From 995b3efce88474644e197d51005b97dde9804b37 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:28:12 +0530 Subject: [PATCH 1/4] feat: Add `CountingInversions` new algorithm with Junit tests --- .../divideandconquer/CountingInversions.java | 96 +++++++++++++++++++ .../CountingInversionsTest.java | 32 +++++++ 2 files changed, 128 insertions(+) create mode 100644 src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java create mode 100644 src/test/java/com/thealgorithms/divideandconquer/CountingInversionsTest.java diff --git a/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java new file mode 100644 index 000000000000..11e61e8818a3 --- /dev/null +++ b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java @@ -0,0 +1,96 @@ +package com.thealgorithms.divideandconquer; + +/** + * A utility class for counting the number of inversions in an array. + *

+ * An inversion is a pair (i, j) such that i < j and arr[i] > arr[j]. + * This class implements a divide-and-conquer approach, similar to merge sort, + * to count the number of inversions efficiently. + *

+ * Time Complexity: O(n log n) + * Space Complexity: O(n) (due to temporary arrays during merge step) + * + *

Applications: + * - Used in algorithms related to sorting and permutation analysis. + * - Helps in determining how far an array is from being sorted. + * - Applicable in bioinformatics and signal processing. + * + *

This class cannot be instantiated, as it is intended to provide + * only static utility methods. + */ +public final class CountingInversions { + private CountingInversions() { + } + + /** + * Counts the number of inversions in the given array. + * + * @param arr The input array of integers. + * @return The total number of inversions in the array. + */ + public static int countInversions(int[] arr) { + return mergeSortAndCount(arr, 0, arr.length - 1); + } + + /** + * Recursively divides the array into two halves, sorts them, and counts + * the number of inversions. Uses a modified merge sort approach. + * + * @param arr The input array. + * @param left The starting index of the current segment. + * @param right The ending index of the current segment. + * @return The number of inversions within the segment [left, right]. + */ + private static int mergeSortAndCount(int[] arr, int left, int right) { + if (left >= right) { + return 0; + } + + int mid = left + (right - left) / 2; + int inversions = 0; + + inversions += mergeSortAndCount(arr, left, mid); + inversions += mergeSortAndCount(arr, mid + 1, right); + inversions += mergeAndCount(arr, left, mid, right); + return inversions; + } + + /** + * Merges two sorted subarrays and counts the cross-inversions between them. + * A cross-inversion occurs when an element from the right subarray is + * smaller than an element from the left subarray. + * + * @param arr The input array. + * @param left The starting index of the first subarray. + * @param mid The ending index of the first subarray and midpoint of the segment. + * @param right The ending index of the second subarray. + * @return The number of cross-inversions between the two subarrays. + */ + private static int mergeAndCount(int[] arr, int left, int mid, int right) { + int[] leftArr = new int[mid - left + 1]; + int[] rightArr = new int[right - mid]; + + System.arraycopy(arr, left, leftArr, 0, mid - left + 1); + System.arraycopy(arr, mid + 1, rightArr, 0, right - mid); + + int i = 0, j = 0, k = left, inversions = 0; + + while (i < leftArr.length && j < rightArr.length) { + if (leftArr[i] <= rightArr[j]) { + arr[k++] = leftArr[i++]; + } else { + arr[k++] = rightArr[j++]; + inversions += (mid + 1) - (left + i); + } + } + + while (i < leftArr.length) { + arr[k++] = leftArr[i++]; + } + while (j < rightArr.length) { + arr[k++] = rightArr[j++]; + } + + return inversions; + } +} diff --git a/src/test/java/com/thealgorithms/divideandconquer/CountingInversionsTest.java b/src/test/java/com/thealgorithms/divideandconquer/CountingInversionsTest.java new file mode 100644 index 000000000000..d12614d6fd06 --- /dev/null +++ b/src/test/java/com/thealgorithms/divideandconquer/CountingInversionsTest.java @@ -0,0 +1,32 @@ +package com.thealgorithms.divideandconquer; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import org.junit.jupiter.api.Test; + +public class CountingInversionsTest { + + @Test + public void testCountInversions() { + int[] arr = {2, 3, 8, 6, 1}; + assertEquals(5, CountingInversions.countInversions(arr)); + } + + @Test + public void testNoInversions() { + int[] arr = {1, 2, 3, 4, 5}; + assertEquals(0, CountingInversions.countInversions(arr)); + } + + @Test + public void testSingleElement() { + int[] arr = {1}; + assertEquals(0, CountingInversions.countInversions(arr)); + } + + @Test + public void testAllInversions() { + int[] arr = {5, 4, 3, 2, 1}; + assertEquals(10, CountingInversions.countInversions(arr)); + } +} From 5418a73fba39e55e0aef2bb8c9449d38b0b18fc8 Mon Sep 17 00:00:00 2001 From: Hardvan Date: Sun, 13 Oct 2024 02:58:30 +0000 Subject: [PATCH 2/4] Update directory --- DIRECTORY.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 30fa2cbee199..ba54da17c8f8 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -25,9 +25,11 @@ * bitmanipulation * [BinaryPalindromeCheck](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BinaryPalindromeCheck.java) * [BitSwap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BitSwap.java) + * [BooleanAlgebraGates](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/BooleanAlgebraGates.java) * [ClearLeftmostSetBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/ClearLeftmostSetBit.java) * [CountLeadingZeros](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountLeadingZeros.java) * [CountSetBits](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/CountSetBits.java) + * [FindNthBit](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/FindNthBit.java) * [GrayCodeConversion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/GrayCodeConversion.java) * [HammingDistance](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HammingDistance.java) * [HigherLowerPowerOfTwo](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwo.java) @@ -54,6 +56,7 @@ * [CompositeLFSR](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/CompositeLFSR.java) * [LFSR](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/LFSR.java) * [Utils](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/a5/Utils.java) + * [ADFGVXCipher](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/ADFGVXCipher.java) * [AES](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AES.java) * [AESEncryption](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AESEncryption.java) * [AffineCipher](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/ciphers/AffineCipher.java) @@ -133,6 +136,7 @@ * [FordFulkerson](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java) * [Graphs](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Graphs.java) * [HamiltonianCycle](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/HamiltonianCycle.java) + * [JohnsonsAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithm.java) * [KahnsAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/KahnsAlgorithm.java) * [Kosaraju](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Kosaraju.java) * [Kruskal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java) @@ -244,6 +248,7 @@ * divideandconquer * [BinaryExponentiation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/BinaryExponentiation.java) * [ClosestPair](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/ClosestPair.java) + * [CountingInversions](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java) * [MedianOfTwoSortedArrays](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/MedianOfTwoSortedArrays.java) * [SkylineAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/SkylineAlgorithm.java) * [StrassenMatrixMultiplication](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/StrassenMatrixMultiplication.java) @@ -340,6 +345,7 @@ * [EulersFunction](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/EulersFunction.java) * [Factorial](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/Factorial.java) * [FactorialRecursion](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FactorialRecursion.java) + * [FastExponentiation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FastExponentiation.java) * [FastInverseSqrt](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FastInverseSqrt.java) * [FFT](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FFT.java) * [FFTBluestein](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/FFTBluestein.java) @@ -656,9 +662,11 @@ * bitmanipulation * [BinaryPalindromeCheckTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BinaryPalindromeCheckTest.java) * [BitSwapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BitSwapTest.java) + * [BooleanAlgebraGatesTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/BooleanAlgebraGatesTest.java) * [ClearLeftmostSetBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/ClearLeftmostSetBitTest.java) * [CountLeadingZerosTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountLeadingZerosTest.java) * [CountSetBitsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/CountSetBitsTest.java) + * [FindNthBitTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/FindNthBitTest.java) * [GrayCodeConversionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/GrayCodeConversionTest.java) * [HammingDistanceTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HammingDistanceTest.java) * [HigherLowerPowerOfTwoTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/bitmanipulation/HigherLowerPowerOfTwoTest.java) @@ -682,6 +690,7 @@ * [A5CipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/A5CipherTest.java) * [A5KeyStreamGeneratorTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/A5KeyStreamGeneratorTest.java) * [LFSRTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/a5/LFSRTest.java) + * [ADFGVXCipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/ADFGVXCipherTest.java) * [AESEncryptionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AESEncryptionTest.java) * [AffineCipherTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AffineCipherTest.java) * [AtbashTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/ciphers/AtbashTest.java) @@ -750,6 +759,7 @@ * [FloydWarshallTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FloydWarshallTest.java) * [FordFulkersonTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java) * [HamiltonianCycleTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/HamiltonianCycleTest.java) + * [JohnsonsAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithmTest.java) * [KosarajuTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java) * [TarjansAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/TarjansAlgorithmTest.java) * [WelshPowellTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java) @@ -814,6 +824,7 @@ * divideandconquer * [BinaryExponentiationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/BinaryExponentiationTest.java) * [ClosestPairTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/ClosestPairTest.java) + * [CountingInversionsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/CountingInversionsTest.java) * [MedianOfTwoSortedArraysTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/MedianOfTwoSortedArraysTest.java) * [SkylineAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/SkylineAlgorithmTest.java) * [StrassenMatrixMultiplicationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/StrassenMatrixMultiplicationTest.java) @@ -902,6 +913,7 @@ * [EulersFunctionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/EulersFunctionTest.java) * [FactorialRecursionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialRecursionTest.java) * [FactorialTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialTest.java) + * [FastExponentiationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FastExponentiationTest.java) * [FastInverseSqrtTests](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FastInverseSqrtTests.java) * [FFTTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FFTTest.java) * [FibonacciJavaStreamsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FibonacciJavaStreamsTest.java) From 95a15344f749342fc2d1461b8b44d7a1ad85a4c2 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:31:29 +0530 Subject: [PATCH 3/4] Fix --- .../thealgorithms/divideandconquer/CountingInversions.java | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java index 11e61e8818a3..eece39012c70 100644 --- a/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java +++ b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java @@ -73,7 +73,10 @@ private static int mergeAndCount(int[] arr, int left, int mid, int right) { System.arraycopy(arr, left, leftArr, 0, mid - left + 1); System.arraycopy(arr, mid + 1, rightArr, 0, right - mid); - int i = 0, j = 0, k = left, inversions = 0; + int i = 0; + int j = 0; + int k = left; + int inversions = 0; while (i < leftArr.length && j < rightArr.length) { if (leftArr[i] <= rightArr[j]) { From d65cc0cbad19204e3bb03c12f0d2804e247b5e01 Mon Sep 17 00:00:00 2001 From: Hardik Pawar Date: Sun, 13 Oct 2024 08:41:29 +0530 Subject: [PATCH 4/4] Fix --- .../thealgorithms/divideandconquer/CountingInversions.java | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java index eece39012c70..15c8bc33b58f 100644 --- a/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java +++ b/src/main/java/com/thealgorithms/divideandconquer/CountingInversions.java @@ -17,6 +17,8 @@ * *

This class cannot be instantiated, as it is intended to provide * only static utility methods. + * + * @author Hardvan */ public final class CountingInversions { private CountingInversions() { @@ -83,7 +85,7 @@ private static int mergeAndCount(int[] arr, int left, int mid, int right) { arr[k++] = leftArr[i++]; } else { arr[k++] = rightArr[j++]; - inversions += (mid + 1) - (left + i); + inversions += mid + 1 - left - i; } }