Triangle

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.

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解題技巧：

該題可以採用動態規劃求解。從上層到下層，依次計算並更新dp數組，最後求出dp數組中的最小數。

對於第j層，狀態轉移方程: dp[i] = min(dp[i], dp[i-1]) + triangle[j][i];

代碼：

int minimumTotal(vector< vector<int> >& triangle)
{
    int res = 0x3f3f3f;
    int dp[100000];
    dp[0] = triangle[0][0];
    for(int j = 1; j < triangle.size(); j ++)
    {
        for(int i = triangle[j].size() - 1; i >= 0; i--)
        {
            if(i == triangle[j].size() - 1)
            {
                dp[i] = dp[i-1] + triangle[j][i];
            }
            else if(i == 0)
            {
                dp[i] = dp[i] + triangle[j][i];
            }
            else
            {
                dp[i] = min(dp[i], dp[i-1]) + triangle[j][i];
            }
        }
    }
    int l1, l2;
    l1 = triangle.size();
    l2 = triangle[l1-1].size();
    for(int i = 0; i < l2; i ++)
    {
        if(dp[i] < res) res = dp[i];
    }
    return res;
}