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krahets
2023-10-08 01:43:28 +08:00
parent 3d2d669b43
commit baac2d11a7
52 changed files with 999 additions and 625 deletions
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zh/chapter_dynamic_programming/intro_to_dynamic_programming.md
+16 -16
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@@ -109,7 +109,7 @@ comments: true
```csharp title="climbing_stairs_backtrack.cs"
/* 回溯 */
void backtrack(List<int> choices, int state, int n, List<int> res) {
void Backtrack(List<int> choices, int state, int n, List<int> res) {
// 当爬到第 n 阶时，方案数量加 1
if (state == n)
res[0]++;
@@ -119,17 +119,17 @@ comments: true
if (state + choice > n)
break;
// 尝试：做出选择，更新状态
backtrack(choices, state + choice, n, res);
Backtrack(choices, state + choice, n, res);
// 回退
}
}
/* 爬楼梯：回溯 */
int climbingStairsBacktrack(int n) {
List<int> choices = new List<int> { 1, 2 }; // 可选择向上爬 1 或 2 阶
int ClimbingStairsBacktrack(int n) {
List<int> choices = new() { 1, 2 }; // 可选择向上爬 1 或 2 阶
int state = 0; // 从第 0 阶开始爬
List<int> res = new List<int> { 0 }; // 使用 res[0] 记录方案数量
backtrack(choices, state, n, res);
List<int> res = new() { 0 }; // 使用 res[0] 记录方案数量
Backtrack(choices, state, n, res);
return res[0];
}
```
@@ -472,18 +472,18 @@ $$
```csharp title="climbing_stairs_dfs.cs"
/* 搜索 */
int dfs(int i) {
int Dfs(int i) {
// 已知 dp[1] 和 dp[2] ，返回之
if (i == 1 || i == 2)
return i;
// dp[i] = dp[i-1] + dp[i-2]
int count = dfs(i - 1) + dfs(i - 2);
int count = Dfs(i - 1) + Dfs(i - 2);
return count;
}
/* 爬楼梯：搜索 */
int climbingStairsDFS(int n) {
return dfs(n);
int ClimbingStairsDFS(int n) {
return Dfs(n);
}
```
@@ -736,7 +736,7 @@ $$
```csharp title="climbing_stairs_dfs_mem.cs"
/* 记忆化搜索 */
int dfs(int i, int[] mem) {
int Dfs(int i, int[] mem) {
// 已知 dp[1] 和 dp[2] ，返回之
if (i == 1 || i == 2)
return i;
@@ -744,18 +744,18 @@ $$
if (mem[i] != -1)
return mem[i];
// dp[i] = dp[i-1] + dp[i-2]
int count = dfs(i - 1, mem) + dfs(i - 2, mem);
int count = Dfs(i - 1, mem) + Dfs(i - 2, mem);
// 记录 dp[i]
mem[i] = count;
return count;
}
/* 爬楼梯：记忆化搜索 */
int climbingStairsDFSMem(int n) {
int ClimbingStairsDFSMem(int n) {
// mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
int[] mem = new int[n + 1];
Array.Fill(mem, -1);
return dfs(n, mem);
return Dfs(n, mem);
}
```
@@ -1048,7 +1048,7 @@ $$
```csharp title="climbing_stairs_dp.cs"
/* 爬楼梯：动态规划 */
int climbingStairsDP(int n) {
int ClimbingStairsDP(int n) {
if (n == 1 || n == 2)
return n;
// 初始化 dp 表，用于存储子问题的解
@@ -1296,7 +1296,7 @@ $$
```csharp title="climbing_stairs_dp.cs"
/* 爬楼梯：空间优化后的动态规划 */
int climbingStairsDPComp(int n) {
int ClimbingStairsDPComp(int n) {
if (n == 1 || n == 2)
return n;
int a = 1, b = 2;