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feat: update solutions to lc problems: No.375,276 #3013

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feat: update solutions to lc problems: No.375,276 #3013

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94 changes: 55 additions & 39 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -90,7 +90,13 @@ tags:

<!-- solution:start -->

### 方法一
### 方法一：动态规划

我们定义 $f[i][j]$ 表示在区间 $[i, j]$ 中猜中任意一个数最少需要花费的钱数。初始时 $f[i][i] = 0$，因为猜中了唯一的数不需要花费，对于 $i \gt j$ 的情况，也有 $f[i][j] = 0$。答案即为 $f[1][n]$。

对于 $f[i][j]$，我们可以枚举 $[i, j]$ 中的任意一个数 $k$，将区间 $[i, j]$ 分为 $[i, k - 1]$ 和 $[k + 1, j]$ 两部分，选择其中的较大值加上 $k$ 的花费，即 $\max(f[i][k - 1], f[k + 1][j]) + k$ 的最小值。

时间复杂度 $O(n^3)$，空间复杂度 $O(n^2)$。其中 $n$ 为猜测的数字范围。

<!-- tabs:start -->

Expand All @@ -99,34 +105,30 @@ tags:
```python
class Solution:
def getMoneyAmount(self, n: int) -> int:
dp = [[0] * (n + 10) for _ in range(n + 10)]
for l in range(2, n + 1):
for i in range(1, n - l + 2):
j = i + l - 1
dp[i][j] = inf
for k in range(i, j + 1):
t = max(dp[i][k - 1], dp[k + 1][j]) + k
dp[i][j] = min(dp[i][j], t)
return dp[1][n]
f = [[0] * (n + 1) for _ in range(n + 1)]
for i in range(n - 1, 0, -1):
for j in range(i + 1, n + 1):
f[i][j] = j + f[i][j - 1]
for k in range(i, j):
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k)
return f[1][n]
```

#### Java

```java
class Solution {
public int getMoneyAmount(int n) {
int[][] dp = new int[n + 10][n + 10];
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = Integer.MAX_VALUE;
for (int k = i; k <= j; ++k) {
int t = Math.max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = Math.min(dp[i][j], t);
int[][] f = new int[n + 1][n + 1];
for (int i = n - 1; i > 0; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], Math.max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
}
```
Expand All @@ -137,18 +139,17 @@ class Solution {
class Solution {
public:
int getMoneyAmount(int n) {
vector<vector<int>> dp(n + 10, vector<int>(n + 10));
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = INT_MAX;
for (int k = i; k <= j; ++k) {
int t = max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = min(dp[i][j], t);
int f[n + 1][n + 1];
memset(f, 0, sizeof(f));
for (int i = n - 1; i; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
};
```
Expand All @@ -157,21 +158,36 @@ public:

```go
func getMoneyAmount(n int) int {
dp := make([][]int, n+10)
for i := 0; i < len(dp); i++ {
dp[i] = make([]int, n+10)
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, n+1)
}
for l := 2; l <= n; l++ {
for i := 1; i+l-1 <= n; i++ {
j := i + l - 1
dp[i][j] = math.MaxInt32
for k := i; k <= j; k++ {
t := max(dp[i][k-1], dp[k+1][j]) + k
dp[i][j] = min(dp[i][j], t)
for i := n - 1; i > 0; i-- {
for j := i + 1; j <= n; j++ {
f[i][j] = j + f[i][j-1]
for k := i; k < j; k++ {
f[i][j] = min(f[i][j], k+max(f[i][k-1], f[k+1][j]))
}
}
}
return dp[1][n]
return f[1][n]
}
```

#### TypeScript

```ts
function getMoneyAmount(n: number): number {
const f: number[][] = Array.from({ length: n + 1 }, () => Array(n + 1).fill(0));
for (let i = n - 1; i; --i) {
for (let j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (let k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], k + Math.max(f[i][k - 1], f[k + 1][j]));
}
}
}
return f[1][n];
}
```

Expand Down
92 changes: 53 additions & 39 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/README_EN.md
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Original file line number Diff line number Diff line change
Expand Up @@ -88,7 +88,11 @@ The worst case is that you pay $1.

<!-- solution:start -->

### Solution 1
### Solution 1: Dynamic Programming

We define $f[i][j]$ as the minimum cost required to guess any number in the interval $[i, j]$. Initially, $f[i][i] = 0$ because there is no cost to guess the only number, and for $i > j$, we also have $f[i][j] = 0$. The answer is $f[1][n]$.

For $f[i][j]$, we can enumerate any number $k$ in $[i, j]$, divide the interval $[i, j]$ into two parts, $[i, k - 1]$ and $[k + 1, j]$, choose the larger value of the two parts plus the cost of $k$,

<!-- tabs:start -->

Expand All @@ -97,34 +101,30 @@ The worst case is that you pay $1.
```python
class Solution:
def getMoneyAmount(self, n: int) -> int:
dp = [[0] * (n + 10) for _ in range(n + 10)]
for l in range(2, n + 1):
for i in range(1, n - l + 2):
j = i + l - 1
dp[i][j] = inf
for k in range(i, j + 1):
t = max(dp[i][k - 1], dp[k + 1][j]) + k
dp[i][j] = min(dp[i][j], t)
return dp[1][n]
f = [[0] * (n + 1) for _ in range(n + 1)]
for i in range(n - 1, 0, -1):
for j in range(i + 1, n + 1):
f[i][j] = j + f[i][j - 1]
for k in range(i, j):
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k)
return f[1][n]
```

#### Java

```java
class Solution {
public int getMoneyAmount(int n) {
int[][] dp = new int[n + 10][n + 10];
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = Integer.MAX_VALUE;
for (int k = i; k <= j; ++k) {
int t = Math.max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = Math.min(dp[i][j], t);
int[][] f = new int[n + 1][n + 1];
for (int i = n - 1; i > 0; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], Math.max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
}
```
Expand All @@ -135,18 +135,17 @@ class Solution {
class Solution {
public:
int getMoneyAmount(int n) {
vector<vector<int>> dp(n + 10, vector<int>(n + 10));
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = INT_MAX;
for (int k = i; k <= j; ++k) {
int t = max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = min(dp[i][j], t);
int f[n + 1][n + 1];
memset(f, 0, sizeof(f));
for (int i = n - 1; i; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
};
```
Expand All @@ -155,21 +154,36 @@ public:

```go
func getMoneyAmount(n int) int {
dp := make([][]int, n+10)
for i := 0; i < len(dp); i++ {
dp[i] = make([]int, n+10)
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, n+1)
}
for l := 2; l <= n; l++ {
for i := 1; i+l-1 <= n; i++ {
j := i + l - 1
dp[i][j] = math.MaxInt32
for k := i; k <= j; k++ {
t := max(dp[i][k-1], dp[k+1][j]) + k
dp[i][j] = min(dp[i][j], t)
for i := n - 1; i > 0; i-- {
for j := i + 1; j <= n; j++ {
f[i][j] = j + f[i][j-1]
for k := i; k < j; k++ {
f[i][j] = min(f[i][j], k+max(f[i][k-1], f[k+1][j]))
}
}
}
return dp[1][n]
return f[1][n]
}
```

#### TypeScript

```ts
function getMoneyAmount(n: number): number {
const f: number[][] = Array.from({ length: n + 1 }, () => Array(n + 1).fill(0));
for (let i = n - 1; i; --i) {
for (let j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (let k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], k + Math.max(f[i][k - 1], f[k + 1][j]));
}
}
}
return f[1][n];
}
```

Expand Down
17 changes: 8 additions & 9 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -1,17 +1,16 @@
class Solution {
public:
int getMoneyAmount(int n) {
vector<vector<int>> dp(n + 10, vector<int>(n + 10));
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = INT_MAX;
for (int k = i; k <= j; ++k) {
int t = max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = min(dp[i][j], t);
int f[n + 1][n + 1];
memset(f, 0, sizeof(f));
for (int i = n - 1; i; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
};
20 changes: 9 additions & 11 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/Solution.go
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Original file line number Diff line number Diff line change
@@ -1,17 +1,15 @@
func getMoneyAmount(n int) int {
dp := make([][]int, n+10)
for i := 0; i < len(dp); i++ {
dp[i] = make([]int, n+10)
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, n+1)
}
for l := 2; l <= n; l++ {
for i := 1; i+l-1 <= n; i++ {
j := i + l - 1
dp[i][j] = math.MaxInt32
for k := i; k <= j; k++ {
t := max(dp[i][k-1], dp[k+1][j]) + k
dp[i][j] = min(dp[i][j], t)
for i := n - 1; i > 0; i-- {
for j := i + 1; j <= n; j++ {
f[i][j] = j + f[i][j-1]
for k := i; k < j; k++ {
f[i][j] = min(f[i][j], k+max(f[i][k-1], f[k+1][j]))
}
}
}
return dp[1][n]
return f[1][n]
}
16 changes: 7 additions & 9 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,16 +1,14 @@
class Solution {
public int getMoneyAmount(int n) {
int[][] dp = new int[n + 10][n + 10];
for (int l = 2; l <= n; ++l) {
for (int i = 1; i + l - 1 <= n; ++i) {
int j = i + l - 1;
dp[i][j] = Integer.MAX_VALUE;
for (int k = i; k <= j; ++k) {
int t = Math.max(dp[i][k - 1], dp[k + 1][j]) + k;
dp[i][j] = Math.min(dp[i][j], t);
int[][] f = new int[n + 1][n + 1];
for (int i = n - 1; i > 0; --i) {
for (int j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (int k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], Math.max(f[i][k - 1], f[k + 1][j]) + k);
}
}
}
return dp[1][n];
return f[1][n];
}
}
16 changes: 7 additions & 9 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/Solution.py
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Original file line number Diff line number Diff line change
@@ -1,11 +1,9 @@
class Solution:
def getMoneyAmount(self, n: int) -> int:
dp = [[0] * (n + 10) for _ in range(n + 10)]
for l in range(2, n + 1):
for i in range(1, n - l + 2):
j = i + l - 1
dp[i][j] = inf
for k in range(i, j + 1):
t = max(dp[i][k - 1], dp[k + 1][j]) + k
dp[i][j] = min(dp[i][j], t)
return dp[1][n]
f = [[0] * (n + 1) for _ in range(n + 1)]
for i in range(n - 1, 0, -1):
for j in range(i + 1, n + 1):
f[i][j] = j + f[i][j - 1]
for k in range(i, j):
f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k)
return f[1][n]
12 changes: 12 additions & 0 deletions solution/0300-0399/0375.Guess Number Higher or Lower II/Solution.ts
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Original file line number Diff line number Diff line change
@@ -0,0 +1,12 @@
function getMoneyAmount(n: number): number {
const f: number[][] = Array.from({ length: n + 1 }, () => Array(n + 1).fill(0));
for (let i = n - 1; i; --i) {
for (let j = i + 1; j <= n; ++j) {
f[i][j] = j + f[i][j - 1];
for (let k = i; k < j; ++k) {
f[i][j] = Math.min(f[i][j], k + Math.max(f[i][k - 1], f[k + 1][j]));
}
}
}
return f[1][n];
}
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