Skip to content

feat: add solutions to lc/lcof problems #1625

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Sep 14, 2023
Merged

feat: add solutions to lc/lcof problems #1625

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
142 changes: 72 additions & 70 deletions lcof/面试题14- II. 剪绳子 II/README.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
# [面试题 14- II. 剪绳子 II](这里是题目链接，如：https://leetcode.cn/problems/shu-zu-zhong-zhong-fu-de-shu-zi-lcof/)
# [面试题 14- II. 剪绳子 II](https://leetcode.cn/problems/jian-sheng-zi-ii-lcof/)

## 题目描述

Expand Down Expand Up @@ -36,7 +36,7 @@

当 $n \lt 4$，此时 $n$ 不能拆分成至少两个正整数的和，因此 $n - 1$ 是最大乘积。当 $n \ge 4$ 时，我们尽可能多地拆分 $3$，当剩下的最后一段为 $4$ 时，我们将其拆分为 $2 + 2$，这样乘积最大。

时间复杂度 $O(1)$，空间复杂度 $O(1)$。
时间复杂度 $O(\log n)$，空间复杂度 $O(1)$。

<!-- tabs:start -->

Expand All @@ -59,30 +59,30 @@ class Solution:

```java
class Solution {
private final int mod = (int) 1e9 + 7;

public int cuttingRope(int n) {
if (n < 4) {
return n - 1;
}
final int mod = (int) 1e9 + 7;
if (n % 3 == 0) {
return (int) qmi(3, n / 3, mod);
return qpow(3, n / 3);
}
if (n % 3 == 1) {
return (int) (qmi(3, n / 3 - 1, mod) * 4 % mod);
return (int) (4L * qpow(3, n / 3 - 1) % mod);
}
return (int) (qmi(3, n / 3, mod) * 2 % mod);
return 2 * qpow(3, n / 3) % mod;
}

long qmi(long a, long k, long p) {
long res = 1;
while (k != 0) {
if ((k & 1) == 1) {
res = res * a % p;
private int qpow(long a, long n) {
long ans = 1;
for (; n > 0; n >>= 1) {
if ((n & 1) == 1) {
ans = ans * a % mod;
}
k >>= 1;
a = a * a % p;
a = a * a % mod;
}
return res;
return (int) ans;
}
}
```
Expand All @@ -97,53 +97,24 @@ public:
return n - 1;
}
const int mod = 1e9 + 7;
auto qpow = [&](long long a, long long n) {
long long ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
return (int) ans;
};
if (n % 3 == 0) {
return qmi(3, n / 3, mod);
return qpow(3, n / 3);
}
if (n % 3 == 1) {
return qmi(3, n / 3 - 1, mod) * 4 % mod;
}
return qmi(3, n / 3, mod) * 2 % mod;
}

long qmi(long a, long k, long p) {
long res = 1;
while (k != 0) {
if ((k & 1) == 1) {
res = res * a % p;
}
k >>= 1;
a = a * a % p;
}
return res;
}
};
```

### **JavaScript**

```js
/**
* @param {number} n
* @return {number}
*/
var cuttingRope = function (n) {
if (n <= 3) return n - 1;
let a = ~~(n / 3);
let b = n % 3;
const MOD = 1e9 + 7;
function myPow(x) {
let r = 1;
for (let i = 0; i < x; i++) {
r = (r * 3) % MOD;
return qpow(3, n / 3 - 1) * 4L % mod;
}
return r;
}
if (b === 1) {
return (myPow(a - 1) * 4) % MOD;
return qpow(3, n / 3) * 2 % mod;
}
if (b === 0) return myPow(a) % MOD;
return (myPow(a) * 2) % MOD;
};
```

Expand All @@ -155,26 +126,57 @@ func cuttingRope(n int) int {
return n - 1
}
const mod = 1e9 + 7
qpow := func(a, n int) int {
ans := 1
for ; n > 0; n >>= 1 {
if n&1 == 1 {
ans = ans * a % mod
}
a = a * a % mod
}
return ans
}
if n%3 == 0 {
return qmi(3, n/3, mod)
return qpow(3, n/3)
}
if n%3 == 1 {
return qmi(3, n/3-1, mod) * 4 % mod
return qpow(3, n/3-1) * 4 % mod
}
return qmi(3, n/3, mod) * 2 % mod
return qpow(3, n/3) * 2 % mod
}
```

func qmi(a, k, p int) int {
res := 1
for k != 0 {
if k&1 == 1 {
res = res * a % p
}
k >>= 1
a = a * a % p
}
return res
}
### **JavaScript**

```js
/**
* @param {number} n
* @return {number}
*/
var cuttingRope = function (n) {
if (n < 4) {
return n - 1;
}
const mod = 1e9 + 7;
const qpow = (a, n) => {
let ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = Number((BigInt(ans) * BigInt(a)) % BigInt(mod));
}
a = Number((BigInt(a) * BigInt(a)) % BigInt(mod));
}
return ans;
};
const k = Math.floor(n / 3);
if (n % 3 === 0) {
return qpow(3, k);
}
if (n % 3 === 1) {
return (4 * qpow(3, k - 1)) % mod;
}
return (2 * qpow(3, k)) % mod;
};
```

### **Rust**
Expand Down
52 changes: 25 additions & 27 deletions lcof/面试题14- II. 剪绳子 II/Solution.cpp
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,28 +1,26 @@
class Solution {
public:
int cuttingRope(int n) {
if (n < 4) {
return n - 1;
}
const int mod = 1e9 + 7;
if (n % 3 == 0) {
return qmi(3, n / 3, mod);
}
if (n % 3 == 1) {
return qmi(3, n / 3 - 1, mod) * 4 % mod;
}
return qmi(3, n / 3, mod) * 2 % mod;
}

long qmi(long a, long k, long p) {
long res = 1;
while (k != 0) {
if ((k & 1) == 1) {
res = res * a % p;
}
k >>= 1;
a = a * a % p;
}
return res;
}
class Solution {
public:
int cuttingRope(int n) {
if (n < 4) {
return n - 1;
}
const int mod = 1e9 + 7;
auto qpow = [&](long long a, long long n) {
long long ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
return (int) ans;
};
if (n % 3 == 0) {
return qpow(3, n / 3);
}
if (n % 3 == 1) {
return qpow(3, n / 3 - 1) * 4L % mod;
}
return qpow(3, n / 3) * 2 % mod;
}
};
28 changes: 13 additions & 15 deletions lcof/面试题14- II. 剪绳子 II/Solution.go
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3,23 +3,21 @@ func cuttingRope(n int) int {
return n - 1
}
const mod = 1e9 + 7
qpow := func(a, n int) int {
ans := 1
for ; n > 0; n >>= 1 {
if n&1 == 1 {
ans = ans * a % mod
}
a = a * a % mod
}
return ans
}
if n%3 == 0 {
return qmi(3, n/3, mod)
return qpow(3, n/3)
}
if n%3 == 1 {
return qmi(3, n/3-1, mod) * 4 % mod
}
return qmi(3, n/3, mod) * 2 % mod
}

func qmi(a, k, p int) int {
res := 1
for k != 0 {
if k&1 == 1 {
res = res * a % p
}
k >>= 1
a = a * a % p
return qpow(3, n/3-1) * 4 % mod
}
return res
return qpow(3, n/3) * 2 % mod
}
52 changes: 26 additions & 26 deletions lcof/面试题14- II. 剪绳子 II/Solution.java
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,27 +1,27 @@
class Solution {
public int cuttingRope(int n) {
if (n < 4) {
return n - 1;
}
final int mod = (int) 1e9 + 7;
if (n % 3 == 0) {
return (int) qmi(3, n / 3, mod);
}
if (n % 3 == 1) {
return (int) (qmi(3, n / 3 - 1, mod) * 4 % mod);
}
return (int) (qmi(3, n / 3, mod) * 2 % mod);
}

long qmi(long a, long k, long p) {
long res = 1;
while (k != 0) {
if ((k & 1) == 1) {
res = res * a % p;
}
k >>= 1;
a = a * a % p;
}
return res;
}
class Solution {
private final int mod = (int) 1e9 + 7;
public int cuttingRope(int n) {
if (n < 4) {
return n - 1;
}
if (n % 3 == 0) {
return qpow(3, n / 3);
}
if (n % 3 == 1) {
return (int) (4L * qpow(3, n / 3 - 1) % mod);
}
return 2 * qpow(3, n / 3) % mod;
}
private int qpow(long a, long n) {
long ans = 1;
for (; n > 0; n >>= 1) {
if ((n & 1) == 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
return (int) ans;
}
}
32 changes: 19 additions & 13 deletions lcof/面试题14- II. 剪绳子 II/Solution.js
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3,20 +3,26 @@
* @return {number}
*/
var cuttingRope = function (n) {
if (n <= 3) return n - 1;
let a = ~~(n / 3);
let b = n % 3;
const MOD = 1e9 + 7;
function myPow(x) {
let r = 1;
for (let i = 0; i < x; i++) {
r = (r * 3) % MOD;
if (n < 4) {
return n - 1;
}
const mod = 1e9 + 7;
const qpow = (a, n) => {
let ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = Number((BigInt(ans) * BigInt(a)) % BigInt(mod));
}
a = Number((BigInt(a) * BigInt(a)) % BigInt(mod));
}
return r;
return ans;
};
const k = Math.floor(n / 3);
if (n % 3 === 0) {
return qpow(3, k);
}
if (b === 1) {
return (myPow(a - 1) * 4) % MOD;
if (n % 3 === 1) {
return (4 * qpow(3, k - 1)) % mod;
}
if (b === 0) return myPow(a) % MOD;
return (myPow(a) * 2) % MOD;
return (2 * qpow(3, k)) % mod;
};
Loading