一些递归的练习题

Posted 2023-02-04 GoldenaArcher

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一些递归的练习题

每道题前面大概会留个十来行空行所以答案会被折叠这样……？

数字和

/**











*/
// find the sum of digits of a positive integer number using recursion
// 35 => 3 + 5
const sumOfDigits = (num: number) => 
  if (num < 0) throw new Error('input should be a positive integer');

  let sum = 0;

  if (num === 0) return 0;

  sum += (num % 10) + sumOfDigits(Math.floor(num / 10));

  return sum;
;

console.log(sumOfDigits(35));
console.log(sumOfDigits(45));

数字的乘方

/**











*/
// calculate the power of a number
const powOfNum = (num: number, pow: number) => 
  if (!Number.isInteger(pow)) throw new Error('power can only be integer');

  // base case, all number's pow of 0 is 1
  if (pow === 0) return 1;

  if (pow < 0) return (1 / num) * powOfNum(num, pow + 1);

  return num * powOfNum(num, pow - 1);
;

console.log(powOfNum(2, 2));
console.log(powOfNum(2, -2));
console.log(powOfNum(0.5, 2));

最大公约数

用的是欧几里得算法

/**
 










*/
// euclidean algorithm
const gcd = (a: number, b: number) => 
  if (!(Number.isInteger(a) && Number.isInteger(b)))
    throw new Error('both numbers must be integer');
  if (b === 0) return a;

  if (a < 0) a = -a;

  if (b < 0) b = -b;

  return gcd(b, a % b);
;

console.log(gcd(48, 18));
console.log(gcd(48, -18));

十进制转二进制

没有做 2’s complement

/**











*/
// euclidean algorithm
const decimalToBinary = (num: number) => 
  // did not implement 2's complement
  if (!Number.isInteger(num)) throw new Error('input should be an integer');

  if (num == 0) return 0;

  return (num % 2) + decimalToBinary(Math.trunc(num / 2)) * 10;
;

console.log(decimalToBinary(10));
console.log(decimalToBinary(-10));

阶乘

/**











*/
const factorial = (num: number) => 
  if (!Number.isInteger(num)) throw new Error('input should be an integer');

  if (num == 1) return 1;

  return num * factorial(num - 1);
;

console.log(factorial(4));

数组的乘积和

/**











*/
const productOfArray = (arr: number[]) => 
  if (!arr) throw new Error('input should be an array');

  if (arr.length == 1) return arr[0];

  return arr[0] * productOfArray(arr.slice(1));
;

console.log(productOfArray([1, 2, 3]));
console.log(productOfArray([1, 2, 3, 4]));
console.log(productOfArray([1, 2, 3, 10]));

获得区间和

0-n 的和

/**











*/
// accepts a number and adds up all the numbers from 0 to the number passed to the function
const getRange = (num: number) => 
  if (!Number.isInteger(num) || num < 0)
    throw new Error('input should be a positive integer');

  if (num === 0) return num;

  return num + getRange(num - 1);
;

console.log(getRange(6));
console.log(getRange(10));

斐波那契数字

/**











*/
const fibNum = (num: number) => 
  if (!Number.isInteger(num) || num < 0)
    throw new Error('input should be a positive integer');

  if (num < 2) return num;

  return fibNum(num - 1) + fibNum(num - 2);
;

console.log(fibNum(4));
console.log(fibNum(10));
console.log(fibNum(28));

翻转字符串

/**











*/
const reverseStr = (str: string) => 
  if (!str.length) return '';

  return reverseStr(str.slice(1)) + str[0];
;

console.log(reverseStr('javascript'));
console.log(reverseStr('typescript'));

是否为回文字符串

/**











*/
const isPalindrome = (str) => 
  if (typeof str !== 'string') throw new Error('input should be a string');

  if (!str.length || str.length === 1) return true;

  return (
    str[0] === str[str.length - 1] &&
    isPalindrome(str.substring(1, str.length - 1))
  );
;

console.log(isPalindrome('abcba'));
console.log(isPalindrome('tacocat'));
console.log(isPalindrome('abbcad'));

some 递归调用回调函数

/**











*/
// array.some(cb)
const someRecursiveCallback = (
  arr: number[],
  cb: (num: number) => boolean
) => 
  if (!arr) throw new Error('input should be an array');

  if (arr.length === 1) return cb(arr[0]);

  if (!cb(arr[0])) return someRecursiveCallback(arr.slice(1), cb);

  return true;
;

console.log(someRecursiveCallback([1, 2, 3, 4, 5], isOdd));
console.log(someRecursiveCallback([2, 4, 6], isOdd));

flat 数组

/**











*/
// arr.flat()
const flatten = (arr: any) => 
  arr.flat;

  if (!arr) throw new Error('input should be an array');
  const res: any[] = [];

  for (const val of arr) 
    if (val instanceof Array) res.push(...flatten(val));
    else res.push(val);
  

  return res;
;

console.log(flatten([1, [2, [3, [4, [5], 6]]]]));

大写数组中的首字母

/**











*/
const capitalizeFirst = (arr) => 
  if (!arr) throw new Error('input should be an array');

  if (!arr.length) return [];

  return [arr[0][0].toUpperCase() + arr[0].substring(1)].concat(
    ...capitalizeFirst(arr.slice(1))
  );
;

console.log(capitalizeFirst(['car', 'wash', 'wasabi']));

计算对象中出现的和

/**











*/
const obj1 = 
  outer: 2,
  obj: 
    inner: 2,
    otherObj: 
      superInner: 2,
      notANumber: true,
      alsoNotANumber: 'yup',
    ,
  ,
;

const obj2 = 
  a: 2,
  b:  b: 2, bb:  b: 3, bb:  b: 2   ,
  c:  c:  c: 2 , cc: 'ball', ccc: 5 ,
  d: 1,
  e:  e:  e: 2 , ee: 'car' ,
;

const nestedEvenSum = (obj: any, sum = 0) => 
  for (const [, val] of Object.entries(obj)) 
    if (typeof val === 'number' && !isOdd(val)) sum += val;
    else if (val instanceof Object) sum += nestedEvenSum(val);
  

  return sum;
;

console.log(nestedEvenSum(obj1));

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