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[leetcode]Pascal's Triangle II
问题描述:
Given an index k, return the kth row of the Pascal‘s triangle.
For example, given k = 3,
Return [1,3,3,1]
.
Note:
Could you optimize your algorithm to use only O(k) extra space?
思路:
the mth element of the nth row of the Pascal‘s triangle is C(n, m) = n!/(m! * (n-m)!)
C(n, m-1) = n!/((m-1)! * (n-m+1)!)
so C(n, m) = C(n, m-1) * (n-m+1) / m
In additional, C(n, m) == C(n, n-m)
代码:
public List<Integer> getRow(int rowIndex) { if(rowIndex < 0) return new ArrayList<Integer>(); int num = rowIndex+1; List<Integer> list = new ArrayList<Integer>(num); double [] factor = new double[num]; double result = 1; factor[0] = 1; list.add(1); for(int i=1; i<num ; i++){ result = result*(num-i)/i; factor[i] = result; list.add((int)factor[i]); } return list; }
[leetcode]Pascal's Triangle II
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