Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.（Medium）
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.
分析：
经典的动态规划题，可以有自顶向下，自底向上的解法，是自己学动态规划的第一道题，就不分析了，写一个自底向上的解法。
代码：
class Solution {
public:
int minimumTotal(vector<vector<int>>& triangle) {
int sz = triangle.size();
if (sz == ) {
return ;
}
int dp[sz][sz];
for (int i = ; i < sz; ++i) {
dp[sz - ][i] = triangle[sz - ][i];
}
for (int i = sz - ; i >= ; --i) {
for (int j = ; j <= i; ++j) {
dp[i][j] = min(dp[i + ][j], dp[i + ][j + ]) + triangle[i][j];
}
}
return dp[][];
}
};