LeetCode - Pascal's Triangle

Pascal's Triangle

2014.1.8 22:44

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]

]

Solution:

　　Pascal's Triangle is a typical O(n^2) dynamic programming problem. Here is the recurrence relation:

　　　　1. f[i][0] = 1, i ∈ N

　　　　2. f[i][i] = 1, i ∈ N

　　　　3. f[i][j] = f[i - 1][j - 1] + f[i - 1][j], i ∈ N+, j ∈ N ∩ [0, i - 1]

　　Time complexity is O(n^2). Space complexity is O(1).

Accepted code:

 1 // Too careless, 2WA!!

 2 class Solution {

 3 public:

 4     vector<vector<int> > generate(int numRows) {

 5         // IMPORTANT: Please reset any member data you declared, as

 6         // the same Solution instance will be reused for each test case.

 7         result.clear();

 8         

 9         if(numRows <= 0){

10             return result;

11         }

12         

13         int i, j;

14         for(i = 0; i < numRows; ++i){

15             result.push_back(vector<int>());

16             for(j = 0; j <= i; ++j){

17                 result[i].push_back(0);

18             }

19         }

20         

21         for(i = 0; i < numRows; ++i){

22             result[i][i] = result[i][0] = 1;

23         }

24         

25         for(i = 1; i < numRows; ++i){

26             for(j = 1; j < i; ++j){

27                 result[i][j] = result[i - 1][j] + result[i - 1][j - 1];

28             }

29         }

30         

31         return result;

32     }

33 private:

34     vector<vector<int>> result;

35 };