javascript – Problem mit dem rekursiven Algorithmus.

Question

Wenn Ihr Chef Ihnen am ersten Tag einen Yuan gibt, gibt er Ihnen jeden Tag das Doppelte des Vortages. Das sind 1, 2, 4, 8.... . Wie viel Geld haben Sie nun nach 30 Tagen insgesamt erhalten?
Anforderung: Zur Implementierung eine rekursive Funktion verwenden

Answer 1

问题很简单，关键在于思路，下面是代码。

/*
·递归
  1. salarySum(n) = salarySum(n-1) + salary(n)
  2. salary(n) = 2 ^ (n-1)

·非递归
  循环
*/

function salary(nthDay){
  return Math.pow(2, nthDay-1)
}

// 递归
function salarySum(nthDay) {
  if (nthDay > 1) {
    return salarySum(nthDay - 1) + salary(nthDay)
  } else {
    return 1
  }
}

// 非递归
function salarySum(nthDay) {
  let day = 1
  let sum = 0
  while (day <= nthDay) {
    sum += salary(day)
    day++
  }
  return sum
}

Answer 2

PHP版本

function recursion($day){
    if($day == 1){
        return 1;
    }else{
        return recursion($day - 1) + pow(2,$day - 1);
    }
}
echo recursion(30);

Answer 3

哈哈，汗颜，看错题目

#不递归的实现方式
def fn(n):
    return 2 ** (n - 1)

#递归的实现方式
def fn1(n):
    return 1 if n <= 1 else fn1(n-1) * 2

Answer 4

#!/usr/bin/env python

def salary(n):
    '''Your salary everyday'''
    if n <= 1:
        return 1
    return 2*salary(n-1)


def money(n):
    '''Total money you get for n days.'''
    if n <= 0:
        return 0
    s = salary(n)  # or s = 2**(n-1)
    m = money(n-1)
    print("day %d: salary[%d] total[%d]" % (n, s, (s+m)))
    return s+m 

money(30)

day 1: salary[1] total[1]
day 2: salary[2] total[3]
day 3: salary[4] total[7]
day 4: salary[8] total[15]
day 5: salary[16] total[31]
day 6: salary[32] total[63]
day 7: salary[64] total[127]
day 8: salary[128] total[255]
day 9: salary[256] total[511]
day 10: salary[512] total[1023]
day 11: salary[1024] total[2047]
day 12: salary[2048] total[4095]
day 13: salary[4096] total[8191]
day 14: salary[8192] total[16383]
day 15: salary[16384] total[32767]
day 16: salary[32768] total[65535]
day 17: salary[65536] total[131071]
day 18: salary[131072] total[262143]
day 19: salary[262144] total[524287]
day 20: salary[524288] total[1048575]
day 21: salary[1048576] total[2097151]
day 22: salary[2097152] total[4194303]
day 23: salary[4194304] total[8388607]
day 24: salary[8388608] total[16777215]
day 25: salary[16777216] total[33554431]
day 26: salary[33554432] total[67108863]
day 27: salary[67108864] total[134217727]
day 28: salary[134217728] total[268435455]
day 29: salary[268435456] total[536870911]
day 30: salary[536870912] total[1073741823]

Answer 5

我的思路是：先算出当前的金额，然后把今天的日期和金额传递下去，直到计算满30天为止。

function total(all, day,money){
    var day = day || 1,
        money = money || 0.5;

    money *= 2;
    // console.log( 'day'+day+': '+ money ); // 输出当前的金额
    day++;
    if(day<=all){
        return money + total(all, day, money);
    }
    return money;
}

然后调用total()即可：

total(1); // 1
total(2); // 3
total(7); // 127
total(30); // 1073741823