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Add cpp codes for the chapter

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computational complexity, sorting, searching.
This commit is contained in:
Yudong Jin
2022-11-27 04:20:30 +08:00
parent 431a0f6caf
commit 19a4ccd86a
32 changed files with 1362 additions and 52 deletions
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115
docs/chapter_computational_complexity/space_complexity.md
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@@ -56,7 +56,26 @@ comments: true
=== "C++"
```cpp title=""
/* 结构体 */
struct Node {
int val;
Node *next;
Node(int x) : val(x), next(nullptr) {}
};
/* 函数（或称方法） */
int func() {
// do something...
return 0;
}
int algorithm(int n) { // 输入数据
const int a = 0; // 暂存数据（常量）
int b = 0; // 暂存数据（变量）
Node* node = new Node(0); // 暂存数据（对象）
int c = func(); // 栈帧空间（调用函数）
return a + b + c; // 输出数据
}
```
=== "Python"
@@ -74,7 +93,6 @@ comments: true
return 0
def algorithm(n): # 输入数据
a = 0 # 暂存数据（常量）
b = 0 # 暂存数据（变量）
node = Node(0) # 暂存数据（对象）
c = function() # 栈帧空间（调用函数）
@@ -104,7 +122,12 @@ comments: true
=== "C++"
```cpp title=""
void algorithm(int n) {
int a = 0; // O(1)
vector<int> b(10000); // O(1)
if (n > 10)
vector<int> nums(n); // O(n)
}
```
=== "Python"
@@ -142,7 +165,21 @@ comments: true
=== "C++"
```cpp title=""
int func() {
// do something
return 0;
}
/* 循环 O(1) */
void loop(int n) {
for (int i = 0; i < n; i++) {
func();
}
}
/* 递归 O(n) */
void recur(int n) {
if (n == 1) return;
return recur(n - 1);
}
```
=== "Python"
@@ -212,7 +249,22 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 常数阶 */
void constant(int n) {
// 常量、变量、对象占用 O(1) 空间
const int a = 0;
int b = 0;
vector<int> nums(10000);
ListNode* node = new ListNode(0);
// 循环中的变量占用 O(1) 空间
for (int i = 0; i < n; i++) {
int c = 0;
}
// 循环中的函数占用 O(1) 空间
for (int i = 0; i < n; i++) {
func();
}
}
```
=== "Python"
@@ -259,7 +311,21 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 线性阶 */
void linear(int n) {
// 长度为 n 的数组占用 O(n) 空间
vector<int> nums(n);
// 长度为 n 的列表占用 O(n) 空间
vector<ListNode*> nodes;
for (int i = 0; i < n; i++) {
nodes.push_back(new ListNode(i));
}
// 长度为 n 的哈希表占用 O(n) 空间
unordered_map<int, string> map;
for (int i = 0; i < n; i++) {
map[i] = to_string(i);
}
}
```
=== "Python"
@@ -291,7 +357,12 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 线性阶（递归实现） */
void linearRecur(int n) {
cout << "递归 n = " << n << endl;
if (n == 1) return;
linearRecur(n - 1);
}
```
=== "Python"
@@ -318,7 +389,7 @@ $$
/* 平方阶 */
void quadratic(int n) {
// 矩阵占用 O(n^2) 空间
int numMatrix[][] = new int[n][n];
int [][]numMatrix = new int[n][n];
// 二维列表占用 O(n^2) 空间
List<List<Integer>> numList = new ArrayList<>();
for (int i = 0; i < n; i++) {
@@ -334,7 +405,18 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 平方阶 */
void quadratic(int n) {
// 二维列表占用 O(n^2) 空间
vector<vector<int>> numMatrix;
for (int i = 0; i < n; i++) {
vector<int> tmp;
for (int j = 0; j < n; j++) {
tmp.push_back(0);
}
numMatrix.push_back(tmp);
}
}
```
=== "Python"
@@ -363,7 +445,13 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 平方阶（递归实现） */
int quadraticRecur(int n) {
if (n <= 0) return 0;
vector<int> nums(n);
cout << "递归 n = " << n << " 中的 nums 长度 = " << nums.size() << endl;
return quadraticRecur(n - 1);
}
```
=== "Python"
@@ -401,7 +489,14 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
/* 指数阶（建立满二叉树） */
TreeNode* buildTree(int n) {
if (n == 0) return nullptr;
TreeNode* root = new TreeNode(0);
root->left = buildTree(n - 1);
root->right = buildTree(n - 1);
return root;
}
```
=== "Python"

32
docs/chapter_computational_complexity/space_time_tradeoff.md
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@@ -39,7 +39,20 @@ comments: true
=== "C++"
```cpp title="leetcode_two_sum.cpp"
class SolutionBruteForce {
public:
vector<int> twoSum(vector<int>& nums, int target) {
int size = nums.size();
// 两层循环，时间复杂度 O(n^2)
for (int i = 0; i < size - 1; i++) {
for (int j = i + 1; j < size; j++) {
if (nums[i] + nums[j] == target)
return { i, j };
}
}
return {};
}
};
```
=== "Python"
@@ -101,7 +114,22 @@ comments: true
=== "C++"
```cpp title="leetcode_two_sum.cpp"
class SolutionHashMap {
public:
vector<int> twoSum(vector<int>& nums, int target) {
int size = nums.size();
// 辅助哈希表，空间复杂度 O(n)
unordered_map<int, int> dic;
// 单层循环，时间复杂度 O(n)
for (int i = 0; i < size; i++) {
if (dic.find(target - nums[i]) != dic.end()) {
return { dic[target - nums[i]], i };
}
dic.emplace(nums[i], i);
}
return {};
}
};
```
=== "Python"

206
docs/chapter_computational_complexity/time_complexity.md
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@@ -36,7 +36,16 @@ $$
=== "C++"
```cpp title=""
// 在某运行平台下
void algorithm(int n) {
int a = 2; // 1 ns
a = a + 1; // 1 ns
a = a * 2; // 10 ns
// 循环 n 次
for (int i = 0; i < n; i++) { // 1 ns ，每轮都要执行 i++
cout << 0 << endl; // 5 ns
}
}
```
=== "Python"
@@ -88,7 +97,22 @@ $$
=== "C++"
```cpp title=""
// 算法 A 时间复杂度：常数阶
void algorithm_A(int n) {
cout << 0 << endl;
}
// 算法 B 时间复杂度：线性阶
void algorithm_B(int n) {
for (int i = 0; i < n; i++) {
cout << 0 << endl;
}
}
// 算法 C 时间复杂度：常数阶
void algorithm_C(int n) {
for (int i = 0; i < 1000000; i++) {
cout << 0 << endl;
}
}
```
=== "Python"
@@ -144,7 +168,15 @@ $$
=== "C++"
```cpp title=""
void algorithm(int n) {
int a = 1; // +1
a = a + 1; // +1
a = a * 2; // +1
// 循环 n 次
for (int i = 0; i < n; i++) { // +1（每轮都执行 i ++）
cout << 0 << endl; // +1
}
}
```
=== "Python"
@@ -233,7 +265,20 @@ $$
=== "C++"
```cpp title=""
void algorithm(int n) {
int a = 1; // +0（技巧 1）
a = a + n; // +0（技巧 1）
// +n（技巧 2）
for (int i = 0; i < 5 * n + 1; i++) {
cout << 0 << endl;
}
// +n*n（技巧 3）
for (int i = 0; i < 2 * n; i++) {
for (int j = 0; j < n + 1; j++) {
cout << 0 << endl;
}
}
}
```
=== "Python"
@@ -310,7 +355,14 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 常数阶 */
int constant(int n) {
int count = 0;
int size = 100000;
for (int i = 0; i < size; i++)
count++;
return count;
}
```
=== "Python"
@@ -344,7 +396,13 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 线性阶 */
int linear(int n) {
int count = 0;
for (int i = 0; i < n; i++)
count++;
return count;
}
```
=== "Python"
@@ -381,7 +439,15 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 线性阶（遍历数组） */
int arrayTraversal(vector<int>& nums) {
int count = 0;
// 循环次数与数组长度成正比
for (int num : nums) {
count++;
}
return count;
}
```
=== "Python"
@@ -419,7 +485,17 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 平方阶 */
int quadratic(int n) {
int count = 0;
// 循环次数与数组长度成平方关系
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
count++;
}
}
return count;
}
```
=== "Python"
@@ -471,7 +547,24 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 平方阶（冒泡排序） */
int bubbleSort(vector<int>& nums) {
int count = 0; // 计数器
// 外循环：待排序元素数量为 n-1, n-2, ..., 1
for (int i = nums.size() - 1; i > 0; i--) {
// 内循环：冒泡操作
for (int j = 0; j < i; j++) {
if (nums[j] > nums[j + 1]) {
// 交换 nums[j] 与 nums[j + 1]
int tmp = nums[j];
nums[j] = nums[j + 1];
nums[j + 1] = tmp;
count += 3; // 元素交换包含 3 个单元操作
}
}
}
return count;
}
```
=== "Python"
@@ -522,7 +615,19 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 指数阶（循环实现） */
int exponential(int n) {
int count = 0, base = 1;
// cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
for (int i = 0; i < n; i++) {
for (int j = 0; j < base; j++) {
count++;
}
base *= 2;
}
// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
return count;
}
```
=== "Python"
@@ -559,7 +664,11 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 指数阶（递归实现） */
int expRecur(int n) {
if (n == 1) return 1;
return expRecur(n - 1) + expRecur(n - 1) + 1;
}
```
=== "Python"
@@ -596,7 +705,15 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 对数阶（循环实现） */
int logarithmic(float n) {
int count = 0;
while (n > 1) {
n = n / 2;
count++;
}
return count;
}
```
=== "Python"
@@ -630,7 +747,11 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 对数阶（递归实现） */
int logRecur(float n) {
if (n <= 1) return 0;
return logRecur(n / 2) + 1;
}
```
=== "Python"
@@ -666,7 +787,16 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 线性对数阶 */
int linearLogRecur(float n) {
if (n <= 1) return 1;
int count = linearLogRecur(n / 2) +
linearLogRecur(n / 2);
for (int i = 0; i < n; i++) {
count++;
}
return count;
}
```
=== "Python"
@@ -714,7 +844,16 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
/* 阶乘阶（递归实现） */
int factorialRecur(int n) {
if (n == 0) return 1;
int count = 0;
// 从 1 个分裂出 n 个
for (int i = 0; i < n; i++) {
count += factorialRecur(n - 1);
}
return count;
}
```
=== "Python"
@@ -789,7 +928,42 @@ $$
=== "C++"
```cpp title="worst_best_time_complexity.cpp"
/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
vector<int> randomNumbers(int n) {
vector<int> nums(n);
// 生成数组 nums = { 1, 2, 3, ..., n }
for (int i = 0; i < n; i++) {
nums[i] = i + 1;
}
// 使用系统时间生成随机种子
unsigned seed = chrono::system_clock::now().time_since_epoch().count();
// 随机打乱数组元素
shuffle(nums.begin(), nums.end(), default_random_engine(seed));
return nums;
}
/* 查找数组 nums 中数字 1 所在索引 */
int findOne(vector<int>& nums) {
for (int i = 0; i < nums.size(); i++) {
if (nums[i] == 1)
return i;
}
return -1;
}
/* Driver Code */
int main() {
for (int i = 0; i < 1000; i++) {
int n = 100;
vector<int> nums = randomNumbers(n);
int index = findOne(nums);
cout << "\n数组 [ 1, 2, ..., n ] 被打乱后 = ";
PrintUtil::printVector(nums);
cout << "数字 1 的索引为 " << index << endl;
}
return 0;
}
```
=== "Python"