[leetcode] 120 Min Triangle Path

/*
http://leetcode.com/onlinejudge#question_120

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.
*/
class Solution {
public:
    typedef size_t level_pos_t; // rectangle level no
    typedef size_t row_pos_t; // position within triangle row
    typedef std::pair<level_pos_t, row_pos_t> tri_pos_t; // position within triangle

    typedef std::map<tri_pos_t, int> cache_t; // mapping: position -> return
    typedef std::vector<int> row_t;
    typedef std::vector<row_t> tri_t;

    int minTriPath(const tri_t & T, const tri_pos_t & pos, cache_t & cache)
    {
        const level_pos_t & level = pos.first;
        const row_pos_t & row = pos.second;

        if(level >= T.size() || row >= T[level].size()) { return 0;}

        cache_t::iterator cache_pos = cache.find(pos);
        if(cache.end() != cache_pos) { return cache_pos->second; }

        const int L = minTriPath(T, std::make_pair(level+1, row), cache);
        const int R = minTriPath(T, std::make_pair(level+1, row+1), cache);

        const int ret = T[level][row] + std::min(L, R);

        cache[pos] = ret;
        return ret;
    }
    int minimumTotal(tri_t &T) {
        cache_t cache;
        return minTriPath(T, make_pair(0,0), cache);
    }
};