title: Pascals Triangle
tags:
- pascals-triangle
- No.118
- simple
- discrete-mathematics

Description

Given a non-negative integer numRows, generate the first numRows of Pascal's triangle.

img

In Pascal's triangle, each number is the sum of the two numbers directly above it.

Example:

Input: 5
Output:
[
     [1],
    [1,1],
   [1,2,1],
  [1,3,3,1],
 [1,4,6,4,1]
]

Corner Cases

• 0

Solutions

Naive

The naive way. Running time is 1 + 2 + 3 + \cdots + n = \frac{n^2 + n}{2} = O(n^2)

class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> llst = new LinkedList<List<Integer>>();
        if (numRows == 0) {return llst;}
        
        List<Integer> l0   = new LinkedList<Integer>();
        List<Integer> last = l0;
        l0.add(1);
        llst.add(l0);
        
        for (int i=1; i<numRows; i++) {
            List<Integer> li = new LinkedList<Integer>();
            li.add(1);
            for (int j=1; j<i; j++) {
                li.add(last.get(j-1) + last.get(j));
            }
            li.add(1);
            llst.add(li);
            last = li;
        }        
        return llst;
    }
}