Unique Paths III Solutions in C++

// Source : https://leetcode.com/problems/unique-paths-iii/
// Author : Hao Chen
// Date   : 2019-02-03


class Solution {
public:
    int uniquePathsIII(vector<vector<int>>& grid) {
        
        int path = 0;
        int startX, startY;
	if (!findStartPoint( grid, startX, startY)) return 0;
        uniquePathsHelper(grid, startX, startY, path);
        return path;
    }
    
    bool findStartPoint(vector<vector<int>> &grid, int& x, int& y) {
         for(int i=0; i<grid.size(); i++) {
            for(int j=0; j<grid[0].size(); j++) {
                if (grid[i][j] == 1) {
                    x = i; y =j;
                    return true;
                }
            }
         }
        return false;
    }
    bool check(vector<vector<int>> &grid ) {
        for(int i=0; i<grid.size(); i++) {
            for(int j=0; j<grid[0].size(); j++) {
                if (grid[i][j]  == 0 ) return false;
            }
        }
        return true;
    }
    
    
    void uniquePathsHelper(vector<vector<int>> &grid, int x, int y, int& path ) {
        
        if (x < 0 || y < 0 || x>= grid.size() || y>=grid[0].size()) return;
        
        if ( grid[x][y] < 0)  return;
 
        if ( grid[x][y] == 2) {  
            if (check(grid)) path++;
            return;
        }
        
        //back tracing - mark -2 means already passed.
        grid[x][y] = -2;
        uniquePathsHelper(grid, x, y-1, path); // up
        uniquePathsHelper(grid, x, y+1, path); // down
        uniquePathsHelper(grid, x+1, y, path); // right
        uniquePathsHelper(grid, x-1, y, path); // left
        grid[x][y] = 0;
    
    }
};

/// Source : https://leetcode.com/problems/unique-paths-iii/
/// Author : liuyubobobo
/// Time   : 2019-01-21

#include <iostream>
#include <vector>

using namespace std;


/// Backtrack
/// Time Complexity: O(4 ^ (m * n))
/// Space Complexity: O(m * n)
class Solution {

private:
    int m, n, end;
    const int d[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

public:
    int uniquePathsIII(vector<vector<int>>& grid) {

        m = grid.size();
        n = grid[0].size();
        int start, todo = 0;
        for(int i = 0; i < m; i ++)
            for(int j = 0; j < n; j ++){
                int pos = i * n + j;
                if(grid[i][j] == 1)
                    start = pos;
                else if(grid[i][j] == 2)
                    end = pos, grid[i][j] = 0, todo ++;
                else if(grid[i][j] == 0)
                    todo ++;
            }
        return dfs(grid, start, todo);
    }

private:
    int dfs(vector<vector<int>>& grid, int pos, int todo){

        if(pos == end)
            return !todo;

        int x = pos / n, y = pos % n, res = 0;
        for(int i = 0; i < 4; i ++){
            int nextx = x + d[i][0], nexty = y + d[i][1];
            if(nextx >= 0 && nextx < m && nexty >= 0 && nexty < n && grid[nextx][nexty] == 0){
                grid[nextx][nexty] = 1;
                res += dfs(grid, nextx * n + nexty, todo - 1);
                grid[nextx][nexty] = 0;
            }
        }
        return res;
    }
};


int main() {

    vector<vector<int>> g0 = {
            {1,0},
            {0,0},
            {0,2}
    };
    cout << Solution().uniquePathsIII(g0) << endl;
    // 1

    vector<vector<int>> g1 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,2,-1}
    };
    cout << Solution().uniquePathsIII(g1) << endl;
    // 2

    vector<vector<int>> g2 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,0,2}
    };
    cout << Solution().uniquePathsIII(g2) << endl;
    // 4

    return 0;
}

/// Source : https://leetcode.com/problems/unique-paths-iii/
/// Author : liuyubobobo
/// Time   : 2020-04-28

#include <iostream>
#include <vector>

using namespace std;


/// State Compression + Memory Search
/// Time Complexity: O(m * n * 2 ^ (m * n))
/// Space Complexity: O(m * n * 2 ^ (m * n))
class Solution {

private:
    int m, n, end;
    const int d[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

public:
    int uniquePathsIII(vector<vector<int>>& grid) {

        m = grid.size(), n = grid[0].size();
        int start, state = 0;
        for(int i = 0; i < m; i ++)
            for(int j = 0; j < n; j ++){
                int pos = i * n + j;
                if(grid[i][j] == 1)
                    start = pos;
                else if(grid[i][j] == 2)
                    end = pos, grid[i][j] = 0;
                else if(grid[i][j] == -1)
                    state |= (1 << pos);
            }
        vector<vector<int>> dp((m * n), vector<int>(1 << (m * n), -1));
        return dfs(grid, state | (1 << start), start, dp);
    }

private:
    int dfs(vector<vector<int>>& grid, int state, int pos, vector<vector<int>>& dp){

        if(pos == end)
            return state == (1 << (m * n)) - 1 ? 1 : 0;
        if(dp[pos][state] != -1) return dp[pos][state];

        int x = pos / n, y = pos % n, res = 0;
        for(int i = 0; i < 4; i ++){
            int nextx = x + d[i][0], nexty = y + d[i][1];
            int next = nextx * n + nexty;
            if(in_area(nextx, nexty) && (state & (1 << next)) == 0){
                res += dfs(grid, state | (1 << next), next, dp);
            }
        }
        return dp[pos][state] = res;
    }

    bool in_area(int x, int y){
        return x >= 0 && x < m && y >= 0 && y < n;
    }
};


int main() {

    vector<vector<int>> g0 = {
            {1,0},
            {0,0},
            {0,2}
    };
    cout << Solution().uniquePathsIII(g0) << endl;
    // 1

    vector<vector<int>> g1 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,2,-1}
    };
    cout << Solution().uniquePathsIII(g1) << endl;
    // 2

    vector<vector<int>> g2 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,0,2}
    };
    cout << Solution().uniquePathsIII(g2) << endl;
    // 4

    vector<vector<int>> g3 = {
            {0,0,0,0,0},
            {0,2,1,0,0},
            {0,0,0,0,0},
            {0,0,0,0,0}
    };
    cout << Solution().uniquePathsIII(g3) << endl;
    // 8

    return 0;
}

/// Source : https://leetcode.com/problems/unique-paths-iii/
/// Author : liuyubobobo
/// Time   : 2020-04-28

#include <iostream>
#include <vector>
#include <map>

using namespace std;


/// State Compression + Dynamic Programming
/// Time Complexity: O(m * n * 2 ^ (m * n))
/// Space Complexity: O(m * n * 2 ^ (m * n))
class Solution {

private:
    int m, n;
    const int dirs[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};

public:
    int uniquePathsIII(vector<vector<int>>& grid) {

        m = grid.size(), n = grid[0].size();
        int start, end, k = 0;
        map<int, int> posToIndex, indexToPos;
        for(int i = 0; i < m; i ++)
            for(int j = 0; j < n; j ++){
                int pos = i * n + j;
                if(grid[i][j] == 1)
                    start = pos, grid[i][j] = 0;
                else if(grid[i][j] == 2)
                    end = pos, grid[i][j] = 0;

                if(grid[i][j] == -1) continue;

                posToIndex[pos] = k;
                indexToPos[k] = pos;
                k ++;
            }
        vector<vector<int>> dp(k, vector<int>(1 << k, 0));
        dp[posToIndex[start]][1 << posToIndex[start]] = 1;
        for(int state = 1; state < (1 << k); state ++)
            for(int i = 0; i < k; i ++)
                if((state & (1 << i)) && dp[i][state]){
                    int pos = indexToPos[i], x = pos / n, y = pos %n;
                    for(int d = 0; d < 4; d ++) {
                        int nextx = x + dirs[d][0], nexty = y + dirs[d][1], next = nextx * n + nexty;
                        if(in_area(nextx, nexty) && grid[nextx][nexty] != -1 && (state & (1 << next)) == 0)
                            dp[posToIndex[next]][state | (1 << posToIndex[next])] += dp[i][state];
                    }
                }
        return dp[posToIndex[end]][(1 << k) - 1];
    }

private:
    bool in_area(int x, int y){
        return x >= 0 && x < m && y >= 0 && y < n;
    }
};


int main() {

    vector<vector<int>> g0 = {
            {1,0},
            {0,0},
            {0,2}
    };
    cout << Solution().uniquePathsIII(g0) << endl;
    // 1

    vector<vector<int>> g1 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,2,-1}
    };
    cout << Solution().uniquePathsIII(g1) << endl;
    // 2

    vector<vector<int>> g2 = {
            {1,0,0,0},
            {0,0,0,0},
            {0,0,0,2}
    };
    cout << Solution().uniquePathsIII(g2) << endl;
    // 4

    vector<vector<int>> g3 = {
            {0,0,0,0,0},
            {0,2,1,0,0},
            {0,0,0,0,0},
            {0,0,0,0,0}
    };
    cout << Solution().uniquePathsIII(g3) << endl;
    // 8

    return 0;
}