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feat: add binomial theorem

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Hatter Jiang
2025-07-27 17:15:15 +08:00
parent 51a52abb5e
commit 241e7e2222
2 changed files with 52 additions and 14 deletions
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30
README.md
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# math
| Class | Comments | MuBoard Link |
|-------------------------|--------------------|-----------------------------------------------------------------------------------------------------------------------------|
| BinaryExponentiation | 快速幂 | [binary-exponentiation](https://hatter.ink/static/resource/muboard/?id=binary-exponentiation&version=latest&full=1) |
| BirthdayParadox | 生日悖论 | [birthday-paradox](https://hatter.ink/static/resource/muboard/?id=birthday-paradox&version=latest&full=1) |
| ChineseRemainderTheorem | 中国剩余定理 | [chinese-remainder-theorem](https://hatter.ink/static/resource/muboard/?id=chinese-remainder-theorem&version=latest&full=1) |
| ChudnovskyAlgorithm | 楚德诺夫斯基算法 | [chudnovsky-algorithm](https://hatter.ink/static/resource/muboard/?id=chudnovsky-algorithm&version=latest&full=1) |
| EulerNumber | 欧拉数 | [eulers-number](https://hatter.ink/static/resource/muboard/?id=eulers-number&version=latest&full=1) |
| EulerTheorem | 欧拉定理 | [euler-theorem](https://hatter.ink/static/resource/muboard/?id=euler-theorem&version=latest&full=1) |
| FibonacciSequence | 斐波那契数列 | [fibonacci-sequence](https://hatter.ink/static/resource/muboard/?id=fibonacci-sequence&version=latest&full=1) |
| LeibnizFormula | $\pi$ 的莱布尼茨公式 | [leibniz-formula](https://hatter.ink/static/resource/muboard/?id=leibniz-formula&version=1) |
| ModularInv | 求乘法逆元【扩展欧几里得法】 | - |
| Prime | 试除法 | - |
| Sqrt10 | 求 $\sqrt{10}$【连分数】 | [resolve-sqrt-10](https://hatter.ink/static/resource/muboard/?id=resolve-sqrt-10&version=latest&full=1) |
| WallisProduct | 沃里斯乘积 | [wallis-product](https://hatter.ink/static/resource/muboard/?id=wallis-product&version=latest&full=1) |
| Class | Comments | MuBoard Link |
|-------------------------|--------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| BinaryExponentiation | 快速幂 | [binary-exponentiation](https://hatter.ink/static/resource/muboard/?id=binary-exponentiation&version=latest&full=1) |
| BinomialTheorem | 二项式定理 | [binomial-theorem](https://hatter.ink/static/resource/muboard/?id=binomial-theorem&version=latest&full=1) |
| BirthdayParadox | 生日悖论 | [birthday-paradox](https://hatter.ink/static/resource/muboard/?id=birthday-paradox&version=latest&full=1) |
| ChineseRemainderTheorem | 中国剩余定理 | [chinese-remainder-theorem](https://hatter.ink/static/resource/muboard/?id=chinese-remainder-theorem&version=latest&full=1) |
| ChudnovskyAlgorithm | 楚德诺夫斯基算法 | [chudnovsky-algorithm](https://hatter.ink/static/resource/muboard/?id=chudnovsky-algorithm&version=latest&full=1) |
| EulerNumber | 欧拉数 | [eulers-number](https://hatter.ink/static/resource/muboard/?id=eulers-number&version=latest&full=1) |
| EulerTheorem | 欧拉定理 | [euler-theorem](https://hatter.ink/static/resource/muboard/?id=euler-theorem&version=latest&full=1) |
| FibonacciSequence | 斐波那契数列 | [fibonacci-sequence](https://hatter.ink/static/resource/muboard/?id=fibonacci-sequence&version=latest&full=1) |
| LeibnizFormula | $\pi$ 的莱布尼茨公式 | [leibniz-formula](https://hatter.ink/static/resource/muboard/?id=leibniz-formula&version=1) |
| ModularInv | 求乘法逆元【扩展欧几里得法】 | - |
| NormalDistribution | 正态分布 | [normal-distribution](https://hatter.ink/static/resource/muboard/?id=normal-distribution&version=latest&full=1) |
| Prime | 试除法 | - |
| Sqrt10 | 求 $\sqrt{10}$【连分数】 | [resolve-sqrt-10](https://hatter.ink/static/resource/muboard/?id=resolve-sqrt-10&version=latest&full=1) |
| WallisProduct | 沃里斯乘积 | [wallis-product](https://hatter.ink/static/resource/muboard/?id=wallis-product&version=latest&full=1) |
<br>

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src/main/java/me/hatter/math/BinomialTheorem.java Normal file
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package me.hatter.math;
import me.hatter.math.util.MathUtil;
import java.math.BigDecimal;
import java.math.RoundingMode;
// https://zhuanlan.zhihu.com/p/34484169
public class BinomialTheorem {
public static void main(String[] args) {
System.out.println(power(BigDecimal.valueOf(0.5), BigDecimal.valueOf(-0.3)));
System.out.println(Math.pow(0.5, -0.3));
System.out.println(power(BigDecimal.valueOf(0.6), BigDecimal.valueOf(3.1)));
System.out.println(Math.pow(0.6, 3.1));
}
public static BigDecimal power(BigDecimal x, BigDecimal u) {
return powerWithN(x, u, 100);
}
public static BigDecimal powerWithN(BigDecimal x, BigDecimal u, long n) {
BigDecimal result = BigDecimal.ZERO;
for (long i = 0; i < n; i++) {
BigDecimal ux = BigDecimal.ONE;
for (long j = 0; j < i; j++) {
ux = ux.multiply(u.subtract(BigDecimal.valueOf(j)));
}
result = result.add(
ux.divide(new BigDecimal(MathUtil.factorial(i)), 100, RoundingMode.HALF_UP)
.multiply(x.subtract(BigDecimal.ONE).pow((int) i))
);
}
return result.setScale(100, RoundingMode.HALF_UP);
}
}