Skip to content

Commit

Permalink
Merge pull request krahets#99 from msk397/master
Browse files Browse the repository at this point in the history
time complexity using go
  • Loading branch information
krahets authored Dec 13, 2022
2 parents 58ca52d + 1ec9712 commit ea32a1c
Show file tree
Hide file tree
Showing 7 changed files with 537 additions and 17 deletions.
Original file line number Diff line number Diff line change
@@ -0,0 +1,131 @@
// File: quick_sort_test.go
// Created Time: 2022-12-13
// Author: msk397 ([email protected])

package time_complexity

/* 常数阶 */
func constant(n int) int {
count := 0
size := 100000
for i := 0; i < size; i++ {
count++
}
return count
}

/* 线性阶 */
func linear(n int) int {
count := 0
for i := 0; i < n; i++ {
count++
}
return count
}

/* 线性阶(遍历数组) */
func arrayTraversal(nums []int) int {
count := 0
// 循环次数与数组长度成正比
for range nums {
count++
}
return count
}

/* 平方阶 */
func quadratic(n int) int {
count := 0
// 循环次数与数组长度成平方关系
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
count++
}
}
return count
}

/* 平方阶(冒泡排序) */
func bubbleSort(nums []int) int {
count := 0 // 计数器
// 外循环:待排序元素数量为 n-1, n-2, ..., 1
for i := len(nums) - 1; i > 0; i-- {
// 内循环:冒泡操作
for j := 0; j < i; j++ {
if nums[j] > nums[j+1] {
// 交换 nums[j] 与 nums[j + 1]
tmp := nums[j]
nums[j] = nums[j+1]
nums[j+1] = tmp
count += 3 // 元素交换包含 3 个单元操作
}
}
}
return count
}

/* 指数阶(循环实现)*/
func exponential(n int) int {
count, base := 0, 1
// cell 每轮一分为二,形成数列 1, 2, 4, 8, ..., 2^(n-1)
for i := 0; i < n; i++ {
for j := 0; j < base; j++ {
count++
}
base *= 2
}
// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
return count
}

/* 指数阶(递归实现)*/
func expRecur(n int) int {
if n == 1 {
return 1
}
return expRecur(n-1) + expRecur(n-1) + 1
}

/* 对数阶(循环实现)*/
func logarithmic(n float64) int {
count := 0
for n > 1 {
n = n / 2
count++
}
return count
}

/* 对数阶(递归实现)*/
func logRecur(n float64) int {
if n <= 1 {
return 0
}
return logRecur(n/2) + 1
}

/* 线性对数阶 */
func linearLogRecur(n float64) int {
if n <= 1 {
return 1
}
count := linearLogRecur(n/2) +
linearLogRecur(n/2)
for i := 0.0; i < n; i++ {
count++
}
return count
}

/* 阶乘阶(递归实现) */
func factorialRecur(n int) int {
if n == 0 {
return 1
}
count := 0
// 从 1 个分裂出 n 个
for i := 0; i < n; i++ {
count += factorialRecur(n - 1)
}
return count
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,48 @@
// File: quick_sort_test.go
// Created Time: 2022-12-13
// Author: msk397 ([email protected])

package time_complexity

import (
"fmt"
"testing"
)

func TestTimeComplexity(t *testing.T) {
n := 8
fmt.Println("输入数据大小 n =", n)

count := constant(n)
fmt.Println("常数阶的计算操作数量 =", count)

count = linear(n)
fmt.Println("线性阶的计算操作数量 =", count)
count = arrayTraversal(make([]int, n))
fmt.Println("线性阶(遍历数组)的计算操作数量 =", count)

count = quadratic(n)
fmt.Println("平方阶的计算操作数量 =", count)
nums := make([]int, n)
for i := 0; i < n; i++ {
nums[i] = n - i
}
count = bubbleSort(nums)
fmt.Println("平方阶(冒泡排序)的计算操作数量 =", count)

count = exponential(n)
fmt.Println("指数阶(循环实现)的计算操作数量 =", count)
count = expRecur(n)
fmt.Println("指数阶(递归实现)的计算操作数量 =", count)

count = logarithmic(float64(n))
fmt.Println("对数阶(循环实现)的计算操作数量 =", count)
count = logRecur(float64(n))
fmt.Println("对数阶(递归实现)的计算操作数量 =", count)

count = linearLogRecur(float64(n))
fmt.Println("线性对数阶(递归实现)的计算操作数量 =", count)

count = factorialRecur(n)
fmt.Println("阶乘阶(递归实现)的计算操作数量 =", count)
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,45 @@
// File: worst_best_time_complexity.go
// Created Time: 2022-12-13
// Author: msk397 ([email protected])

package time_complexity

import (
"fmt"
"math/rand"
)

/* 生成一个数组,元素为 { 1, 2, ..., n },顺序被打乱 */
func randomNumbers(n int) []int {
nums := make([]int, n)
// 生成数组 nums = { 1, 2, 3, ..., n }
for i := 0; i < n; i++ {
nums[i] = i + 1
}
// 随机打乱数组元素
rand.Shuffle(len(nums), func(i, j int) {
nums[i], nums[j] = nums[j], nums[i]
})
return nums
}

/* 查找数组 nums 中数字 1 所在索引 */
func findOne(nums []int) int {
for i := 0; i < len(nums); i++ {
if nums[i] == 1 {
return i
}
}
return -1
}

/* Driver Code */
func main() {
for i := 0; i < 10; i++ {
n := 100
nums := randomNumbers(n)
index := findOne(nums)
fmt.Println("\n数组 [ 1, 2, ..., n ] 被打乱后 =", nums)
fmt.Println("数字 1 的索引为", index)
}
}
53 changes: 53 additions & 0 deletions codes/go/chapter_sorting/merge_sort/merge_sort.go
Original file line number Diff line number Diff line change
@@ -0,0 +1,53 @@
package merge_sort
// File: merge_sort.go
// Created Time: 2022-12-13
// Author: msk397 ([email protected])

/*
合并左子数组和右子数组
左子数组区间 [left, mid]
右子数组区间 [mid + 1, right]
*/
func merge(nums []int, left, mid, right int) {
// 初始化辅助数组 借助 copy模块
tmp := make([]int, right-left+1)
for i := left; i <= right; i++ {
tmp[i-left] = nums[i]
}
// 左子数组的起始索引和结束索引
left_start, left_end := left-left, mid-left
// 右子数组的起始索引和结束索引
right_start, right_end := mid+1-left, right-left
// i, j 分别指向左子数组、右子数组的首元素
i, j := left_start, right_start
// 通过覆盖原数组 nums 来合并左子数组和右子数组
for k := left; k <= right; k++ {
// 若 “左子数组已全部合并完”,则选取右子数组元素,并且 j++
if i > left_end {
nums[k] = tmp[j]
j++
// 否则,若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”,则选取左子数组元素,并且 i++
} else if j > right_end || tmp[i] <= tmp[j] {
nums[k] = tmp[i]
i++
// 否则,若 “左子数组元素 > 右子数组元素”,则选取右子数组元素,并且 j++
} else {
nums[k] = tmp[j]
j++
}
}
}


func mergeSort(nums []int, left, right int) {
// 终止条件
if left >= right {
return
}
// 划分阶段
mid := (left + right) / 2
mergeSort(nums, left, mid)
mergeSort(nums, mid+1, right)
// 合并阶段
merge(nums, left, mid, right)
}
15 changes: 15 additions & 0 deletions codes/go/chapter_sorting/merge_sort/merge_sort_test.go
Original file line number Diff line number Diff line change
@@ -0,0 +1,15 @@
package merge_sort
// File: merge_sort_test.go
// Created Time: 2022-12-13
// Author: msk397 ([email protected])

import (
"fmt"
"testing"
)

func TestMergeSort(t *testing.T) {
nums := []int{7, 3, 2, 6, 0, 1, 5, 4}
mergeSort(nums, 0, len(nums)-1)
fmt.Println("归并排序完成后 nums = ", nums)
}
Loading

0 comments on commit ea32a1c

Please sign in to comment.