118. Pascal's Triangle

题目：

Given numRows, generate the first numRows of Pascal's triangle.

For example, given numRows = 5,
Return

[

     [1],

    [1,1],

   [1,2,1],

  [1,3,3,1],

 [1,4,6,4,1]

]

代码：

仔细一看，规律就是本层第一个和最后一个的元素都是1，其他的元素分别等于上一层同位置元素加上前一个位置的元素。

一百度，才知道，这就是大名鼎鼎的杨辉三角！只可惜，在欧洲，这个表叫做帕斯卡三角形。

但帕斯卡（1623----1662）是在1654年发现这一规律的，比杨辉要迟393年，比贾宪迟600年。

布莱士·帕斯卡的著作Traité du triangle arithmétique（1655年）介绍了这个三角形。帕斯卡搜集了几个关于它的结果，并以此解决一些概率论上的问题，影响面广泛，Pierre Raymond de Montmort（1708年）和亚伯拉罕·棣·美弗（1730年）都用帕斯卡来称呼这个三角形。

估计由于发现该规律后对数学界的影响吧，于是就成为了Pascal's Triangle.

具体的数学定义还有很多，请自行百度。

用java实现，根据规律，不是很复杂，但由于经验，还是折腾了好久，不过还算顺利：

//Pascal's Triangle（杨辉三角），根据层数构建相应的杨辉三角
    public List<List<Integer>> generate(int numRows) {
       //创建元素为List<Integer>的链表list
       List<List<Integer>> list = new ArrayList<>();
       if (numRows<=0)
       {
           return list;
       }
       //构建一个元素构成的第一次，不依赖上一层
       List<Integer> list1 = new ArrayList<Integer>(1);
       list1.add(0, 1);
       list.add(list1);
       if (numRows==1)
       {
           return list;
       }
       //每层递增，通过循环创建每层的链表，并计算元素值
       //由于链表不能根据任意序号插入元素，所以元素的插入还是按顺序来的
       for (int i = 2;i <= numRows; i++)
        {
           System.out.print("循环： "+i+"\n");
           List<Integer> e = new ArrayList<Integer>(i);
           e.add(0,1);
           //从第三层开始，本次处两端元素为1，其余都根据上层相应元素求出
           if(i>2)
           {
               for (int j = 1;j < i-1;j++)
               {
                   System.out.print("i: "+i+" "+"j: "+j+"\n");
                   int num = list.get(i-2).get(j-1)+ list.get(i-2).get(j);
                   e.add(j, num);
               }
           }
           e.add(i-1,1);
            list.add(e);
        }
       return list;
    }

完全按照定义实现，为了保障返回根据题目要求，返回List<List<Integer>>，所以直接用ArrayList。

结果：

同样代码提交了两次，一次4ms，一次5ms，不明觉厉。

结果分布leetcode还没整出来，只能后面再看啦

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" 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" 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