1.大数相乘
1.1 js 版本 (不计算注释只需要20行)
/**
* 大数乘法
* 思路：逐位相乘，不算进位；最后算进位并拼接字符串
* @param {number} a 被乘数
* @param {number} b 乘数
*/
var LargeNumberTimes = function (a, b) {
var result = []
// 转换为整型数组
a = a.toString().split('').map(t => parseInt(t))
b = b.toString().split('').map(t => parseInt(t))
// 逐位相乘，不算进位，与计算方向无关
for (var i = 0; i < b.length; i++) {
for (var j = 0; j < a.length; j++) {
if (!result[i + j])
result[i + j] = 0
result[i + j] += b[i] * a[j]
}
}
// 右边的高位向左边低位进位, 在0处无需进位
for (var i = result.length - 1; i > 0; i--) {
var more = parseInt(result[i] / 10)
if (more > 0) {
result[i - 1] += more;
}
result[i] = result[i] % 10;
}
return result.join('');
};
// 可在 Google 输入框进行验证，如果输入的乘数大小超过了范围
// （或js会转换为科学计数法），需要以字符串传入
// Result: 999999999998000000000001
//console.log( LargeNumberTimes(999999999999, 999999999999) );
1.2 C语言 大数相乘 无依赖
#include <stdio.h>
#define max_length 1000
int strlen(char *a){
int i;
for( i=0; a[i] != '\0' ;i++);
return i;
}
void printIntArray(int a[]){
for(int i=0;i<max_length*2;i++){
if(a[i] == -1){
break;
}
printf("%d",a[i]);
}
printf("\n");
}
char* LargeNumberTimes(char *a, char *b) {
// 转换为整型数组 , 用 -1 代替 js 的 undefined
int aArr[max_length],bArr[max_length];
int resultInt[max_length *2];
for(int i =0 ;i<max_length;i++){
aArr[i] = -1 ; bArr[i] = -1 ; resultInt[i] = -1; resultInt[i+max_length] = -1;
}
int aLen= strlen(a);
int bLen= strlen(b);
for(int i = 0 ; i < aLen ;i++){
aArr[i] = a[i] - '0';
}
for(int i = 0 ; i< bLen ;i++){
bArr[i] = b[i] - '0';
}
// 逐位相乘，不算进位，与计算方向无关
for (int bIndex=bLen-1; bIndex>=0; bIndex--) {
for (int aIndex=aLen-1; aIndex>=0; aIndex--) {
if(resultInt[bIndex + aIndex] == -1) {
resultInt[bIndex + aIndex] = 0 ;
}
resultInt[bIndex + aIndex] += bArr[bIndex] * aArr[aIndex];
}
}
printIntArray(resultInt);
int resultLength =0;
for(int i =0;i<max_length;i++){
if(resultInt[i] == -1){
resultLength = i;
break;
}
}
// 因为是从左到右的计算顺序，所以进位要反向
// （也方便最高位进位时，数组可扩）。
//reverse
for(int i = 0; i< resultLength /2 ; i++){
int t = resultInt[i];
resultInt[i] = resultInt[resultLength -1 - i];
resultInt[resultLength -1 - i] = t;
}
printIntArray(resultInt);
// 最高位可能会进位，所以每次循环重新计算length。
for (int i=0; i< resultLength ; i++) {
int more;
if(resultInt[i] == -1) {
resultInt[i] = 0 ;
}
more = resultInt[i] / 10;
if (more > 0) {
if(i+1 >= resultLength){
resultLength ++ ;
}
if(resultInt[i+1] == -1) {
resultInt[i+1] = 0 ;
}
resultInt[i + 1] += more;
}
resultInt[i] = resultInt[i] % 10;
}
char resultStr[max_length*2] ;
for(int i = 0; i< resultLength ; i++){
resultStr[i] = resultInt[resultLength-1-i] + '0';
}
resultStr[resultLength] = '\0';
printf("%s\n",resultStr);
return resultStr;
}
int main(){
printf("hello\n");
printf("%s\n", LargeNumberTimes("5000000", "5000000"));
}
简单的 js 转 c 想法:
- 函数之间参数传递用
char *,内部接收后再转 int 计算undefined+ 动态数组 : 使用一个较大的数组初始化为-1,延长长度时就把-1改为0
2. 阿拉伯数字和英文互转
/* 数字转英文 */
function numToEn(str){
str = str + ''
var s3 = ['','thousand','million','billion']
var res = []
while(str > 0){
res.push(s3.shift())
res.push(below1000(str.slice(-3)))
str = str.slice(0,-3)
}
return res.reverse().join(' ')
}
function below1000(str){
str = str - 0;
var under20 = ['','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen','twenty']
var res = '';
if(str / 100 >=1) res += under20[Math.floor(str/100)] + " hundred and";
str = str % 100
if(str > 20){
var ten = Math.floor(str / 10)
res += ' ' + ['','',"twenty","thirty","fourty","fifty","sixty","seventy","eighty","ninety"][ten]
res += ' ' + under20[str % 10]
}else { res += ' ' + under20[str] }
return res;
}
/* 英文转数字 */
function enToNum(str){
str = str.split(/\s+/).concat('$')
var under20Map = ['','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen','twenty'].reduce((sum,x,index)=>{ sum[x]=index; return sum }, {})
var s3Map = ['$','thousand','million','billion'].reduce((sum,x,index)=>{ sum[x]=Math.pow(1000,index); return sum }, {})
var tensMap = ['','ten',"twenty","thirty","fourty","fifty","sixty","seventy","eighty","ninety"].reduce((sum,x,index)=>{ sum[x]=index*10; return sum }, {})
var res = 0, now = 0
str.forEach(x=>{
if(x === "hundred") now *= 100
if(x in tensMap) now += tensMap[x]
else if(x in under20Map) now += under20Map[x]
if(x in s3Map){
res += now*s3Map[x]
now = 0
}
})
return res
}
/* 测试代码 */
function test(count = 10){
window.logs = []
window.errors = []
for(var i=0;i<count;i++){
var testNum = Math.floor(Math.pow(10, 10)*Math.random())
testNum = Math.abs(testNum)
var log = { num : testNum, str : numToEn(testNum), status : true }
log.retNum = enToNum(log.str)
if(log.retNum != testNum){
log.status = false
window.errors.push(log)
}
window.logs.push(log)
}
}
/* 测试结果 */
test(10)
window.errors // [ ]
字符串格式如下图, 可自行对其中空格或逗号进行增删
