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feat: add solutions to lc/lcof problems #1625

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yanglbme merged 1 commit into main from dev
Sep 14, 2023
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142 changes: 72 additions & 70 deletions lcof/面试题14- II. 剪绳子 II/README.md
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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,ドル此时 $n$ 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ドル,ドル当剩下的最后一段为 4ドル$ 时,我们将其拆分为 2ドル + 2,ドル这样乘积最大。

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

<!-- 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
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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
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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;
};
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