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time complexity using go

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pull/99/head
machangxin 2 years ago
parent 58ca52d8ab
commit d4ad75eb7d
3 changed files with 368 additions and 16 deletions
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127
codes/go/chapter_computational_complexity/time_complexity/time_complexity.go
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@ -0,0 +1,127 @@
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
}

44
codes/go/chapter_computational_complexity/time_complexity/time_complexity_test.go
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@ -0,0 +1,44 @@
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)
}

213
docs/chapter_computational_complexity/time_complexity.md
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@ -64,7 +64,16 @@ $$
=== "Go"
```go title=""
// 在某运行平台下
func algorithm(n int) {
a := 2 // 1 ns
a = a + 1 // 1 ns
a = a * 2 // 10 ns
// 循环 n 次
for i := 0; i < n; i++ { // 1 ns
fmt.Println(a) // 5 ns
}
}
```
=== "JavaScript"
@ -164,7 +173,22 @@ $$
=== "Go"
```go title=""
// 算法 A 时间复杂度：常数阶
func algorithm_A(n int) {
fmt.Println(0)
}
// 算法 B 时间复杂度：线性阶
func algorithm_B(n int) {
for i := 0; i < n; i++ {
fmt.Println(0)
}
}
// 算法 C 时间复杂度：常数阶
func algorithm_C(n int) {
for i := 0; i < 1000000; i++ {
fmt.Println(0)
}
}
```
=== "JavaScript"
@ -249,13 +273,20 @@ $$
# 循环 n 次
for i in range(n): # +1
print(0) # +1
}
```
=== "Go"
```go title=""
func algorithm(n int) {
a := 1 // +1
a = a + 1 // +1
a = a * 2 // +1
// 循环 n 次
for i := 0; i < n; i++ { // +1
fmt.Println(a) // +1
}
}
```
=== "JavaScript"
@ -389,7 +420,20 @@ $$
=== "Go"
```go title=""
func algorithm(n int) {
a := 1 // +0（技巧 1）
a = a + n // +0（技巧 1）
// +n（技巧 2）
for i := 0; i < 5 * n + 1; i++ {
fmt.Println(0)
}
// +n*n（技巧 3）
for i := 0; i < 2 * n; i++ {
for j := 0; j < n + 1; j++ {
fmt.Println(0)
}
}
}
```
=== "JavaScript"
@ -500,7 +544,15 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 常数阶 */
func constant(n int) int {
count := 0
size := 100000
for i := 0; i < size; i++ {
count ++
}
return count
}
```
=== "JavaScript"
@ -569,7 +621,14 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 线性阶 */
func linear(n int) int {
count := 0
for i := 0; i < n; i++ {
count++
}
return count
}
```
=== "JavaScript"
@ -645,7 +704,15 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 线性阶（遍历数组） */
func arrayTraversal(nums []int) int {
count := 0
// 循环次数与数组长度成正比
for range nums {
count++
}
return count
}
```
=== "JavaScript"
@ -724,7 +791,17 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 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
}
```
=== "JavaScript"
@ -829,7 +906,24 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 平方阶（冒泡排序） */
func bubbleSort(nums []int) int {
count := 0 // 计数器
// 外循环：待排序元素数量为 n-1, n-2, ..., 1
for i := len(nums) - 1; i > 0; i-- {
// 内循环：冒泡操作
for j := 0; j < i; j++ {
if nums[j] > nums[j+1] {
// 交换 nums[j] 与 nums[j + 1]
tmp := nums[j]
nums[j] = nums[j+1]
nums[j+1] = tmp
count += 3 // 元素交换包含 3 个单元操作
}
}
}
return count
}
```
=== "JavaScript"
@ -918,7 +1012,19 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 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
}
```
=== "JavaScript"
@ -983,7 +1089,13 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 指数阶（递归实现）*/
func expRecur(n int) int {
if n == 1 {
return 1
}
return expRecur(n-1) + expRecur(n-1) + 1
}
```
=== "JavaScript"
@ -1061,7 +1173,15 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 对数阶（循环实现）*/
func logarithmic(n float64) int {
count := 0
for n > 1 {
n = n / 2
count++
}
return count
}
```
=== "JavaScript"
@ -1126,7 +1246,13 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 对数阶（递归实现）*/
func logRecur(n float64) int {
if n <= 1 {
return 0
}
return logRecur(n/2) + 1
}
```
=== "JavaScript"
@ -1205,7 +1331,18 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 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
}
```
=== "JavaScript"
@ -1292,7 +1429,18 @@ $$
=== "Go"
```go title="time_complexity_types.go"
/* 阶乘阶（递归实现） */
func factorialRecur(n int) int {
if n == 0 {
return 1
}
count := 0
// 从 1 个分裂出 n 个
for i := 0; i < n; i++ {
count += factorialRecur(n - 1)
}
return count
}
```
=== "JavaScript"
@ -1447,7 +1595,40 @@ $$
=== "Go"
```go title="worst_best_time_complexity.go"
/* 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)
}
}
```
=== "JavaScript"

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