Triangle

题目原型：

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:
Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

基本思路：

这是一道动态规划经典题，上一层的结果对下一层有影响，所以我们令f(0)....f(n)是第n层的结果，现在我们要计算第n+1层，那么：

1）当j=0时，f(0) = f(0) + triangle.get(n).get(j);

2）当j=triangle.get(n+1).size()-1时，f(j) = f(j-1)+triangle.get(n+1).get(j);

3）其他情况，f(j) = min(f(j-1),f(j))+triangle.get(n+1).get(j);

	public int minimumTotal(ArrayList<ArrayList<Integer>> triangle)
	{
		int ret = Integer.MAX_VALUE;
		int[] f = new int[triangle.size()];
		
		for(int i = 0;i<triangle.size();i++)
		{
			for(int j = triangle.get(i).size()-1;j>=0;j--)
			{
				if(j==0)
				{
					f[j]+=triangle.get(i).get(j);
				}
				else if(j==triangle.get(i).size()-1)
				{
					f[j]=f[j-1]+triangle.get(i).get(j);
				}
				else
				{
					f[j] = (f[j-1]<f[j]?f[j-1]:f[j])+triangle.get(i).get(j);
				}
			}
		}
		
		for(int i = 0;i<triangle.size();i++)
		{
			ret = ret<f[i]?ret:f[i];
		}
		return ret;
	}

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Triangle

原文：http://blog.csdn.net/cow__sky/article/details/21295283