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krahets
2023-02-08 04:17:26 +08:00
parent 7f4efa6d5e
commit 0407cc720c
347 changed files with 150 additions and 132904 deletions
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70
docs/chapter_computational_complexity/space_complexity.md
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@@ -588,22 +588,7 @@ $$
=== "C++"
```cpp title="space_complexity.cpp"
/* 常数阶 */
void constant(int n) {
// 常量、变量、对象占用 O(1) 空间
const int a = 0;
int b = 0;
vector<int> nums(10000);
ListNode node(0);
// 循环中的变量占用 O(1) 空间
for (int i = 0; i < n; i++) {
int c = 0;
}
// 循环中的函数占用 O(1) 空间
for (int i = 0; i < n; i++) {
func();
}
}
[class]{}-[func]{constant}
```
=== "Python"
@@ -769,21 +754,7 @@ $$
=== "C++"
```cpp title="space_complexity.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(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);
}
}
[class]{}-[func]{linear}
```
=== "Python"
@@ -933,12 +904,7 @@ $$
=== "C++"
```cpp title="space_complexity.cpp"
/* 线性阶（递归实现） */
void linearRecur(int n) {
cout << "递归 n = " << n << endl;
if (n == 1) return;
linearRecur(n - 1);
}
[class]{}-[func]{linearRecur}
```
=== "Python"
@@ -1041,18 +1007,7 @@ $$
=== "C++"
```cpp title="space_complexity.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);
}
}
[class]{}-[func]{quadratic}
```
=== "Python"
@@ -1182,13 +1137,7 @@ $$
=== "C++"
```cpp title="space_complexity.cpp"
/* 平方阶（递归实现） */
int quadraticRecur(int n) {
if (n <= 0) return 0;
vector<int> nums(n);
cout << "递归 n = " << n << " 中的 nums 长度 = " << nums.size() << endl;
return quadraticRecur(n - 1);
}
[class]{}-[func]{quadraticRecur}
```
=== "Python"
@@ -1297,14 +1246,7 @@ $$
=== "C++"
```cpp title="space_complexity.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;
}
[class]{}-[func]{buildTree}
```
=== "Python"

32
docs/chapter_computational_complexity/space_time_tradeoff.md
View File

@@ -39,20 +39,7 @@ 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 {};
}
};
[class]{SolutionBruteForce}-[func]{}
```
=== "Python"
@@ -193,22 +180,7 @@ 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 {};
}
};
[class]{SolutionHashMap}-[func]{}
```
=== "Python"

116
docs/chapter_computational_complexity/time_complexity.md
View File

@@ -801,14 +801,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 常数阶 */
int constant(int n) {
int count = 0;
int size = 100000;
for (int i = 0; i < size; i++)
count++;
return count;
}
[class]{}-[func]{constant}
```
=== "Python"
@@ -927,13 +920,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 线性阶 */
int linear(int n) {
int count = 0;
for (int i = 0; i < n; i++)
count++;
return count;
}
[class]{}-[func]{linear}
```
=== "Python"
@@ -1045,15 +1032,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 线性阶（遍历数组） */
int arrayTraversal(vector<int>& nums) {
int count = 0;
// 循环次数与数组长度成正比
for (int num : nums) {
count++;
}
return count;
}
[class]{}-[func]{arrayTraversal}
```
=== "Python"
@@ -1175,17 +1154,7 @@ $$
=== "C++"
```cpp title="time_complexity.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;
}
[class]{}-[func]{quadratic}
```
=== "Python"
@@ -1330,24 +1299,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 平方阶（冒泡排序） */
int bubbleSort(vector<int>& nums) {
int count = 0; // 计数器
// 外循环：待排序元素数量为 n-1, n-2, ..., 1
for (int i = nums.size() - 1; i > 0; i--) {
// 内循环：冒泡操作
for (int j = 0; j < i; j++) {
if (nums[j] > nums[j + 1]) {
// 交换 nums[j] 与 nums[j + 1]
int tmp = nums[j];
nums[j] = nums[j + 1];
nums[j + 1] = tmp;
count += 3; // 元素交换包含 3 个单元操作
}
}
}
return count;
}
[class]{}-[func]{bubbleSort}
```
=== "Python"
@@ -1543,19 +1495,7 @@ $$
=== "C++"
```cpp title="time_complexity.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;
}
[class]{}-[func]{exponential}
```
=== "Python"
@@ -1716,11 +1656,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 指数阶（递归实现） */
int expRecur(int n) {
if (n == 1) return 1;
return expRecur(n - 1) + expRecur(n - 1) + 1;
}
[class]{}-[func]{expRecur}
```
=== "Python"
@@ -1822,15 +1758,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 对数阶（循环实现） */
int logarithmic(float n) {
int count = 0;
while (n > 1) {
n = n / 2;
count++;
}
return count;
}
[class]{}-[func]{logarithmic}
```
=== "Python"
@@ -1958,11 +1886,7 @@ $$
=== "C++"
```cpp title="time_complexity.cpp"
/* 对数阶（递归实现） */
int logRecur(float n) {
if (n <= 1) return 0;
return logRecur(n / 2) + 1;
}
[class]{}-[func]{logRecur}
```
=== "Python"
@@ -2062,16 +1986,7 @@ $$
=== "C++"
```cpp title="time_complexity.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;
}
[class]{}-[func]{linearLogRecur}
```
=== "Python"
@@ -2213,16 +2128,7 @@ $$
=== "C++"
```cpp title="time_complexity.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;
}
[class]{}-[func]{factorialRecur}
```
=== "Python"