From f72136a99f05103c5263609ee1d9b4ef7ff24cac Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:15:17 +0500 Subject: [PATCH 1/7] Uploading merge sort algorithm --- mergesort.java | 48 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 48 insertions(+) create mode 100644 mergesort.java diff --git a/mergesort.java b/mergesort.java new file mode 100644 index 0000000..92e47e2 --- /dev/null +++ b/mergesort.java @@ -0,0 +1,48 @@ +// Merge Sort +import java.util.Arrays; + +public class mergesort { + + public static int[] mergeSort(int[] arr) { + if (arr.length <= 1) { + return arr; + } + + int mid = arr.length / 2; + int[] left = Arrays.copyOfRange(arr, 0, mid); + int[] right = Arrays.copyOfRange(arr, mid, arr.length); + + return merge(mergeSort(left), mergeSort(right)); + } + + public static int[] merge(int[] left, int[] right) { + int[] result = new int[left.length + right.length]; + int i = 0, j = 0, k = 0; + + while (i < left.length && j < right.length) { + if (left[i] < right[j]) { + result[k++] = left[i++]; + } else { + result[k++] = right[j++]; + } + } + + while (i < left.length) { + result[k++] = left[i++]; + } + + while (j < right.length) { + result[k++] = right[j++]; + } + + return result; + } + + public static void main(String[] args) { + int[] arr = {38, 27, 43, 3, 9, 82, 10}; + int[] sortedArr = mergeSort(arr); + System.out.println("Sorted Array: " + Arrays.toString(sortedArr)); + } +} + + From c0e8ccb69f73b210625ae1669691b54873af787f Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:16:46 +0500 Subject: [PATCH 2/7] Uploading merge sort algorithm with tester --- MergeSortWithMetrics.java | 58 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 MergeSortWithMetrics.java diff --git a/MergeSortWithMetrics.java b/MergeSortWithMetrics.java new file mode 100644 index 0000000..82e441b --- /dev/null +++ b/MergeSortWithMetrics.java @@ -0,0 +1,58 @@ +// Merge Sort with Time and Recursion Depth Measurement +import java.util.Arrays; + +public class MergeSortWithMetrics { + + private static int recursionDepth = 0; + + public static int[] mergeSortWithMetrics(int[] arr) { + recursionDepth++; + if (arr.length <= 1) { + recursionDepth--; + return arr; + } + + int mid = arr.length / 2; + int[] left = Arrays.copyOfRange(arr, 0, mid); + int[] right = Arrays.copyOfRange(arr, mid, arr.length); + + return mergeWithMetrics(mergeSortWithMetrics(left), mergeSortWithMetrics(right)); + } + + public static int[] mergeWithMetrics(int[] left, int[] right) { + int[] result = new int[left.length + right.length]; + int i = 0, j = 0, k = 0; + int comparisons = 0; + + while (i < left.length && j < right.length) { + comparisons++; + if (left[i] < right[j]) { + result[k++] = left[i++]; + } else { + result[k++] = right[j++]; + } + } + + while (i < left.length) { + result[k++] = left[i++]; + } + + while (j < right.length) { + result[k++] = right[j++]; + } + + return result; + } + + public static void main(String[] args) { + int[] arr = {38, 27, 43, 3, 9, 82, 10}; + + long startTime = System.nanoTime(); + int[] sortedArr = mergeSortWithMetrics(arr); + long endTime = System.nanoTime(); + + System.out.println("Sorted Array: " + Arrays.toString(sortedArr)); + System.out.println("Time taken: " + (endTime - startTime) / 1_000_000.0 + " ms"); + System.out.println("Recursion Depth: " + recursionDepth); + } +} \ No newline at end of file From bcd9b4b40df0295ac1a4bbf04f287245d5b715f1 Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:17:29 +0500 Subject: [PATCH 3/7] Uploading quick sort algorithm --- QuickSortt.java | 50 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 50 insertions(+) create mode 100644 QuickSortt.java diff --git a/QuickSortt.java b/QuickSortt.java new file mode 100644 index 0000000..eaf8962 --- /dev/null +++ b/QuickSortt.java @@ -0,0 +1,50 @@ +// Quick Sort +import java.util.Random; + +public class QuickSortt { + + public static int partition(int[] arr, int low, int high) { + Random random = new Random(); + int pivotIndex = random.nextInt(high - low + 1) + low; + int temp = arr[pivotIndex]; + arr[pivotIndex] = arr[high]; + arr[high] = temp; + + int pivot = arr[high]; + int i = low - 1; + + for (int j = low; j < high; j++) { + if (arr[j] <= pivot) { + i++; + temp = arr[i]; + arr[i] = arr[j]; + arr[j] = temp; + } + } + + temp = arr[i + 1]; + arr[i + 1] = arr[high]; + arr[high] = temp; + return i + 1; + } + + public static void quickSort(int[] arr, int low, int high) { + while (low < high) { + int pi = partition(arr, low, high); + + if (pi - low < high - pi) { + quickSort(arr, low, pi - 1); + low = pi + 1; + } else { + quickSort(arr, pi + 1, high); + high = pi - 1; + } + } + } + + public static void main(String[] args) { + int[] arr = {38, 27, 43, 3, 9, 82, 10}; + quickSort(arr, 0, arr.length - 1); + System.out.println("Sorted Array: " + java.util.Arrays.toString(arr)); + } +} From 1aec74aef361d3d0eea5bb141358f7ab8ea6c2ce Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:22:34 +0500 Subject: [PATCH 4/7] Uploading Deterministic select --- select.java | 67 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 67 insertions(+) create mode 100644 select.java diff --git a/select.java b/select.java new file mode 100644 index 0000000..7f90eb8 --- /dev/null +++ b/select.java @@ -0,0 +1,67 @@ +// Deterministic select +import java.util.Arrays; + +public class select { + + public static int medianOfMedians(int[] arr) { + int n = arr.length; + int groupsCount = (n + 4) / 5; + int[] medians = new int[groupsCount]; + + for (int i = 0; i < groupsCount; i++) { + int start = i * 5; + int end = Math.min(start + 5, n); + int[] group = Arrays.copyOfRange(arr, start, end); + Arrays.sort(group); + medians[i] = group[group.length / 2]; + } + + if (medians.length <= 5) { + Arrays.sort(medians); + return medians[medians.length / 2]; + } else { + return medianOfMedians(medians); + } + } + + public static int partition(int[] arr, int low, int high, int pivot) { + int i = low; + for (int j = low; j < high; j++) { + if (arr[j] < pivot) { + int temp = arr[i]; + arr[i] = arr[j]; + arr[j] = temp; + i++; + } + } + int temp = arr[i]; + arr[i] = arr[high]; + arr[high] = temp; + return i; + } + + public static int deterministicSelect(int[] arr, int low, int high, int k) { + if (low == high) { + return arr[low]; + } + + int pivot = medianOfMedians(Arrays.copyOfRange(arr, low, high + 1)); + + int pivotIndex = partition(arr, low, high, pivot); + + if (pivotIndex == k) { + return arr[pivotIndex]; + } else if (pivotIndex > k) { + return deterministicSelect(arr, low, pivotIndex - 1, k); + } else { + return deterministicSelect(arr, pivotIndex + 1, high, k); + } + } + + public static void main(String[] args) { + int[] arr = {38, 27, 43, 3, 9, 82, 10}; + int k = 3; + int result = deterministicSelect(arr, 0, arr.length - 1, k); + System.out.println("The " + (k + 1) + "-th smallest element is: " + result); + } +} From 7c79eac737711706bb34d5d2b82f1e66089227a6 Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:23:27 +0500 Subject: [PATCH 5/7] Uploading Closest pair of points --- ClosestPairOfPoints.java | 88 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 88 insertions(+) create mode 100644 ClosestPairOfPoints.java diff --git a/ClosestPairOfPoints.java b/ClosestPairOfPoints.java new file mode 100644 index 0000000..156f354 --- /dev/null +++ b/ClosestPairOfPoints.java @@ -0,0 +1,88 @@ +// Closest pair of points +import java.util.Arrays; +import java.util.Comparator; +import java.util.ArrayList; + +public class ClosestPairOfPoints { + + public static double distance(int[] p1, int[] p2) { + return Math.sqrt(Math.pow(p1[0] - p2[0], 2) + Math.pow(p1[1] - p2[1], 2)); + } + + public static double closestInStrip(int[][] strip, double d) { + double minDist = d; + Arrays.sort(strip, Comparator.comparingInt(p -> p[1])); + + for (int i = 0; i < strip.length; i++) { + for (int j = i + 1; j < Math.min(i + 7, strip.length); j++) { + double dist = distance(strip[i], strip[j]); + if (dist < minDist) { + minDist = dist; + } + } + } + return minDist; + } + + public static double closestPair(int[][] pointsSortedByX, int[][] pointsSortedByY) { + if (pointsSortedByX.length <= 3) { + double minDist = Double.POSITIVE_INFINITY; + for (int i = 0; i < pointsSortedByX.length; i++) { + for (int j = i + 1; j < pointsSortedByX.length; j++) { + minDist = Math.min(minDist, distance(pointsSortedByX[i], pointsSortedByX[j])); + } + } + return minDist; + } + + int mid = pointsSortedByX.length / 2; + int[] midPoint = pointsSortedByX[mid]; + + int[][] leftX = Arrays.copyOfRange(pointsSortedByX, 0, mid); + int[][] rightX = Arrays.copyOfRange(pointsSortedByX, mid, pointsSortedByX.length); + + ArrayList leftY = new ArrayList<>(); + ArrayList rightY = new ArrayList<>(); + + for (int[] p : pointsSortedByY) { + if (p[0] <= midPoint[0]) { + leftY.add(p); + } else { + rightY.add(p); + } + } + + double leftMin = closestPair(leftX, leftY.toArray(new int[0][0])); + double rightMin = closestPair(rightX, rightY.toArray(new int[0][0])); + + double d = Math.min(leftMin, rightMin); + + int[][] strip = new int[pointsSortedByY.length][2]; + int stripCount = 0; + for (int[] p : pointsSortedByY) { + if (Math.abs(p[0] - midPoint[0]) < d) { + strip[stripCount++] = p; + } + } + + return Math.min(d, closestInStrip(Arrays.copyOfRange(strip, 0, stripCount), d)); + } + + public static double closestPairOfPoints(int[][] points) { + int[][] pointsSortedByX = Arrays.copyOf(points, points.length); + Arrays.sort(pointsSortedByX, Comparator.comparingInt(p -> p[0])); + + int[][] pointsSortedByY = Arrays.copyOf(points, points.length); + Arrays.sort(pointsSortedByY, Comparator.comparingInt(p -> p[1])); + + return closestPair(pointsSortedByX, pointsSortedByY); + } + + public static void main(String[] args) { + int[][] points = { + {2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4} + }; + double result = closestPairOfPoints(points); + System.out.println("The closest pair of points has a distance of: " + result); + } +} \ No newline at end of file From 9e2b97a6b693321957fc51c801df699675d10bb5 Mon Sep 17 00:00:00 2001 From: ElzhanZhandos <150348751+Elzhan2007@users.noreply.github.com> Date: Fri, 26 Sep 2025 12:29:07 +0500 Subject: [PATCH 6/7] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 8de955a..f04e515 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,7 @@ #### Assignment 1 i. Implemented algorithms -ii. We implemented 4 algorithms: + 1. Merge Sort 2. Quick Sort 3. 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