * <p>Output contract: pure function returning {@code "<real>+<imaginary>i"} where
+     * {@code real = a*c - b*d} and {@code imaginary = a*d + b*c}, preserving negative signs
+     * directly (for example {@code "0+-2i"}).
+     *
+     * @param num1 first complex number in {@code "a+bi"} form
+     * @param num2 second complex number in {@code "a+bi"} form
+     * @return product formatted as {@code "real+imaginaryi"}
+     * @throws IllegalArgumentException if either input is null or does not match {@code -?\d+\+-?\d+i}
+     */
     public static String multiply(String num1, String num2) {
         int[] a = parse(num1);
         int[] b = parse(num2);

diff --git a/src/test/java/com/thealgorithms/maths/ComplexNumberMultiplyContractTest.java b/src/test/java/com/thealgorithms/maths/ComplexNumberMultiplyContractTest.java
@@ -0,0 +1,151 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Contract regression tests for {@link ComplexNumberMultiply#multiply(String, String)}.
+ *
+ * <p>Source facts ({@code ComplexNumberMultiply.java}):
+ * <ul>
+ * <li>line 9: private constructor {@code ComplexNumberMultiply()} (utility class)</li>
+ * <li>lines 12-21: {@code parse(String)} requires non-null input matching
+ * {@code -?\d+\+-?\d+i} (line 13), throwing {@code IllegalArgumentException} on mismatch
+ * (line 14), splitting on {@code "\\+"} (line 17), and parsing {@code int} parts (lines 18-19)</li>
+ * <li>lines 39-47: {@code multiply(String, String)} computes
+ * {@code real = a[0] * b[0] - a[1] * b[1]} (line 43) and
+ * {@code imaginary = a[0] * b[1] + a[1] * b[0]} (line 44), returning
+ * {@code real + "+" + imaginary + "i"} (line 46)</li>
+ * </ul>
+ *
+ * <p>Expected values are independently calculated literals.
+ */
+public class ComplexNumberMultiplyContractTest {
+
+    private static void logCase(String id, String input, Object expected, Object actual) {
+        System.out.println("[R45-T011] " + id + " | input=" + input
+            + " | expected=" + expected + " | actual=" + actual);
+    }
+
+    /**
+     * Smallest valid inputs: {@code "0+0i"} (zero complex number, minimal digits matching line 13)
+     * and unit elements {@code "1+0i"} and {@code "0+1i"}.
+     */
+    @Test
+    public void smallestValidInputsMatchExpectedContract() {
+        String actualZero = ComplexNumberMultiply.multiply("0+0i", "0+0i");
+        logCase("smallest-zero", "(\"0+0i\", \"0+0i\")", "0+0i", actualZero);
+        assertEquals("0+0i", actualZero);
+
+        String actualRealUnit = ComplexNumberMultiply.multiply("1+0i", "1+0i");
+        logCase("smallest-real-unit", "(\"1+0i\", \"1+0i\")", "1+0i", actualRealUnit);
+        assertEquals("1+0i", actualRealUnit);
+
+        String actualImagUnit = ComplexNumberMultiply.multiply("0+1i", "0+1i");
+        logCase("smallest-imag-unit", "(\"0+1i\", \"0+1i\")", "-1+0i", actualImagUnit);
+        assertEquals("-1+0i", actualImagUnit);
+    }
+
+    /**
+     * Ordinary inputs with positive and negative components:
+     * (2 + 3i)(4 + 5i) = (8 - 15) + (10 + 12)i = -7 + 22i;
+     * (1 - 2i)(-3 + 4i) = (-3 + 8) + (4 + 6)i = 5 + 10i.
+     */
+    @Test
+    public void ordinaryInputsMatchExpectedContract() {
+        String actualPos = ComplexNumberMultiply.multiply("2+3i", "4+5i");
+        logCase("ordinary-positive", "(\"2+3i\", \"4+5i\")", "-7+22i", actualPos);
+        assertEquals("-7+22i", actualPos);
+
+        String actualMixed = ComplexNumberMultiply.multiply("1+-2i", "-3+4i");
+        logCase("ordinary-mixed-signs", "(\"1+-2i\", \"-3+4i\")", "5+10i", actualMixed);
+        assertEquals("5+10i", actualMixed);
+    }
+
+    /**
+     * Repeated-value and domain boundary cases: repeated identical operands, multiplicative identity,
+     * zero absorption, pure imaginary operands, conjugate pairs, and negative-imaginary formatting
+     * ({@code "a+-bi"} per line 46).
+     */
+    @Test
+    public void repeatedValuesAndDomainBoundariesMatchExpectedContract() {
+        String actualRepeatedPos = ComplexNumberMultiply.multiply("1+1i", "1+1i");
+        logCase("repeated-1+1i", "(\"1+1i\", \"1+1i\")", "0+2i", actualRepeatedPos);
+        assertEquals("0+2i", actualRepeatedPos);
+
+        String actualRepeatedNeg = ComplexNumberMultiply.multiply("-1+-1i", "-1+-1i");
+        logCase("repeated--1+-1i", "(\"-1+-1i\", \"-1+-1i\")", "0+2i", actualRepeatedNeg);
+        assertEquals("0+2i", actualRepeatedNeg);
+
+        String actualRepeatedNegI = ComplexNumberMultiply.multiply("0+-1i", "0+-1i");
+        logCase("repeated-0+-1i", "(\"0+-1i\", \"0+-1i\")", "-1+0i", actualRepeatedNegI);
+        assertEquals("-1+0i", actualRepeatedNegI);
+
+        String actualIdentity = ComplexNumberMultiply.multiply("1+0i", "-7+-9i");
+        logCase("boundary-identity", "(\"1+0i\", \"-7+-9i\")", "-7+-9i", actualIdentity);
+        assertEquals("-7+-9i", actualIdentity);
+
+        String actualZeroAbsorb = ComplexNumberMultiply.multiply("0+0i", "-7+-9i");
+        logCase("boundary-zero-absorb", "(\"0+0i\", \"-7+-9i\")", "0+0i", actualZeroAbsorb);
+        assertEquals("0+0i", actualZeroAbsorb);
+
+        String actualPureImag = ComplexNumberMultiply.multiply("0+3i", "0+4i");
+        logCase("boundary-pure-imag", "(\"0+3i\", \"0+4i\")", "-12+0i", actualPureImag);
+        assertEquals("-12+0i", actualPureImag);
+
+        String actualConjugate = ComplexNumberMultiply.multiply("3+4i", "3+-4i");
+        logCase("boundary-conjugate", "(\"3+4i\", \"3+-4i\")", "25+0i", actualConjugate);
+        assertEquals("25+0i", actualConjugate);
+
+        String actualMultiDigit = ComplexNumberMultiply.multiply("-12+15i", "10+-20i");
+        logCase("boundary-multi-digit", "(\"-12+15i\", \"10+-20i\")", "180+390i", actualMultiDigit);
+        assertEquals("180+390i", actualMultiDigit);
+    }
+
+    /**
+     * Invalid format and null-input contract (lines 13-15):
+     * {@code parse(String)} rejects {@code null} and any string not matching {@code -?\d+\+-?\d+i}
+     * with {@code IllegalArgumentException("Invalid complex number format: " + num)}.
+     */
+    @Test
+    public void invalidInputsThrowIllegalArgumentExceptionWithExpectedMessage() {
+        IllegalArgumentException nullFirst = assertThrows(
+            IllegalArgumentException.class, () -> ComplexNumberMultiply.multiply(null, "1+1i"));
+        logCase("invalid-null-first", "(null, \"1+1i\")",
+            "IllegalArgumentException: Invalid complex number format: null", nullFirst.getMessage());
+        assertEquals("Invalid complex number format: null", nullFirst.getMessage());
+
+        IllegalArgumentException nullSecond = assertThrows(
+            IllegalArgumentException.class, () -> ComplexNumberMultiply.multiply("1+1i", null));
+        logCase("invalid-null-second", "(\"1+1i\", null)",
+            "IllegalArgumentException: Invalid complex number format: null", nullSecond.getMessage());
+        assertEquals("Invalid complex number format: null", nullSecond.getMessage());
+
+        String[] badInputs = {"1+1", "1-1i", " 1+1i", "", "a+bi", "+1i"};
+        for (String bad : badInputs) {
+            IllegalArgumentException ex = assertThrows(
+                IllegalArgumentException.class, () -> ComplexNumberMultiply.multiply(bad, "1+0i"));
+            String expectedMsg = "Invalid complex number format: " + bad;
+            logCase("invalid-format-" + bad, "(\"" + bad + "\", \"1+0i\")", expectedMsg, ex.getMessage());
+            assertEquals(expectedMsg, ex.getMessage());
+        }
+    }
+
+    /**
+     * Separately verifies absence of observable state mutation across repeated calls.
+     */
+    @Test
+    public void repeatedCallsHaveNoObservableStateMutation() {
+        String a = new String("2+3i");
+        String b = new String("4+5i");
+        String first = ComplexNumberMultiply.multiply(a, b);
+        String second = ComplexNumberMultiply.multiply(a, b);
+        logCase("purity-repeated-call", "(\"2+3i\", \"4+5i\")", "-7+22i", first + " / " + second);
+        assertEquals("2+3i", a);
+        assertEquals("4+5i", b);
+        assertEquals("-7+22i", first);
+        assertEquals("-7+22i", second);
+    }
+}
diff --git a/work/R45-T011/check.py b/work/R45-T011/check.py
@@ -0,0 +1,70 @@
+#!/usr/bin/env python3
+"""Runner for task R45-T011: contract regression checks for ComplexNumberMultiply.
+
+Runs the focused JUnit test through Maven, requires a nonzero test count,
+saves inputs, expected versus actual results, and tool versions into work/R45-T011/,
+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 = "ComplexNumberMultiplyContractTest"
+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-T011]")]
+    (HERE / "comparisons.txt").write_text(
+        ("\n".join(comparisons) + "\n") if comparisons else "No comparison 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
+    status = "PASS" if passed else "FAIL"
+    summary = (
+        f"command: {' '.join(CMD)}\n"
+        f"tests={tests} failures/errors={failures} skipped={skipped} "
+        f"comparisons={len(comparisons)} 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-T011/comparisons.txt b/work/R45-T011/comparisons.txt
@@ -0,0 +1,22 @@
+[R45-T011] invalid-null-first | input=(null, "1+1i") | expected=IllegalArgumentException: Invalid complex number format: null | actual=Invalid complex number format: null
+[R45-T011] invalid-null-second | input=("1+1i", null) | expected=IllegalArgumentException: Invalid complex number format: null | actual=Invalid complex number format: null
+[R45-T011] invalid-format-1+1 | input=("1+1", "1+0i") | expected=Invalid complex number format: 1+1 | actual=Invalid complex number format: 1+1
+[R45-T011] invalid-format-1-1i | input=("1-1i", "1+0i") | expected=Invalid complex number format: 1-1i | actual=Invalid complex number format: 1-1i
+[R45-T011] invalid-format- 1+1i | input=(" 1+1i", "1+0i") | expected=Invalid complex number format:  1+1i | actual=Invalid complex number format:  1+1i
+[R45-T011] invalid-format- | input=("", "1+0i") | expected=Invalid complex number format:  | actual=Invalid complex number format:
+[R45-T011] invalid-format-a+bi | input=("a+bi", "1+0i") | expected=Invalid complex number format: a+bi | actual=Invalid complex number format: a+bi
+[R45-T011] invalid-format-+1i | input=("+1i", "1+0i") | expected=Invalid complex number format: +1i | actual=Invalid complex number format: +1i
+[R45-T011] purity-repeated-call | input=("2+3i", "4+5i") | expected=-7+22i | actual=-7+22i / -7+22i
+[R45-T011] smallest-zero | input=("0+0i", "0+0i") | expected=0+0i | actual=0+0i
+[R45-T011] smallest-real-unit | input=("1+0i", "1+0i") | expected=1+0i | actual=1+0i
+[R45-T011] smallest-imag-unit | input=("0+1i", "0+1i") | expected=-1+0i | actual=-1+0i
+[R45-T011] repeated-1+1i | input=("1+1i", "1+1i") | expected=0+2i | actual=0+2i
+[R45-T011] repeated--1+-1i | input=("-1+-1i", "-1+-1i") | expected=0+2i | actual=0+2i
+[R45-T011] repeated-0+-1i | input=("0+-1i", "0+-1i") | expected=-1+0i | actual=-1+0i
+[R45-T011] boundary-identity | input=("1+0i", "-7+-9i") | expected=-7+-9i | actual=-7+-9i
+[R45-T011] boundary-zero-absorb | input=("0+0i", "-7+-9i") | expected=0+0i | actual=0+0i
+[R45-T011] boundary-pure-imag | input=("0+3i", "0+4i") | expected=-12+0i | actual=-12+0i
+[R45-T011] boundary-conjugate | input=("3+4i", "3+-4i") | expected=25+0i | actual=25+0i
+[R45-T011] boundary-multi-digit | input=("-12+15i", "10+-20i") | expected=180+390i | actual=180+390i
+[R45-T011] ordinary-positive | input=("2+3i", "4+5i") | expected=-7+22i | actual=-7+22i
+[R45-T011] ordinary-mixed-signs | input=("1+-2i", "-3+4i") | expected=5+10i | actual=5+10i
diff --git a/work/R45-T011/mvn_output.txt b/work/R45-T011/mvn_output.txt
@@ -0,0 +1,71 @@
+[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.maths.ComplexNumberMultiplyContractTest
+[R45-T011] invalid-null-first | input=(null, "1+1i") | expected=IllegalArgumentException: Invalid complex number format: null | actual=Invalid complex number format: null
+[R45-T011] invalid-null-second | input=("1+1i", null) | expected=IllegalArgumentException: Invalid complex number format: null | actual=Invalid complex number format: null
+[R45-T011] invalid-format-1+1 | input=("1+1", "1+0i") | expected=Invalid complex number format: 1+1 | actual=Invalid complex number format: 1+1
+[R45-T011] invalid-format-1-1i | input=("1-1i", "1+0i") | expected=Invalid complex number format: 1-1i | actual=Invalid complex number format: 1-1i
+[R45-T011] invalid-format- 1+1i | input=(" 1+1i", "1+0i") | expected=Invalid complex number format:  1+1i | actual=Invalid complex number format:  1+1i
+[R45-T011] invalid-format- | input=("", "1+0i") | expected=Invalid complex number format:  | actual=Invalid complex number format: 
+[R45-T011] invalid-format-a+bi | input=("a+bi", "1+0i") | expected=Invalid complex number format: a+bi | actual=Invalid complex number format: a+bi
+[R45-T011] invalid-format-+1i | input=("+1i", "1+0i") | expected=Invalid complex number format: +1i | actual=Invalid complex number format: +1i
+[R45-T011] purity-repeated-call | input=("2+3i", "4+5i") | expected=-7+22i | actual=-7+22i / -7+22i
+[R45-T011] smallest-zero | input=("0+0i", "0+0i") | expected=0+0i | actual=0+0i
+[R45-T011] smallest-real-unit | input=("1+0i", "1+0i") | expected=1+0i | actual=1+0i
+[R45-T011] smallest-imag-unit | input=("0+1i", "0+1i") | expected=-1+0i | actual=-1+0i
+[R45-T011] repeated-1+1i | input=("1+1i", "1+1i") | expected=0+2i | actual=0+2i
+[R45-T011] repeated--1+-1i | input=("-1+-1i", "-1+-1i") | expected=0+2i | actual=0+2i
+[R45-T011] repeated-0+-1i | input=("0+-1i", "0+-1i") | expected=-1+0i | actual=-1+0i
+[R45-T011] boundary-identity | input=("1+0i", "-7+-9i") | expected=-7+-9i | actual=-7+-9i
+[R45-T011] boundary-zero-absorb | input=("0+0i", "-7+-9i") | expected=0+0i | actual=0+0i
+[R45-T011] boundary-pure-imag | input=("0+3i", "0+4i") | expected=-12+0i | actual=-12+0i
+[R45-T011] boundary-conjugate | input=("3+4i", "3+-4i") | expected=25+0i | actual=25+0i
+[R45-T011] boundary-multi-digit | input=("-12+15i", "10+-20i") | expected=180+390i | actual=180+390i
+[R45-T011] ordinary-positive | input=("2+3i", "4+5i") | expected=-7+22i | actual=-7+22i
+[R45-T011] ordinary-mixed-signs | input=("1+-2i", "-3+4i") | expected=5+10i | actual=5+10i
+[INFO] Tests run: 5, Failures: 0, Errors: 0, Skipped: 0, Time elapsed: 0.045 s -- in com.thealgorithms.maths.ComplexNumberMultiplyContractTest
+[INFO] 
+[INFO] Results:
+[INFO] 
+[INFO] Tests run: 5, 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:  5.763 s
+[INFO] Finished at: 2026-11-11T16:30:48+05:30
+[INFO] ------------------------------------------------------------------------
diff --git a/work/R45-T011/result.txt b/work/R45-T011/result.txt
@@ -0,0 +1,3 @@
+command: mvn -B test -Dtest=ComplexNumberMultiplyContractTest -Dsurefire.failIfNoSpecifiedTests=false
+tests=5 failures/errors=0 skipped=0 comparisons=22 mvn_exit=0
+status=PASS
diff --git a/work/R45-T011/tool_versions.txt b/work/R45-T011/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)]