131 lines
2.5 KiB
Go
131 lines
2.5 KiB
Go
// File: time_complexity.go
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// Created Time: 2022-12-13
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// Author: msk397 (machangxinq@gmail.com)
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package chapter_computational_complexity
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/* Constant complexity */
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func constant(n int) int {
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count := 0
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size := 100000
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for i := 0; i < size; i++ {
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count++
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}
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return count
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}
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/* Linear complexity */
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func linear(n int) int {
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count := 0
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for i := 0; i < n; i++ {
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count++
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}
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return count
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}
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/* Linear complexity (traversing an array) */
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func arrayTraversal(nums []int) int {
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count := 0
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// Loop count is proportional to the length of the array
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for range nums {
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count++
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}
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return count
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}
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/* Quadratic complexity */
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func quadratic(n int) int {
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count := 0
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// Loop count is squared in relation to the data size n
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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count++
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}
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}
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return count
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}
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/* Quadratic complexity (bubble sort) */
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func bubbleSort(nums []int) int {
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count := 0 // Counter
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// Outer loop: unsorted range is [0, i]
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for i := len(nums) - 1; i > 0; i-- {
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// Inner loop: swap the largest element in the unsorted range [0, i] to the right end of the range
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for j := 0; j < i; j++ {
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if nums[j] > nums[j+1] {
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// Swap nums[j] and nums[j + 1]
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tmp := nums[j]
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nums[j] = nums[j+1]
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nums[j+1] = tmp
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count += 3 // Element swap includes 3 individual operations
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}
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}
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}
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return count
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}
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/* Exponential complexity (loop implementation)*/
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func exponential(n int) int {
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count, base := 0, 1
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// Cells split into two every round, forming the sequence 1, 2, 4, 8, ..., 2^(n-1)
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for i := 0; i < n; i++ {
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for j := 0; j < base; j++ {
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count++
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}
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base *= 2
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}
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// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
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return count
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}
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/* Exponential complexity (recursive implementation)*/
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func expRecur(n int) int {
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if n == 1 {
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return 1
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}
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return expRecur(n-1) + expRecur(n-1) + 1
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}
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/* Logarithmic complexity (loop implementation)*/
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func logarithmic(n int) int {
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count := 0
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for n > 1 {
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n = n / 2
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count++
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}
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return count
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}
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/* Logarithmic complexity (recursive implementation)*/
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func logRecur(n int) int {
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if n <= 1 {
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return 0
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}
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return logRecur(n/2) + 1
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}
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/* Linear logarithmic complexity */
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func linearLogRecur(n int) int {
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if n <= 1 {
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return 1
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}
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count := linearLogRecur(n/2) + linearLogRecur(n/2)
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for i := 0; i < n; i++ {
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count++
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}
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return count
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}
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/* Factorial complexity (recursive implementation) */
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func factorialRecur(n int) int {
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if n == 0 {
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return 1
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}
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count := 0
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// From 1 split into n
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for i := 0; i < n; i++ {
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count += factorialRecur(n - 1)
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}
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return count
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}
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