递增整数序列

Question

在一次采访中，我被要求找到以下算法问题的答案。

假设您输入了一个简短的递增整数，例如“ 2 4”，您能找出4之后的整数吗？如果您假设第二个整数比第一个大+2，则下一个整数应为6；但是如果您假设第二个整数是第一个整数的两倍，那么下一个整数也许是8。但是，如果简短输入是“ 2 4 8”，则几乎可以确定下一个整数是16。

简而言之，获得的数字越多，可以消除的假设就越多。我们希望您用Java编写程序。请清楚指出您要使用哪一个。该程序将一小部分递增的整数作为输入，并假设整数中可能存在的模式，然后在线生成接下来的10个整数。

例如，如果程序收到以下输入： 4 14

程序可能会假设下一个整数是前一个整数加10，因此它将生成：

24 34 44 54 64 74 84 94 104114

，但是如果程序收到以下输入，则： 4 14 34

然后可以假设下一个整数是前一个整数乘以2加6的数字。

74 154 3314 634 1274 2554 5114 10234 20474 40954

这是我们要提出的一个开放性问题，换句话说，整数的输入列表可能具有非常有趣的属性（例如，斐波那契数列），没有特定的我们正在测试的整数序列。所以，要有创造力！尝试找出尽可能多的序列。

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您怎么解决这个算法？

Answer 1

这是对疯狂的一击，因为今天是星期五，它很有趣。 我写了3个tests，但容易添加。让我知道你的想法。

function doubleLast(seq) {
  this.seq = seq;
  this.display = 'Double the last number';
  this.match = (seq) => seq.every((v, i) => (i > 0) ?  v === seq[i-1]*2 : true);
  this.nextValue = (seq) => seq[seq.length-1]*2;
}

function simpleAdd(seq) {
  const addNum = (seq) => seq[1] - seq[0];
  this.seq = seq;
  this.display = 'Add a single number';
  this.match = (seq) => {
    // subtract initial value from the second
    return seq.every((v,i) => (i > 0) ? v === seq[i-1]+addNum(seq) : true);
  };
  this.nextValue = (seq) => seq[seq.length-1]+addNum(seq);
}

function divideAddMod(seq) {
  const modifier = (seq) => seq[1] - (seq[0]*2);
  this.seq = seq;
  this.display = 'Try to divide by 2, then add Mod';
  this.match = (seq) => {
    // subtract initial value from the second
    return seq.every((v,i) => (i > 0) ? v === (seq[i-1]*2)+modifier(seq) : true);
  };
  this.nextValue = (seq) => (seq[seq.length-1]*2)+modifier(seq);
}

const algos = [new doubleLast(), new simpleAdd(), new divideAddMod()];

document.addEventListener('click', (e) => {
  if(e.target.matches('button')) {
    let seq = document.querySelector('input').value.split(' ').map(e => parseInt(e));
    algos.forEach(a => {
      let possibleMatch = a.match(seq);
      if(possibleMatch) {
        console.log(`Match found ${a.display} - Next value ${a.nextValue(seq)}`);
      } else {
        console.log(`${a.display} did not match`);
      }
    });
  }
});

<input type="text"></input>
<button>Work It out</button>
<p>Suppose you get a short input of increasing integers, say, "2 4", can you figure out what integers come after 4? If you assume the second integer is +2 greater than the first, then the next integer should be 6; but if you assume the second integer is double the first integer, then perhaps the next integer is 8. However, if the short input was "2 4 8", then you can almost be sure that the next integer is 16.

In short, the more numbers you get, the more hypotheses you can eliminate. We would like you to write a program, in Javascript. Please clearly indicate which one you would like to use. The program takes in a short list of increasing integers as inputs, hypothesize possible patterns in the integers, and generate the next 10 integers in line.

For instance, if the program receives the following input: 4 14

the program may assume that the next integer is the previous integer plus 10, thus it will generate:

24 34 44 54 64 74 84 94 104 114

but if the program receives the following input instead: 4 14 34

then it may hypothesize that the next integer is the previous multiplied by 2 plus 6.

74 154 3314 634 1274 2554 5114 10234 20474 40954

This is an open-ended problem that we're presenting, in other words, the input list of integers may have very interesting properties (e.g. a fibonacci sequence), there is no particular set of integer sequences that we are testing. So, be creative! try to identify as many sequences as you can think of.</p>