118_PascalTriangle.java

/*
 * 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]
 * ]
 */

//K(i)(j)=K(i-1)(j-1)+K(i-1)(j) except for the first and last element
public class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> triangle = new ArrayList<List<Integer>>();
        if (numRows <=0){
            return triangle;
        }
        for (int i=0; i<numRows; i++){
            List<Integer> row =  new ArrayList<Integer>();
            for (int j=0; j<i+1; j++){
                if (j==0 || j==i){
                    row.add(1);
                } else {
                    row.add(triangle.get(i-1).get(j-1)+triangle.get(i-1).get(j));
                }
            }
            triangle.add(row);
        }
        return triangle;
    }
}

//Math dont understand
public class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> result = new ArrayList<List<Integer>>();
        for (int n = 0; n < numRows; n++) {
            int nCk = 1;
            List<Integer> list = new ArrayList<Integer>();
            for (int k = 0; k <= n; k++) {
                list.add(nCk);
                nCk = nCk * (n - k) / (k + 1);
            }
            result.add(list);
        }
        return result;
    }
}