diff --git a/src/main/java/com/thealgorithms/strings/LongestRepeatedSubstring.java b/src/main/java/com/thealgorithms/strings/LongestRepeatedSubstring.java new file mode 100644 index 000000000000..87c9278fd4bf --- /dev/null +++ b/src/main/java/com/thealgorithms/strings/LongestRepeatedSubstring.java @@ -0,0 +1,83 @@ +package com.thealgorithms.strings; + +/** + * Finds the longest substring that occurs at least twice in a given string. + * + *

Uses the suffix array (via {@link SuffixArray}) and Kasai's algorithm + * to build the LCP (Longest Common Prefix) array, then returns the substring + * corresponding to the maximum LCP value.

+ * + *

Time complexity: O(n log² n) for suffix array construction + O(n) for LCP.

+ * + * @see Longest repeated substring problem + * @see SuffixArray + */ +public final class LongestRepeatedSubstring { + + private LongestRepeatedSubstring() { + } + + /** + * Returns the longest substring that appears at least twice in the given text. + * + * @param text the input string + * @return the longest repeated substring, or an empty string if none exists + */ + public static String longestRepeatedSubstring(String text) { + if (text == null || text.length() <= 1) { + return ""; + } + + final int[] suffixArray = SuffixArray.buildSuffixArray(text); + final int[] lcp = buildLcpArray(text, suffixArray); + + int maxLen = 0; + int maxIdx = 0; + for (int i = 0; i < lcp.length; i++) { + if (lcp[i] > maxLen) { + maxLen = lcp[i]; + maxIdx = suffixArray[i + 1]; + } + } + + return text.substring(maxIdx, maxIdx + maxLen); + } + + /** + * Builds the LCP (Longest Common Prefix) array using Kasai's algorithm. + * + *

LCP[i] is the length of the longest common prefix between the suffixes + * at positions suffixArray[i] and suffixArray[i+1] in sorted order.

+ * + * @param text the original string + * @param suffixArray the suffix array of the string + * @return the LCP array of length n-1 + */ + static int[] buildLcpArray(String text, int[] suffixArray) { + final int n = text.length(); + final int[] rank = new int[n]; + final int[] lcp = new int[n - 1]; + + for (int i = 0; i < n; i++) { + rank[suffixArray[i]] = i; + } + + int k = 0; + for (int i = 0; i < n; i++) { + if (rank[i] == n - 1) { + k = 0; + continue; + } + final int j = suffixArray[rank[i] + 1]; + while (i + k < n && j + k < n && text.charAt(i + k) == text.charAt(j + k)) { + k++; + } + lcp[rank[i]] = k; + if (k > 0) { + k--; + } + } + + return lcp; + } +} diff --git a/src/test/java/com/thealgorithms/strings/LongestRepeatedSubstringTest.java b/src/test/java/com/thealgorithms/strings/LongestRepeatedSubstringTest.java new file mode 100644 index 000000000000..366f6863340d --- /dev/null +++ b/src/test/java/com/thealgorithms/strings/LongestRepeatedSubstringTest.java @@ -0,0 +1,33 @@ +package com.thealgorithms.strings; + +import static org.junit.jupiter.api.Assertions.assertArrayEquals; +import static org.junit.jupiter.api.Assertions.assertEquals; + +import java.util.stream.Stream; +import org.junit.jupiter.params.ParameterizedTest; +import org.junit.jupiter.params.provider.Arguments; +import org.junit.jupiter.params.provider.MethodSource; + +class LongestRepeatedSubstringTest { + + @ParameterizedTest(name = "\"{0}\" -> \"{1}\"") + @MethodSource("provideTestCases") + void testLongestRepeatedSubstring(String input, String expected) { + assertEquals(expected, LongestRepeatedSubstring.longestRepeatedSubstring(input)); + } + + private static Stream provideTestCases() { + return Stream.of(Arguments.of("banana", "ana"), Arguments.of("abcabc", "abc"), Arguments.of("aaaa", "aaa"), Arguments.of("abcd", ""), Arguments.of("a", ""), Arguments.of("", ""), Arguments.of(null, ""), Arguments.of("aab", "a"), Arguments.of("aa", "a"), Arguments.of("mississippi", "issi")); + } + + @ParameterizedTest(name = "\"{0}\" -> LCP={1}") + @MethodSource("provideLcpTestCases") + void testBuildLcpArray(String input, int[] expectedLcp) { + int[] suffixArray = SuffixArray.buildSuffixArray(input); + assertArrayEquals(expectedLcp, LongestRepeatedSubstring.buildLcpArray(input, suffixArray)); + } + + private static Stream provideLcpTestCases() { + return Stream.of(Arguments.of("banana", new int[] {1, 3, 0, 0, 2}), Arguments.of("ab", new int[] {0})); + } +}