105 lines
2.8 KiB
C#
105 lines
2.8 KiB
C#
/**
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* File: space_complexity.cs
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* Created Time: 2022-12-23
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* Author: haptear (haptear@hotmail.com)
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*/
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namespace hello_algo.chapter_computational_complexity;
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public class space_complexity {
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/* Function */
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int Function() {
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// Perform some operations
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return 0;
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}
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/* Constant complexity */
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void Constant(int n) {
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// Constants, variables, objects occupy O(1) space
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int a = 0;
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int b = 0;
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int[] nums = new int[10000];
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ListNode node = new(0);
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// Variables in a loop occupy O(1) space
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for (int i = 0; i < n; i++) {
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int c = 0;
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}
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// Functions in a loop occupy O(1) space
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for (int i = 0; i < n; i++) {
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Function();
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}
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}
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/* Linear complexity */
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void Linear(int n) {
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// Array of length n occupies O(n) space
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int[] nums = new int[n];
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// A list of length n occupies O(n) space
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List<ListNode> nodes = [];
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for (int i = 0; i < n; i++) {
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nodes.Add(new ListNode(i));
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}
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// A hash table of length n occupies O(n) space
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Dictionary<int, string> map = [];
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for (int i = 0; i < n; i++) {
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map.Add(i, i.ToString());
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}
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}
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/* Linear complexity (recursive implementation) */
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void LinearRecur(int n) {
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Console.WriteLine("Recursion n =" + n);
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if (n == 1) return;
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LinearRecur(n - 1);
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}
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/* Quadratic complexity */
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void Quadratic(int n) {
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// Matrix occupies O(n^2) space
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int[,] numMatrix = new int[n, n];
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// A two-dimensional list occupies O(n^2) space
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List<List<int>> numList = [];
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for (int i = 0; i < n; i++) {
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List<int> tmp = [];
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for (int j = 0; j < n; j++) {
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tmp.Add(0);
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}
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numList.Add(tmp);
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}
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}
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/* Quadratic complexity (recursive implementation) */
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int QuadraticRecur(int n) {
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if (n <= 0) return 0;
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int[] nums = new int[n];
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Console.WriteLine("Recursion n = " + n + " in the length of nums =" + nums.Length);
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return QuadraticRecur(n - 1);
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}
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/* Exponential complexity (building a full binary tree) */
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TreeNode? BuildTree(int n) {
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if (n == 0) return null;
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TreeNode root = new(0) {
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left = BuildTree(n - 1),
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right = BuildTree(n - 1)
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};
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return root;
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}
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[Test]
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public void Test() {
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int n = 5;
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// Constant complexity
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Constant(n);
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// Linear complexity
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Linear(n);
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LinearRecur(n);
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// Quadratic complexity
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Quadratic(n);
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QuadraticRecur(n);
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// Exponential complexity
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TreeNode? root = BuildTree(n);
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PrintUtil.PrintTree(root);
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}
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}
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