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https://github.com/faresbakhit/cp
competitive programming âïļ resources and notes ðĪš
https://github.com/faresbakhit/cp
algorithms competitive-programming cpp data-structures problem-solving
Last synced: about 2 months ago
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competitive programming âïļ resources and notes ðĪš
- Host: GitHub
- URL: https://github.com/faresbakhit/cp
- Owner: faresbakhit
- License: 0bsd
- Created: 2023-09-09T02:43:02.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2023-12-11T00:28:45.000Z (about 1 year ago)
- Last Synced: 2024-01-29T11:24:00.553Z (12 months ago)
- Topics: algorithms, competitive-programming, cpp, data-structures, problem-solving
- Homepage:
- Size: 52.7 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Competitive Programming
competitive programming âïļ resources and notes ðĪš
- [Fast I/O](#fast-io)
- [Numeric types](#numeric-types23)
- [Bit manipulation](#bit-manipulation4)
- [Multiply or divide by 2^k](#multiply-or-divide-by-2k)
- [Change the n-th bit](#change-the-n-th-bit)
- [Is a power of 2](#is-a-power-of-2)
- [Is the n-th bit set](#is-the-n-th-bit-set)
- [How-to TeX algorithms](#how-to-tex-algorithms)
- [Arithmetic operations](#arithmetic-operations)
- [Comparison operations](#comparison-operations)
- [Bitwise operations](#bitwise-operations)
- [Constants](#constants)
## Fast I/O
```cpp
ios::sync_with_stdio(false);
cin.tie(nullptr);
```
## Numeric types[^2][^3]
[^2]: [Fundamental types](https://en.cppreference.com/w/cpp/language/types) - cppreference.com
[^3]: [Numeric types](https://doc.rust-lang.org/reference/types/numeric.html) - The Rust Reference
| C/C++ Type | Rust Type | Size | Minimum | Maximum |
|------------|-----------|---------|---------------------------|--------------------------|
| uint8_t | u8 | 8-bit | $0$ | $2^{8}-1$ |
| uint16_t | u16 | 16-bit | $0$ | $2^{16}-1$ |
| uint32_t | u32 | 32-bit | $0$ | $2^{32}-1$ |
| uint64_t | u64 | 64-bit | $0$ | $2^{64}-1$ |
| | u128 | 128-bit | $0$ | $2^{128}-1$ |
| int8_t | i8 | 8-bit | $-2^{7}$ | $2^{7}-1$ |
| int16_t | i16 | 16-bit | $-2^{15}$ | $2^{15}-1$ |
| int32_t | i32 | 32-bit | $-2^{31}$ | $2^{31}-1$ |
| int64_t | i64 | 64-bit | $-2^{63}$ | $2^{63}-1$ |
| | i128 | 128-bit | $-2^{127}$ | $2^{127}-1$ |
| size_t | isize | arch | | |
| ssize_t | usize | arch | | |
| float | f32 | 32-bit | $-3.40282 \cdot 10^{38}$ | $3.40282 \cdot 10^{38}$ |
| double | f64 | 64-bit | $-1.79769 \cdot 10^{308}$ | $1.79769 \cdot 10^{308}$ |
---
## Bit manipulation[^4]
[^4]: [Bit Twiddling Hacks](https://graphics.stanford.edu/~seander/bithacks.html) - Sean Anderson
### Multiply or divide by $2^k$
- $x \cdot 2^k = x \ll k$
- $x / 2^k = x \gg k$
### Change the $n$-th bit
- set â $x \lor (1 \ll n)$
- unset â $x \land \lnot(1 \ll n)$
- toggle â $x \oplus (1 \ll n)$
### Is a power of $2$
$$f_1(x) = x \land (x - 1)$$
$$
f_2(x) =
\begin{cases}
\top & x = 0 \\
\bot & x \neq 0
\end{cases}
$$
$$f(x) = (f_2 \circ f_1)(x)$$
#### Is the $n$-th bit set
$$f_1(x, n) = x \land (1 \ll n)$$
$$
f_2(x) =
\begin{cases}
\top & x \neq 0 \\
\bot & x = 0
\end{cases}
$$
$$f(x, n) = (f_2 \circ f_1)(x, n)$$
---
## Language Syntax
### Arithmetic operations
| Operation | C/C++ Syntax | Rust Syntax | LaTex | LaTex (Rendered) |
|------------------|-----------------|-------------|-------------|------------------|
| *Addition* | `x + y` | `x + y` | `+` | $x + y$ |
| *Subtraction* | `x - y` | `x - y` | `-` | $x - y$ |
| *Multiplication* | `x * y` | `x * y` | `\cdot` | $x \cdot y$ |
| *Division* | `x / y` | `x / y` | `/` | $x / y$ |
| *Remainder* | `x % y` | `x % y` | `\bmod` | $x \bmod y$ |
| *Exponentiation* | `pow` | `T::pow` | `^` | $x ^ y$ |
| *Square root* | `sqrt` | `T::sqrt` | `\sqrt{}` | $\sqrt{x}$ |
| $n$*-th root* | | | `\sqrt[]{}` | $\sqrt[n]{x}$ |
### Comparison operations
| Operation | C/C++ Syntax | Rust Syntax | LaTex | Latex (Rendered) |
|-------------------------|--------------|-------------|-----------|------------------|
| *Equality* | `x == y` | `x == y` | `=` | $x = y$ |
| *Approximate-equality* | | | `\approx` | $x \approx y$ |
| *Inequality* | `x != y` | `x != y` | `\neq` | $x \neq y$ |
| *Greater than* | `x > y` | `x > y` | `>` | $x > y$ |
| *Less than* | `x < y` | `x < y` | `<` | $x < y$ |
| *Greater than or equal* | `x >= y` | `x >= y` | `\geq` | $x \geq y$ |
| *Less than or equal* | `x <= y` | `x <= y` | `\leq` | $x \leq y$ |
### Bitwise operations
| Operation | C/C++ Syntax | Rust Syntax | LaTex | LaTex (Rendered) |
|------------------------|-----------------------|-------------------|----------|------------------|
| *Bitwise NOT* | `~x` | `!x` | `\lnot` | $\lnot x$ |
| *Bitwise AND* | `x & y` | `x & y` | `\land` | $x \land y$ |
| *Bitwise OR* | `x \| y` | `x \| y` | `\lor` | $x \lor y$ |
| *Bitwise XOR* | `x ^ y` | `x ^ y` | `\oplus` | $x \oplus y$ |
| *Bitwise left shift* | `x << n` | `x << n` | `\ll` | $x \ll n$ |
| *Bitwise right shift* | `x >> n` | `x >> n` | `\gg` | $x \gg n$ |
| *Bitwise left rotate* | `std::rotl` **C++20** | `T::rotate_left` | `\lll` | $x \lll n$ |
| *Bitwise right rotate* | `std::rotl` **C++20** | `T::rotate_right` | `\ggg` | $x \ggg n$ |
### Constants
| Constant | [C/C++ Syntax][constants-c] | [Rust Syntax][constants-rust] | LaTeX | LaTeX (Rendered) |
|:-------------------------------|-----------------------------|-------------------------------|----------------|------------------|
| true | `true` | `true` | `\top` | $\top$ |
| false | `false` | `false` | `\bot` | $\bot$ |
| Archimedes' constant | `M_PI` | `PI` | `\pi` | $\pi$ |
| Euler's number | `M_E` | `E` | `e` | $e$ |
| The full circle constant | | `TAU` | `\tau` | $\tau$ |
| The logarithm to base 10 of e | `M_LOG2E` | `LOG2_E` | `\log_{2}{e}` | $\log_{2}{e}$ |
| The logarithm to base 10 of e | `M_LOG10E` | `LOG10_E` | `\log_{10}{e}` | $\log_{10}{e}$ |
| The logarithm to base 2 of ten | | `LOG2_10` | `\log_{2}{10}` | $\log_{2}{10}$ |
| The logarithm to base 10 of 2 | | `LOG10_2` | `\log_{10}{2}` | $\log_{10}{2}$ |
| The natural logarithm of 2 | `M_LN2` | `LN_2` | `\ln{2}` | $\ln{2}$ |
| The natural logarithm of 10 | `M_LN10` | `LN_10` | `\ln{10}` | $\ln{10}$ |
| The square root of 2 | `M_SQRT2` | `SQRT_2` | `\sqrt{2}` | $\sqrt{2}$ |
[constants-c]: https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html "math.h"
[constants-rust]: https://doc.rust-lang.org/core/f64/consts/index.html "core::{f64, f32}::consts"