An answer of http://nabetani.sakura.ne.jp/hena/ord23snakemoinc/

yhpg.cpp

#include <iostream>
#include <cstring>
#include <climits>

using namespace std;

constexpr int FIELD_SIZE = 5;

int field[FIELD_SIZE][FIELD_SIZE];
int memo[10][FIELD_SIZE][FIELD_SIZE];

typedef pair<int, int> point_t;

constexpr point_t points[] = { make_pair(-1, 0), make_pair(1, 0), make_pair(0, -1), make_pair(0, 1), };

constexpr int size = sizeof(points) / sizeof(*points);

auto dfs(int d, int i, int j, int n)-> int 
{
    if(memo[d][i][j] != -1) return memo[d][i][j];

    int res = INT_MIN;
    for(size_t x = 0; x < size; ++x) {
        const int ii = i + points[x].first;
        const int jj = j + points[x].second;
        if( (0 <= ii && ii < FIELD_SIZE) && (0 <= jj && jj < FIELD_SIZE) && (field[i][j] < field[ii][jj]) ) { 
            res = max( res, dfs(d + 1, ii, jj, n + 1) );
        }   
    }   

    return memo[d][i][j] = max(res, n); 
}

auto solve(const string &src)-> int
{
    for(size_t i = 0, j = 0; i < src.length(); ++i) {
        if(src[i] == '/') {
            j += 1;
            continue;
        }
        field[j][i % 6] = src[i] - '0';
    }

    memset( memo, -1, sizeof(memo) );

    int res = INT_MIN;
    for(size_t j = 0; j < FIELD_SIZE; ++j) {
        for(size_t i = 0; i < FIELD_SIZE; ++i) {
            res = max( res, dfs(0, i, j, 1) );
        }
    }
    return res;
}

void test(const string &src, int expected)
{
    const int actual = solve(src);
    cout << (actual == expected ? "ok" : "***NG***") << endl;
}

int main()
{
    pair<string, int> d[] = {
        make_pair("01224/82925/69076/32298/21065", 6),
        make_pair("03478/12569/03478/12569/03478", 10),
        make_pair("09900/28127/87036/76545/87650", 10),
        // 略
    };
    
    for(size_t i = 0; i < sizeof(d) / sizeof(*d); ++i) {
        test(d[i].first, d[i].second);
    }
    return 0;
}