大正整数乘法(非BigInteger)及几种阶乘算法

本文介绍了一种实现大整数相乘的方法，避免使用BigInteger类，并提供了三种不同的阶乘算法实现，适用于处理非常大的数值运算。

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大正整数乘法(非BigInteger)及几种阶乘算法

1,2个大整数相乘：

String bignumMult(String num1,String num2){
  int[] b1 = fromStr2IntArray(num1);
  if (b1 == null || b1.length == 0){
    return null;
  }
  int[] b2 = fromStr2IntArray(num2);
  if (b2 == null || b2.length == 0){
    return null;
  }
  //outBytes的最大长度不会超过b1.length+b2.length+1
  int[] outBytes =  new int[b1.length+b2.length+1];

  for (int i = 0; i < b1.length; i ++){
    for (int j = 0; j < b2.length; j++){
      int index = i+j;

      //暂时不进位
      outBytes[index] = outBytes[index] + b1[i]*b2[j];
    }
  }
  for (int i = 0; i < outBytes.length; i ++){
    int r = outBytes[i];
    if(r >= 10){
      outBytes[i] = r%10;
      outBytes[i+1] = r/10 + outBytes[i+1];
    }
  }

  StringBuilder sb = new StringBuilder("");
  int begin = -1;
  for (int i = outBytes.length-1; i >= 0; i --){
    if (outBytes[i] != 0){
      begin = i;
      break;
    }
  }
  if (begin == -1){
    return "0";
  }
  for (int i = begin; i >= 0; i --){
    sb.append(outBytes[i]);
  }

  return sb.toString();
}
int[] fromStr2IntArray(String src){
  if (src == null || src.trim().equals("")){
    return null;
  }
  int len = src.length();
  int []rt = new int[len];
  for (int i = 0; i < len; i ++){
    int tmp = src.charAt(len-1-i)-48;
    if (tmp < 0 || tmp >= 10){
      return null;
    }
    rt[i] = tmp;
  }

  return rt;
}

2,阶乘算法一：

String sp(int n) {
  if (n <= 1) {
    return "1";
  }

  String result = "1";
  for (int i = 1; i <= n; i ++){
    result = new BigInteger(result).multiply(BigInteger.valueOf(i)).toString();
  }
  return result;
}

3，阶乘算法二：

String sp1(int n){
  if (n <= 1) {
    return "1";
  }
  String result = "1";
  for (int i = 1; i <= n; i ++){
    result = bignumMult(result,Integer.toString(i));
  }

  return result;
}

4，阶乘算法三：

void sp2(int n){
  int size = 1000000;
  int[] bigArray = new int[size];
  bigArray[0] = 1;
  for (int i = 1; i < size; i++) {
    bigArray[i] = -1;
  }
  int tempCount = 0;
  int k1;
  for (int i = n; i > 0; i--) {
    for (int j = 0; j < size; j++) {
      if (bigArray[j] == -1) {
        k1 = j;
        //向高位进位
    while (tempCount > 0) {
          bigArray[k1] = tempCount % 10;
          tempCount = tempCount / 10;
          k1++;
        }
        break;
      }
      int tempMul = bigArray[j] * i;
      tempCount = tempCount + tempMul;
      bigArray[j] = tempCount % 10;
      tempCount = tempCount / 10;
    }
  }

  int i = size - 1;
  while (i >= 0) {
    if (bigArray[i] != -1) {
      System.out.print(bigArray[i]);
    }
    i--;
  }
}