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Sep 14, 2023
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feat: add solutions to lc problem: No.0372 #1623

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120 changes: 73 additions & 47 deletions solution/0300-0399/0372.Super Pow/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -53,7 +53,15 @@

<!-- 这里可写通用的实现逻辑 -->

乘方快速幂。
**方法一：快速幂**

我们初始化答案变量 $ans = 1$。

接下来，倒序遍历数组 $b$，每次遍历到一个元素 $e$，我们将答案变量 $ans$ 自乘 $a^e$ 并对 $1337$ 取模，然后将 $a$ 自乘 $10$ 次并对 $1337$ 取模。这里需要用到快速幂。

遍历完数组后，返回答案即可。

时间复杂度 $O(\sum_{i=0}^{n-1} \log b_i)$，空间复杂度 $O(1)$。

<!-- tabs:start -->

Expand All @@ -64,11 +72,11 @@
```python
class Solution:
def superPow(self, a: int, b: List[int]) -> int:
MOD = 1337
mod = 1337
ans = 1
for e in b[::-1]:
ans = ans * pow(a, e, MOD) % MOD
a = pow(a, 10, MOD)
ans = ans * pow(a, e, mod) % mod
a = pow(a, 10, mod)
return ans
```

Expand All @@ -78,25 +86,24 @@ class Solution:

```java
class Solution {
private static final int MOD = 1337;
private final int mod = 1337;

public int superPow(int a, int[] b) {
int ans = 1;
long ans = 1;
for (int i = b.length - 1; i >= 0; --i) {
ans = (int) ((long) ans * quickPowAndMod(a, b[i]) % MOD);
a = quickPowAndMod(a, 10);
ans = ans * qpow(a, b[i]) % mod;
a = qpow(a, 10);
}
return ans;
return (int) ans;
}

private int quickPowAndMod(int a, int b) {
int ans = 1;
while (b > 0) {
if ((b & 1) == 1) {
ans = (ans * (a % MOD)) % MOD;
private long qpow(long a, int n) {
long ans = 1;
for (; n > 0; n >>= 1) {
if ((n & 1) == 1) {
ans = ans * a % mod;
}
b >>= 1;
a = (a % MOD) * (a % MOD) % MOD;
a = a * a % mod;
}
return ans;
}
Expand All @@ -107,26 +114,24 @@ class Solution {

```cpp
class Solution {
const int MOD = 1337;

public:
int superPow(int a, vector<int>& b) {
int ans = 1;
for (int i = b.size() - 1; i >= 0; --i) {
ans = (long) ans * quickPowAndMod(a, b[i]) % MOD;
a = quickPowAndMod(a, 10);
}
return ans;
}

int quickPowAndMod(int a, int b) {
int ans = 1;
while (b) {
if (b & 1) {
ans = (ans * (a % MOD)) % MOD;
using ll = long long;
const int mod = 1337;
ll ans = 1;
auto qpow = [&](ll a, int n) {
ll ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
b >>= 1;
a = ((a % MOD) * (a % MOD)) % MOD;
return (int) ans;
};
for (int i = b.size() - 1; ~i; --i) {
ans = ans * qpow(a, b[i]) % mod;
a = qpow(a, 10);
}
return ans;
}
Expand All @@ -136,27 +141,48 @@ public:
### **Go**

```go
const mod = 1337

func superPow(a int, b []int) int {
const mod int = 1337
ans := 1
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
}
for i := len(b) - 1; i >= 0; i-- {
ans = ans * quickPowAndMod(a, b[i]) % mod
a = quickPowAndMod(a, 10)
ans = ans * qpow(a, b[i]) % mod
a = qpow(a, 10)
}
return ans
}
```

func quickPowAndMod(a, b int) int {
ans := 1
for b > 0 {
if b&1 > 0 {
ans = ans * a % mod
}
b >>= 1
a = ((a % mod) * (a % mod)) % mod
}
return ans
### **TypeScript**

```ts
function superPow(a: number, b: number[]): number {
let ans = 1;
const mod = 1337;
const qpow = (a: number, n: number): number => {
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;
};
for (let i = b.length - 1; ~i; --i) {
ans = Number((BigInt(ans) * BigInt(qpow(a, b[i]))) % BigInt(mod));
a = qpow(a, 10);
}
return ans;
}
```

Expand Down
110 changes: 64 additions & 46 deletions solution/0300-0399/0372.Super Pow/README_EN.md
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Original file line number Diff line number Diff line change
Expand Up @@ -47,37 +47,36 @@
```python
class Solution:
def superPow(self, a: int, b: List[int]) -> int:
MOD = 1337
mod = 1337
ans = 1
for e in b[::-1]:
ans = ans * pow(a, e, MOD) % MOD
a = pow(a, 10, MOD)
ans = ans * pow(a, e, mod) % mod
a = pow(a, 10, mod)
return ans
```

### **Java**

```java
class Solution {
private static final int MOD = 1337;
private final int mod = 1337;

public int superPow(int a, int[] b) {
int ans = 1;
long ans = 1;
for (int i = b.length - 1; i >= 0; --i) {
ans = (int) ((long) ans * quickPowAndMod(a, b[i]) % MOD);
a = quickPowAndMod(a, 10);
ans = ans * qpow(a, b[i]) % mod;
a = qpow(a, 10);
}
return ans;
return (int) ans;
}

private int quickPowAndMod(int a, int b) {
int ans = 1;
while (b > 0) {
if ((b & 1) == 1) {
ans = (ans * (a % MOD)) % MOD;
private long qpow(long a, int n) {
long ans = 1;
for (; n > 0; n >>= 1) {
if ((n & 1) == 1) {
ans = ans * a % mod;
}
b >>= 1;
a = (a % MOD) * (a % MOD) % MOD;
a = a * a % mod;
}
return ans;
}
Expand All @@ -88,26 +87,24 @@ class Solution {

```cpp
class Solution {
const int MOD = 1337;

public:
int superPow(int a, vector<int>& b) {
int ans = 1;
for (int i = b.size() - 1; i >= 0; --i) {
ans = (long) ans * quickPowAndMod(a, b[i]) % MOD;
a = quickPowAndMod(a, 10);
}
return ans;
}

int quickPowAndMod(int a, int b) {
int ans = 1;
while (b) {
if (b & 1) {
ans = (ans * (a % MOD)) % MOD;
using ll = long long;
const int mod = 1337;
ll ans = 1;
auto qpow = [&](ll a, int n) {
ll ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
b >>= 1;
a = ((a % MOD) * (a % MOD)) % MOD;
return (int) ans;
};
for (int i = b.size() - 1; ~i; --i) {
ans = ans * qpow(a, b[i]) % mod;
a = qpow(a, 10);
}
return ans;
}
Expand All @@ -117,27 +114,48 @@ public:
### **Go**

```go
const mod = 1337

func superPow(a int, b []int) int {
const mod int = 1337
ans := 1
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
}
for i := len(b) - 1; i >= 0; i-- {
ans = ans * quickPowAndMod(a, b[i]) % mod
a = quickPowAndMod(a, 10)
ans = ans * qpow(a, b[i]) % mod
a = qpow(a, 10)
}
return ans
}
```

func quickPowAndMod(a, b int) int {
ans := 1
for b > 0 {
if b&1 > 0 {
ans = ans * a % mod
}
b >>= 1
a = ((a % mod) * (a % mod)) % mod
}
return ans
### **TypeScript**

```ts
function superPow(a: number, b: number[]): number {
let ans = 1;
const mod = 1337;
const qpow = (a: number, n: number): number => {
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;
};
for (let i = b.length - 1; ~i; --i) {
ans = Number((BigInt(ans) * BigInt(qpow(a, b[i]))) % BigInt(mod));
a = qpow(a, 10);
}
return ans;
}
```

Expand Down
46 changes: 22 additions & 24 deletions solution/0300-0399/0372.Super Pow/Solution.cpp
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Open in desktop
Original file line number Diff line number Diff line change
@@ -1,25 +1,23 @@
class Solution {
const int MOD = 1337;

public:
int superPow(int a, vector<int>& b) {
int ans = 1;
for (int i = b.size() - 1; i >= 0; --i) {
ans = (long) ans * quickPowAndMod(a, b[i]) % MOD;
a = quickPowAndMod(a, 10);
}
return ans;
}

int quickPowAndMod(int a, int b) {
int ans = 1;
while (b) {
if (b & 1) {
ans = (ans * (a % MOD)) % MOD;
}
b >>= 1;
a = ((a % MOD) * (a % MOD)) % MOD;
}
return ans;
}
class Solution {
public:
int superPow(int a, vector<int>& b) {
using ll = long long;
const int mod = 1337;
ll ans = 1;
auto qpow = [&](ll a, int n) {
ll ans = 1;
for (; n; n >>= 1) {
if (n & 1) {
ans = ans * a % mod;
}
a = a * a % mod;
}
return (int) ans;
};
for (int i = b.size() - 1; ~i; --i) {
ans = ans * qpow(a, b[i]) % mod;
a = qpow(a, 10);
}
return ans;
}
};
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