滑雪场最长路径问题

解法很简单，遍历求解每个元素的最长深度，有点类似图的深度遍历算法，但是还是有些不同，
另外，需要有个中间表用来记录已经计算过的节元素的深度，提高运行效率， 算法并不是最优的，比如说，如果某个节点计算过了就不要重复计算了

#include <iostream>
#include <vector>
using namespace std;

void Output(const vector<vector<int> > & vecMatrix)
{
    for (auto itr=vecMatrix.begin();
          itr!=vecMatrix.end();
          ++itr)
    {
        for (auto itr2=itr->begin();
              itr2!=itr->end();
              ++itr2)
        {
            cout << *itr2 << " ";
        }
        cout << endl;
    }
}

void CalculateLength(const vector<vector<int> > & vecMatrix,
        vector<vector<int> > & vecLength,
        int i,
        int j,
        int R,
        int C)
{
    int nLeft  = 0;
    int nRight = 0;
    int nTop   = 0;
    int nDown  = 0;

    if (j-1 >= 0 && vecMatrix[i][j-1] < vecMatrix[i][j]) {
        if (vecLength[i][j-1] == 0) {
            CalculateLength(vecMatrix, vecLength, i, j-1, R, C);
        }
        nLeft = vecLength[i][j-1];
    }
    if (j+1 < C && vecMatrix[i][j+1] < vecMatrix[i][j]) {
        if (vecLength[i][j+1] == 0) {
            CalculateLength(vecMatrix, vecLength, i, j+1, R, C);
        }
        nRight = vecLength[i][j+1];
    }
    if (i-1 >= 0 && vecMatrix[i-1][j] < vecMatrix[i][j]) {
        if (vecLength[i-1][j] == 0) {
            CalculateLength(vecMatrix, vecLength, i-1, j, R, C);
        }
        nTop = vecLength[i-1][j];
    }
    if (i+1 < R && vecMatrix[i+1][j] < vecMatrix[i][j]) {
        if (vecLength[i+1][j] == 0) {
            CalculateLength(vecMatrix, vecLength, i+1, j, R, C);
        }
        nDown = vecLength[i+1][j];
    }

    int nMax = nLeft;
    nMax = nMax < nRight ? nRight : nMax;
    nMax = nMax < nTop ? nTop : nMax;
    nMax = nMax < nDown ? nDown : nMax;
    
    vecLength[i][j] = nMax + 1;
}

int CalculateMaxLength(const vector<vector<int> > & vecMatrix) 
{
    vector<vector<int> > vecLength;
    int R = vecMatrix.size();
    int C = vecMatrix[0].size();
    for (int i=0; i<R; ++i) {
        vector<int> vecTmp(C, 0);
        vecLength.push_back(vecTmp);
    }

    for (int i=0; i<R; ++i)
    {
        for (int j=0; j<C; ++j)
        {
            CalculateLength(vecMatrix, vecLength, i, j, R, C);
        }
    }

    int nMaxLength = 0;
    for (int i=0; i<R; ++i)
    {
        for (int j=0; j<C; ++j)
        {
            nMaxLength = nMaxLength < vecLength[i][j] ? vecLength[i][j] : nMaxLength;
        }
    }

    return nMaxLength;
}

int main(int argc, char ** argv)
{
    vector<vector<int> > vecMatrix;
    
    vector<int> vecTmpNum;
    vecTmpNum.resize(5);
    vecTmpNum[0] = 1;
    vecTmpNum[1] = 2;
    vecTmpNum[2] = 3;
    vecTmpNum[3] = 4;
    vecTmpNum[4] = 5;
    vecMatrix.push_back(vecTmpNum);
    vecTmpNum[0] = 16;
    vecTmpNum[1] = 17;
    vecTmpNum[2] = 18;
    vecTmpNum[3] = 19;
    vecTmpNum[4] = 6;
    vecMatrix.push_back(vecTmpNum);
    vecTmpNum[0] = 15;
    vecTmpNum[1] = 24;
    vecTmpNum[2] = 25;
    vecTmpNum[3] = 20;
    vecTmpNum[4] = 7;
    vecMatrix.push_back(vecTmpNum);
    vecTmpNum[0] = 14;
    vecTmpNum[1] = 23;
    vecTmpNum[2] = 22;
    vecTmpNum[3] = 21;
    vecTmpNum[4] = 8;
    vecMatrix.push_back(vecTmpNum);
    vecTmpNum[0] = 13;
    vecTmpNum[1] = 12;
    vecTmpNum[2] = 11;
    vecTmpNum[3] = 10;
    vecTmpNum[4] = 9;
    vecMatrix.push_back(vecTmpNum);

    Output(vecMatrix);

    cout << "MaxLength:" << CalculateMaxLength(vecMatrix) << endl;;

    return 0;
}