LeetCode 算法题解 & js 大数相加计算解析 All In One

LeetCode 算法题解 & js 大数相加计算解析 All In One

js 大数相加

原理

JavaScript 的安全整数范围是 -2^53-1 ~ 2^53-1 ，即: -9007199254740991 ~ 9007199254740991;
换句话说，整数超过这个范围就会丢失精度，那超过这个范围的基本运算就会出错了;

换一种思路，用字符串表示数字，如 "9007199254740999"，也不存在四舍五入精度丢失的问题，这样无论整数数值是多大都没任何的影响;
把整数数字表示字符串之后，那么整数数字的运算就转换成字符串的运算;

big number add

从最后一个数字开始向前依次相加，逢10进1，下一位数字相加的时候加上次计算的进位；

const bigNumsAdd = (num1, num2) => {
  // 获取最大长度
  const len = Math.max(num1.length, num2.length);
  // 对齐
  num1 = num1.padStart(len, 0);
  num2 = num2.padStart(len, 0);
  // 进位
  let carry = 0;
  let result = ``;
  let temp = 0;
  for(let i=len-1; i>=0;  i--){
    temp = carry + parseInt(num1[i]) + parseInt(num2[i]);
    // 字符串相加，要注意先后顺序
    result = (temp % 10) + result;
    // 取余进位
    carry = parseInt(temp / 10);
  }
  // 判断是否进位
  return result = (carry === 1 ? '1' : '') + result;
}

// test

const n1 = "9007199254740990"
const n2 = "1229007199254740993443"
bigNumsAdd(n1, n2);
// "1229016206453995734433"

// 不支持负数 ⚠️ ❌
const n1 = "-9007199254740990"
const n2 = "1229007199254740993443"
bigNumsAdd(n1, n2);
 // 'NaNNaNNaNNaNNaNNaN6206453995734433'

//  (算法性能优化: 取短的，减少循环次数)

solutions

function addStrings(num1: string, num2: string): string {
  return (BigInt(num1) + BigInt(num2)).toString();
};

Runtime 52 ms Beats 96.39% of users with TypeScript
Memory 51.12 MB Beats 97.94% of users with TypeScript

https://leetcode.com/problems/add-strings/solutions/5256888/leetcode-415-add-strings-solution-with-bigint/

leetcode

https://leetcode.com/problems/add-strings/

https://leetcode-cn.com/problems/add-strings/

/**
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var addStrings = function(num1, num2) {
  let res = '';
  let temp = 0;
  const arr1 = num1.split('');
  const arr2 = num2.split('');
  while (arr1.length || arr2.length || temp) {
    // ~~ ??? bitwise not 双非位运算
    temp += ~~arr1.pop() + ~~arr2.pop();
    // 字符串相加，要注意先后顺序
    res = (temp % 10) + res;
    // 进位
    temp = temp > 9;
  }
  // console.log('res =', res, typeof res);
  return res === "0" ? res : res.replace(/^0+/, '');
}

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BigInt

digits = [6,1,4,5,3,9,0,1,9,5,1,8,6,7,0,5,5,4,3]
// (19) [6, 1, 4, 5, 3, 9, 0, 1, 9, 5, 1, 8, 6, 7, 0, 5, 5, 4, 3]
BigInt(digits.join(''))
// 6145390195186705543n

BigInt(digits.join('')).toString().split("").map(Number)
// (19) [6, 1, 4, 5, 3, 9, 0, 1, 9, 5, 1, 8, 6, 7, 0, 5, 5, 4, 3]

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt

Number.MAX_SAFE_INTEGER

The Number.MAX_SAFE_INTEGER static data property represents the maximum safe integer in JavaScript (2**53 – 1).

Number.MAX_SAFE_INTEGER 静态数据属性表示 JavaScript 中的最大安全整数 (2**53 – 1)。

Number.MAX_SAFE_INTEGER
9007199254740991
2 ** 64 - 1
18446744073709552000
2 ** 32 - 1
4294967295

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/MAX_SAFE_INTEGER

MathML

Mathematical Markup Language (MathML) Version 3.0 2nd Edition

W3C Recommendation 10 April 2014

https://www.w3.org/TR/MathML/

HTML var tag

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/var

<table width="100%">
  <tbody>
      <tr>
        <td id="eqnoc2"><var>E</var> = <var>m</var><var>c</var><sup>2</sup></td>
      </tr>
  </tbody>
</table>

E = mc²

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/kbd

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/code

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/samp

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/sup

<p><var>a<sup>2</sup></var> + <var>b<sup>2</sup></var> = <var>c<sup>2</sup></var></p>

a² + b² = c²

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/sub

H<sub>2</sub>O

H₂O

https://developer.mozilla.org/en-US/docs/Web/HTML/Element/wbr

MathJax

xml for math

https://mathjax.github.io/MathJax-demos-web/tex-chtml.html

refs

https://www.cnblogs.com/xgqfrms/p/18230786

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