DynamicProgrammingStriver/CherryPickup3DLecture13.cpp at main · dhruvkej9/DynamicProgrammingStriver · GitHub

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#include <vector>
#include <iostream>
using namespace std;
int solve1(int i,int j1,int j2 ,int r,int c,vector<vector<int>> &grid,vector<vector<vector<int>>> &dp)
{
    if(j1 < 0 || j2 < 0 || j1 >= c || j2 >= c)
    {
        return -1e8;
    }
    if(dp[i][j1][j2] != -1) return dp[i][j1][j2];
    if(i == r-1)
    {
        if(j1 == j2) return grid[i][j1];
        else return grid[i][j1] + grid[i][j2];
    }
    // explore all paths of alice and bob simultaneously
    int maxi = -1e8;
    for(int dj1 = -1;dj1 <= 1;dj1++)
    {
        for(int dj2 = -1;dj2 <= 1;dj2++)
        {
            int value = 0;
            if(j1 == j2) value = grid[i][j1];
            else value = grid[i][j2] + grid[i][j1];
            value += solve1(i+1,j1+dj1,j2+dj2,r,c,grid,dp);

            maxi = max(maxi,value);
        }
    }
    return dp[i][j1][j2] = maxi;
}
int solve2(int n, int m, vector<vector<int>> &grid)
{
    // int dp[r][c][c];
    vector<vector<vector<int>>> dp(n,vector<vector<int>> (m,vector<int>(m,-1)));
    for(int j1 = 0;j1 < m;j1++)
    {
        for(int j2 = 0;j2 < m;j2++)
        {
            if(j1 == j2) dp[n-1][j1][j2] = grid[n-1][j1];
            else dp[n-1][j1][j2] = grid[n-1][j1] + grid[n-1][j2];
        }
    }
    for(int i = n-2;i >= 0;i--)
    {
        for(int j1 = 0;j1 < m;j1++)
        {
            for(int j2 = 0;j2 < m;j2++)
            {
                int maxi = -1e8;
                for(int dj1 = -1;dj1 <= 1;dj1++)
                {
                    for(int dj2 = -1;dj2 <= 1;dj2++)
                    {
                        int value = 0;
                        if(j1 == j2) value = grid[i][j1];
                        else value = grid[i][j2] + grid[i][j1];

                        if(j1+dj1 >= 0 && j1+dj1 < m &&j2+dj2 >= 0 && j2+dj2 < m)
                        value += dp[i+1][j1+dj1][j2+dj2];
                        else
                            value += -1e8;
                        maxi = max(maxi,value);
                    }
                }
                dp[i][j1][j2] = maxi;
            }
        }
    }
    return dp[0][0][m-1];
}
int solve3(int n, int m, vector<vector<int>> &grid)
{
    // int dp[r][c][c];
    vector<vector<int>> front(m,vector<int>(m)) ;
    vector<vector<int>> cur(m,vector<int>(m)) ;
    for(int j1 = 0;j1 < m;j1++)
    {
        for(int j2 = 0;j2 < m;j2++)
        {
            if(j1 == j2) front[j1][j2] = grid[n-1][j1];
            else front[j1][j2] = grid[n-1][j1] + grid[n-1][j2];
        }
    }
    for(int i = n-2;i >= 0;i--)
    {
        for(int j1 = 0;j1 < m;j1++)
        {
            for(int j2 = 0;j2 < m;j2++)
            {
                int maxi = -1e8;
                for(int dj1 = -1;dj1 <= 1;dj1++)
                {
                    for(int dj2 = -1;dj2 <= 1;dj2++)
                    {
                        int value = 0;
                        if(j1 == j2) value = grid[i][j1];
                        else value = grid[i][j2] + grid[i][j1];

                        if(j1+dj1 >= 0 && j1+dj1 < m &&j2+dj2 >= 0 && j2+dj2 < m)
                        value += front[j1+dj1][j2+dj2];
                        else
                            value += -1e8;
                        maxi = max(maxi,value);
                    }
                }
                cur[j1][j2] = maxi;
            }
        }
        front = cur;
    }
    return front[0][m-1];
}
int maximumChocolates(int r, int c, vector<vector<int>> &grid)
{
    // int dp[r][c][c];
    vector<vector<vector<int>>> dp(r,vector<vector<int>> (c,vector<int>(c,-1)));
//     return solve1(0,0,c-1,r,c,grid,dp);
//     return solve2(r,c,grid);
    return solve3(r,c,grid);

}