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‎algorithm-analysis/PrimeNumber.java

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package algorithm_analysis;
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import java.util.Scanner;
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// For a given integer n, determine whether the number is prime or not.
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public class PrimeNumber {
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// Time: O(sqrt(n))
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public static boolean isPrime(long n) {
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if (n < 2) {
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return false;
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}
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int limit = (int)Math.sqrt(n);
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for (long i = 2; i <= limit; i++) { // It's enough to check until sqrt(n)
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if (n % i == 0) {
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return false;
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}
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}
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return true;
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}
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public static void main(String[] args) {
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Scanner sc = new Scanner(System.in);
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long n = sc.nextLong();
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long startTime = System.nanoTime();
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System.out.println(isPrime(n));
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long endTime = System.nanoTime();
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long totalTime = endTime - startTime;
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System.out.printf("Time: %.4fs", (totalTime / 1000000000.0)); // print execution time
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sc.close();
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}
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}
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// For each number, we can divide its divisors into two groups
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// 1) integers smaller than the square root
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// 2) integers greater than the square root
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// 1 2 3 4 6 | 9 12 18 36
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// 1 * 36 = 36
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// 2 * 18 = 36
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// 3 * 12 = 36
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// 4 * 9
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// 6 * 6 = 36
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// For testing purpose:
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// Prime numbers: 7, 101, 103703 1000000007 32416190039

‎algorithm-analysis/SpaceComplexityExamples.java

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package algorithm_analysis;
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public class SpaceComplexityExamples {
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// Space: O(1)
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public static int example1(int n) {
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int sum = 0;
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for (int i = 1; i <= n; i++) {
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sum += i;
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}
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return sum;
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}
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// Space: O(n)
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public static int[] example2(int[] array) {
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int n = array.length;
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int[] result = new int[2 * n];
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for (int i = 0; i < n; i++) {
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result[i] = array[i];
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result[n + i] = array[i];
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}
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return result;
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}
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// Space: O(n * m)
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public static int example3(int[][] matrix) {
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int n = matrix.length;
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int m = matrix[0].length;
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int sum = 0;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < m; j++) {
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sum += matrix[i][j];
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}
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}
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int[] array = new int[n];
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for (int i = 0; i < n; i++) {
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array[i] = matrix[i][0];
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}
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return sum;
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}
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}

‎algorithm-analysis/TimeComplexityExamples.java

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package algorithm_analysis;
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public class TimeComplexityExamples {
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// Time: O(n^2)
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public static boolean hasDuplicates(int[] array) {
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int n = array.length;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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if (i != j && array[i] == array[j]) {
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return true;
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}
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}
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}
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return false;
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}
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// Time: O(n^2)
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public static int f(int n) {
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int sum = 0;
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for (int i = 1; i <= n; i++) {
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for (int j = 1; j <= i; j++) {
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sum += i * j;
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}
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}
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for (int i = 0; i < n; i++) {
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sum = sum - i;
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}
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for (int i = 0; i < 100; i++) {
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sum += i;
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}
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return sum;
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}
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// Time: O(n + m)
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public static int[] union(int[] A, int[] B) {
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int n = A.length;
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int m = B.length;
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int[] C = new int[n + m];
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int index = 0;
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for (int i = 0; i < n; i++) {
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C[index] = A[i];
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index++;
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}
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for (int i = 0; i < m; i++) {
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C[index] = B[i];
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index++;
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}
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return C;
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}
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// Time: O(n * m)
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public static int matrixSum(int[][] matrix) {
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int n = matrix.length;
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int m = matrix[0].length;
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int sum = 0;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < m; j++) {
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sum += matrix[i][j];
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}
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}
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return sum;
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}
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// Time: O(logn)
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public static int g(int n) {
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int result = 0;
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int i = n;
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while (i > 1) {
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result += i;
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i /= 2;
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}
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return result;
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}
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}

‎binary-search/BinarySearch.java

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package binarySearch;
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public class BinarySearch {
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public static int search(int[] array, int target) { // O(logn)
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int lo = 0;
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int hi = array.length - 1;
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while (lo <= hi) {
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int mid = (lo + hi) / 2;
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if (target > array[mid]) {
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lo = mid + 1;
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} else if (target < array[mid]) {
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hi = mid - 1;
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} else {
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return mid; // match
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}
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}
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return -1; // no match
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}
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public static void main(String[] args) {
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int[] array = {1, 3, 3, 3, 4, 4, 6, 6, 6, 6, 7, 7, 7, 8, 8, 11, 15, 22};
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int index = search(array, 2);
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System.out.println(index);
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}
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}

‎binary-search/FirstOccurrence.java

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package binarySearch;
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public class FirstOccurrence {
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public static int firstOccurrence(int[] array, int target) {
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int lo = 0;
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int hi = array.length - 1;
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while (lo < hi) {
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int mid = (lo + hi) / 2;
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if (target > array[mid]) {
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lo = mid + 1; // search the right half [mid + 1, hi]
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} else {
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hi = mid; // search left half + middle element [lo, mid]
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}
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}
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if (array[lo] == target) {
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return lo;
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} else {
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return -1;
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}
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}
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public static void main(String[] args) {
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int[] array = {1, 3, 3, 3, 4, 4, 6, 6, 6, 6, 7, 7, 7, 8, 8, 11, 15, 22};
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int index = firstOccurrence(array, 13);
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System.out.println(index);
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}
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}

‎binary-search/LastOccurrence.java

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package binarySearch;
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public class LastOccurrence {
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public static int lastOccurrence(int[] array, int target) {
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int lo = 0;
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int hi = array.length - 1;
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while (lo < hi) {
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int mid = (lo + hi + 1) / 2; // [1, 2]
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if (target < array[mid]) {
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hi = mid - 1; // [lo, mid-1]
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} else {
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lo = mid; // [mid, hi]
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}
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}
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if (array[lo] == target) {
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return lo;
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} else {
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return -1;
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}
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}
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public static void main(String[] args) {
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int[] array = {1, 2};
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int index = lastOccurrence(array, 1);
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System.out.println(index);
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}
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// lo = 0, hi = 1, mid = 1
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// lo = 0, hi = 0
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}

‎binary-search/NumberOfOccurrences.java

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package binarySearch;
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public class NumberOfOccurrences {
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public static int firstOccurrence(int[] array, int target) {
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int lo = 0;
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int hi = array.length - 1;
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while (lo < hi) {
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int mid = (lo + hi) / 2;
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if (target > array[mid]) {
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lo = mid + 1;
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} else {
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hi = mid;
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}
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}
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if (array[lo] == target) {
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return lo;
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} else {
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return -1;
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}
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}
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public static int lastOccurrence(int[] array, int target) {
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int lo = 0;
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int hi = array.length - 1;
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while (lo < hi) {
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int mid = (lo + hi + 1) / 2;
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if (target < array[mid]) {
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hi = mid - 1;
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} else {
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lo = mid;
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}
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}
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if (array[lo] == target) {
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return lo;
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} else {
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return -1;
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}
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}
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public static int numberOfOccurrences(int[] array, int target) { // O(logn)
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int first = firstOccurrence(array, target); // O(logn)
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int last = lastOccurrence(array, target); // O(logn)
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if (first == -1) {
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return 0;
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} else {
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return last - first + 1; // [lo, hi] => hi - lo + 1
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}
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}
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public static void main(String[] args) {
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int[] array = {1, 3, 3, 3, 4, 4, 6, 6, 6, 6, 7, 7, 7, 8, 8, 11, 15, 22};
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int count = numberOfOccurrences(array, 4);
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System.out.println(count);
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}
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// linear solution O(n)
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}

‎sorting/BubbleSort.java

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package sorting;
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public class BubbleSort {
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public static void sort(int[] array) {
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int n = array.length;
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while (true) {
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boolean swapped = false;
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for (int i = 0; i < n - 1; i++) {
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if (array[i + 1] < array[i]) {
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swap(array, i, i + 1);
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swapped = true;
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}
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}
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if (!swapped) break;
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}
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}
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private static void swap(int[] array, int i, int j) {
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int temp = array[i];
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array[i] = array[j];
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array[j] = temp;
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}
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private static void print(int[] A) {
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System.out.print("[");
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for (int i = 0; i < A.length; i++) {
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System.out.print(A[i]);
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if (i < A.length - 1) {
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System.out.print(", ");
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}
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}
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System.out.println("]");
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}
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public static void main(String[] args) {
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int[] A = {105, 8, 4, 22, 16, 3, 9, 11, 1, 19, 8, 6, 7};
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sort(A);
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print(A);
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}
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}
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