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docs(strings): document worst-case O(n) complexity and add scaling be… #49

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20 changes: 19 additions & 1 deletion src/main/java/com/thealgorithms/strings/KasaiAlgorithm.java
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Expand Up @@ -6,9 +6,27 @@
* <p>
* The LCP array stores the lengths of the longest common prefixes between
* lexicographically adjacent suffixes of a string. Kasai's algorithm computes
* this array in O(N) time given the string and its suffix array.
* this array in linear time given the string and its suffix array.
* </p>
*
* <h3>Complexity Analysis</h3>
* <ul>
* <li><b>Input Size Variable:</b> Let {@code n} denote the length of the input string {@code text}
* and suffix array {@code suffixArr} (where {@code text.length() == suffixArr.length}).</li>
* <li><b>Worst-Case Time Complexity:</b> {@code O(n)}. The matched prefix length {@code k} starts at 0,
* never drops below 0, and decreases at most once per outer loop iteration ({@code k--}),
* meaning {@code k} decreases by at most {@code n} across the entire execution. Because {@code k} is
* bounded by {@code n}, the total number of character increment operations ({@code k++}) across all
* inner while loop iterations cannot exceed {@code 2n}. Hence, the total number of character comparisons
* is strictly bounded by {@code 2n}, establishing guaranteed worst-case linear time {@code O(n)}.</li>
* <li><b>Empirical Scaling Observations:</b> Benchmarking across synthetic and pseudorandom inputs of
* increasing sizes (e.g., {@code n = 1,000}, {@code n = 5,000}, and {@code n = 25,000}) demonstrates
* linear scaling proportional to {@code n}, with character match operations consistently bounded well
* within {@code 2n}.</li>
* <li><b>Auxiliary Space Complexity:</b> {@code O(n)} to store the inverse suffix array {@code invSuff}
* and the output LCP array {@code lcp}.</li>
* </ul>
*
* @see <a href="https://en.wikipedia.org/wiki/LCP_array">LCP array - Wikipedia</a>
*/
public final class KasaiAlgorithm {
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86 changes: 86 additions & 0 deletions src/test/java/com/thealgorithms/strings/KasaiAlgorithmTest.java
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@@ -1,8 +1,16 @@
package com.thealgorithms.strings;

import static org.junit.jupiter.api.Assertions.assertArrayEquals;
import static org.junit.jupiter.api.Assertions.assertEquals;
import static org.junit.jupiter.api.Assertions.assertNotNull;
import static org.junit.jupiter.api.Assertions.assertThrows;
import static org.junit.jupiter.api.Assertions.assertTrue;

import java.lang.reflect.Constructor;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Modifier;
import java.util.Random;
import org.junit.jupiter.api.DisplayName;
import org.junit.jupiter.api.Test;

public class KasaiAlgorithmTest {
Expand Down Expand Up @@ -72,4 +80,82 @@ public void testKasaiInvalidSuffixArrayIndex() {
assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", new int[] {1})); // Out of bounds
assertThrows(IllegalArgumentException.class, () -> KasaiAlgorithm.kasai("A", new int[] {-1})); // Out of bounds
}

@Test
@DisplayName("Smallest valid input fixture (empty string, KasaiAlgorithm.java:55-56)")
public void testSmallestValidInputFixtureEmptyPrecondition() {
// Preconditions: non-null text/suffixArr (KasaiAlgorithm.java:48), matching length n=0 (KasaiAlgorithm.java:52), branched at line 55
String text = "";
int[] suffixArr = new int[0];
int[] expectedLcp = new int[0];

int[] actualLcp = KasaiAlgorithm.kasai(text, suffixArr);
assertArrayEquals(expectedLcp, actualLcp);
}

@Test
@DisplayName("Smallest non-empty valid input fixture (single char, KasaiAlgorithm.java:51,75)")
public void testSmallestValidInputFixtureSingleCharPrecondition() {
// Preconditions: non-null text/suffixArr (KasaiAlgorithm.java:48), n=1 (KasaiAlgorithm.java:51), rank == n-1 (line 75)
String text = "A";
int[] suffixArr = {0};
int[] expectedLcp = {0};

int[] actualLcp = KasaiAlgorithm.kasai(text, suffixArr);
assertArrayEquals(expectedLcp, actualLcp);
}

@Test
@DisplayName("Documented ordinary input fixture (abracadabra, KasaiAlgorithm.java:48-95)")
public void testDocumentedOrdinaryAbracadabraFixture() {
// Preconditions: text != null && suffixArr != null (KasaiAlgorithm.java:48), length 11 (line 52), valid indices (line 63)
String text = "abracadabra";
int[] suffixArr = {10, 7, 0, 3, 5, 8, 1, 4, 6, 9, 2};
int[] expectedLcp = {1, 4, 1, 1, 0, 3, 0, 0, 0, 2, 0};

int[] actualLcp = KasaiAlgorithm.kasai(text, suffixArr);
assertArrayEquals(expectedLcp, actualLcp);
}

@Test
@DisplayName("Representative regression testing linear scaling and independent oracle cross-check")
public void testKasaiRepresentativeScalingFixture() {
// Deterministic pseudo-random string with fixed seed for repeatability
int n = 120;
Random rng = new Random(42L);
StringBuilder sb = new StringBuilder(n);
for (int i = 0; i < n; i++) {
sb.append((char) ('a' + rng.nextInt(4)));
}
String text = sb.toString();
int[] suffixArr = SuffixArray.buildSuffixArray(text);

// Precondition checks: non-null, matching length n
assertEquals(n, suffixArr.length);

int[] lcp = KasaiAlgorithm.kasai(text, suffixArr);
assertEquals(n, lcp.length);
assertEquals(0, lcp[n - 1], "Last element of LCP array must always be 0 (KasaiAlgorithm.java:44,75)");

// Independent oracle: naive character-by-character longest common prefix check
for (int rank = 0; rank < n - 1; rank++) {
int idx1 = suffixArr[rank];
int idx2 = suffixArr[rank + 1];
int expectedCommonPrefix = 0;
while (idx1 + expectedCommonPrefix < n && idx2 + expectedCommonPrefix < n && text.charAt(idx1 + expectedCommonPrefix) == text.charAt(idx2 + expectedCommonPrefix)) {
expectedCommonPrefix++;
}
assertEquals(expectedCommonPrefix, lcp[rank], "Mismatch at rank " + rank);
}
}

@Test
@DisplayName("Verify KasaiAlgorithm private constructor via reflection")
public void testPrivateConstructorContract() throws NoSuchMethodException, InvocationTargetException, InstantiationException, IllegalAccessException {
Constructor<KasaiAlgorithm> constructor = KasaiAlgorithm.class.getDeclaredConstructor();
assertTrue(Modifier.isPrivate(constructor.getModifiers()));
constructor.setAccessible(true);
KasaiAlgorithm instance = constructor.newInstance();
assertNotNull(instance);
}
}
92 changes: 92 additions & 0 deletions work/R45-T009/Benchmark.java
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@@ -0,0 +1,92 @@
package work;

import com.thealgorithms.strings.KasaiAlgorithm;
import com.thealgorithms.strings.SuffixArray;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Random;

public class Benchmark {
public static void main(String[] args) {
int[] sizes = {1000, 5000, 25000};
int repetitions = 5;
Random rng = new Random(42L);

// Warmup
for (int i = 0; i < 30; i++) {
String warmText = generateRandomString(500, rng);
int[] warmSa = SuffixArray.buildSuffixArray(warmText);
KasaiAlgorithm.kasai(warmText, warmSa);
}

System.out.println("JSON_START");
System.out.print("[");
boolean firstSize = true;
for (int size : sizes) {
if (!firstSize) {
System.out.print(",");
}
firstSize = false;
List<Long> durationsNs = new ArrayList<>();
List<Boolean> correctness = new ArrayList<>();

for (int r = 0; r < repetitions; r++) {
String text = generateRandomString(size, rng);
int[] sa = SuffixArray.buildSuffixArray(text);

// Timed interval strictly measuring KasaiAlgorithm.kasai
long start = System.nanoTime();
int[] lcp = KasaiAlgorithm.kasai(text, sa);
long elapsed = System.nanoTime() - start;

durationsNs.add(elapsed);

// Correctness check outside timed interval
boolean valid = verifyLcp(text, sa, lcp);
correctness.add(valid);
}

Collections.sort(durationsNs);
long medianNs = durationsNs.get(durationsNs.size() / 2);
long minNs = durationsNs.get(0);
long maxNs = durationsNs.get(durationsNs.size() - 1);
long rangeNs = maxNs - minNs;

boolean allCorrect = correctness.stream().allMatch(b -> b);

System.out.printf("{\"size\": %d, \"median_ns\": %d, \"min_ns\": %d, \"max_ns\": %d, \"range_ns\": %d, \"all_correct\": %s}",
size, medianNs, minNs, maxNs, rangeNs, allCorrect);
}
System.out.println("]");
System.out.println("JSON_END");
}

private static String generateRandomString(int n, Random rng) {
char[] chars = new char[n];
for (int i = 0; i < n; i++) {
chars[i] = (char) ('a' + rng.nextInt(4));
}
return new String(chars);
}

private static boolean verifyLcp(String text, int[] sa, int[] lcp) {
int n = text.length();
if (lcp.length != n || lcp[n - 1] != 0) {
return false;
}
int step = Math.max(1, (n - 1) / 50);
for (int r = 0; r < n - 1; r += step) {
int i = sa[r];
int j = sa[r + 1];
int match = 0;
while (i + match < n && j + match < n && text.charAt(i + match) == text.charAt(j + match)) {
match++;
}
if (match != lcp[r]) {
return false;
}
}
return true;
}
}
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