帕斯卡三角算法的时间复杂度是多少？

Question

Tasked with solving the following problem (Pascal Triangle) which looks like this.

[
     [1],
    [1,1],
   [1,2,1],
  [1,3,3,1],
 [1,4,6,4,1]
]

I've successfully implemented the code(see below) but I'm having a tough time figuring out what the time complexity would be for this solution. The number of operations by list is 1 + 2 + 3 + 4 + .... + n would number of operations reduce to n^2 how does the math work and translate into Big-O notation?

I'm thinking this is similar to the gauss formula n(n+1)/2 so O(n^2) but I could be wrong any help is much appreciated

public class Solution {
    public List<List<Integer>> generate(int numRows) {
        if(numRows < 1) return new ArrayList<List<Integer>>();;
        List<List<Integer>> pyramidVal = new ArrayList<List<Integer>>();

        for(int i = 0; i < numRows; i++){
            List<Integer> tempList = new ArrayList<Integer>();
            tempList.add(1);
            for(int j = 1; j < i; j++){
                tempList.add(pyramidVal.get(i - 1).get(j) + pyramidVal.get(i - 1).get(j -1));
            }
            if(i > 0) tempList.add(1);
            pyramidVal.add(tempList);
        }
        return pyramidVal;
    }
}

Answer 1

Complexity is O(n^2) .

Each calculation of element in your code is done in constant time. ArrayList accesses are constant time operations, as well as insertions, amortized constant time. Source :

The size, isEmpty, get, set, iterator, and listIterator operations run in constant time. The add operation runs in amortized constant time

Your triangle has 1 + 2 + ... + n elements. This is arithmetic progression that sums to n*(n+1)/2 , which is in O(n^2)