LeetCode

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:

// Too careless, 2WA!!
class Solution {
public:
    vector<vector<int> > generate(int numRows) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        result.clear();
        
        if(numRows <= 0){
            return result;
        }
        
        int i, j;
        for(i = 0; i < numRows; ++i){
            result.push_back(vector<int>());
            for(j = 0; j <= i; ++j){
                result[i].push_back(0);
            }
        }
        
        for(i = 0; i < numRows; ++i){
            result[i][i] = result[i][0] = 1;
        }
        
        for(i = 1; i < numRows; ++i){
            for(j = 1; j < i; ++j){
                result[i][j] = result[i - 1][j] + result[i - 1][j - 1];
            }
        }
        
        return result;
    }
private:
    vector<vector<int>> result;
};