feat: add binomial theorem

README.md

@@ -1,8 +1,9 @@
 # math
 
 | 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)                                                                                                                        |
@@ -11,6 +12,7 @@
 | 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)                                                                                                                                    |

src/main/java/me/hatter/math/BinomialTheorem.java

@@ -0,0 +1,36 @@
+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);
+    }
+}