给定两个以字符串形式表示的非负整数 num1 和 num2，返回 num1 和 num2 的乘积，它们的乘积也表示为字符串形式。

注意：不能使用任何内置的 BigInteger 库或直接将输入转换为整数。

思路

  1. 模拟笔算过程
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var multiply = function (num1, num2) {
  if (num1 === '0' || num2 === '0') {
    return '0'
  }
  const items1 = num1
    .split('')
    .reverse()
    .map((item) => Number(item))
  const items2 = num2
    .split('')
    .reverse()
    .map((item) => Number(item))
  let sumItems = [0]
  const calcSum = (factor1, factor2) => {
    let inc = 0
    let cur = 0
    const sumItems = []
    while (cur < factor1.length || cur < factor2.length || inc) {
      let sumVal = inc
      if (cur < factor1.length) {
        sumVal += factor1[cur]
      }
      if (cur < factor2.length) {
        sumVal += factor2[cur]
      }
      sumItems.push(sumVal % 10)
      inc = Math.floor(sumVal / 10)
      ++cur
    }
    return sumItems
  }
  for (let i = 0; i < items1.length; ++i) {
    const val1 = items1[i]
    let factor = new Array(i).fill(0)
    let inc = 0
    for (let j = 0; j < items2.length; ++j) {
      const val = val1 * items2[j] + inc
      inc = Math.floor(val / 10)
      factor.push(val % 10)
    }
    if (inc > 0) {
      factor.push(inc)
    }
    sumItems = calcSum(sumItems, factor)
  }
  return sumItems.reverse().join('')
}