How to add large integers using PHP arrays

As modern computers are more and more widely used in daily life, it has become increasingly difficult for modern computers to meet the needs of processing large-scale data. In actual development, we often need to perform operations such as addition, subtraction, multiplication, and division on large integers, and these operations often exceed the range of integers usually supported by computers. In order to solve these problems, we have to make use of data structures and algorithms in computers. This article will introduce how to use PHP arrays to add large integers.

1. Representation method of large integers

In computers, the two's complement representation of integers is usually used. Among them, the complement of a positive integer is its binary representation, and the two's complement of a negative integer is The two's complement is the bitwise inversion of the binary representation of its absolute value plus 1. However, if you want to handle large integers that exceed the range of integers supported by your computer, you need to use other representation methods.

A common way to represent large integers is to use string representation, where each digit is represented by one character. For example, a string representing the decimal number 1234567890 can be represented as "1234567890". However, using strings to represent numbers is inefficient when performing numerical operations, so we need to use other data structures to represent large integers.

Another commonly used method of representing large integers is to use array representation. In this method, we convert a large integer into an array, where each element represents an integer bit. For example, an array representing the decimal number 1234567890 can be represented as [1,2,3,4,5,6,7,8,9,0]. The advantage of using an array to represent large integers is that numerical operations can be performed more efficiently, and it can also save storage space, because if some of the higher-order numbers are 0, they do not need to be represented in the array.

2. How to add large integers using PHP arrays

In PHP, we can use arrays to represent and add large integers. The following is the PHP code:

function addBigIntegers($a, $b) {
  //将数组a和b的长度对齐
  while (count($a) < count($b)) {
    $a[] = 0;
  }
  while (count($b) < count($a)) {
    $b[] = 0;
  }
  $carry = 0; //表示进位数
  $result = array(); //保存结果的数组
  for ($i = count($a) - 1; $i >= 0; $i--) {
    $sum = $a[$i] + $b[$i] + $carry; //计算当前位上的和
    $carry = intval($sum / 10); //计算进位数
    $result[$i] = $sum % 10; //计算当前位上的结果
  }
  if ($carry > 0) {
    array_unshift($result, $carry); //如果最高位有进位，将进位添加到结果数组中
  }
  return $result;
}

$a = array(1, 2, 3, 4, 5); 
$b = array(9, 8, 7, 6, 5);
$result = addBigIntegers($a, $b);
echo implode("", $result); //输出结果的十进制表示

In the above code, the addBigIntegers function is used to add two arrays of large integers and return the result array. In the function, we first align the lengths of the two arrays by adding 0 to the end of the shorter array. Then, we add starting from the highest bit of the array, calculate the sum, carry number and result at the current bit, and save the result to a new array. Finally, if there is a carry from the highest bit, the carry is added to the front of the result array.

For input to this function, we can use arrays of arbitrary lengths to represent large integers because the function automatically aligns the lengths of these arrays. The output is an array, where each element represents an integer bit of the result. If you need to represent the result as a decimal number, you can do so by converting the numbers in the output array to characters and then concatenating them together.

Summary

This article introduces the method of adding large integers with PHP arrays. In actual development, this method is very practical because it can efficiently handle large integer operations and save storage space. When using this method, we just need to convert the big integers into arrays and add them using the addBigIntegers function. If you need to perform other numerical operations, you can extend this method.

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