<p>You have a 2-D <code>grid</code> of size <code>m x n</code> representing a box, and you have <code>n</code> balls. The box is open on the top and bottom sides.</p>

<p>Each cell in the box has a diagonal board spanning two corners of the cell that can redirect a ball to the right or to the left.</p>

<ul>
	<li>A board that redirects the ball to the right spans the top-left corner to the bottom-right corner and is represented in the grid as <code>1</code>.</li>
	<li>A board that redirects the ball to the left spans the top-right corner to the bottom-left corner and is represented in the grid as <code>-1</code>.</li>
</ul>

<p>We drop one ball at the top of each column of the box. Each ball can get stuck in the box or fall out of the bottom. A ball gets stuck if it hits a &quot;V&quot; shaped pattern between two boards or if a board redirects the ball into either wall of the box.</p>

<p>Return <em>an array </em><code>answer</code><em> of size </em><code>n</code><em> where </em><code>answer[i]</code><em> is the column that the ball falls out of at the bottom after dropping the ball from the </em><code>i<sup>th</sup></code><em> column at the top, or <code>-1</code><em> if the ball gets stuck in the box</em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/26/ball.jpg" style="width: 500px; height: 385px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,-1,-1],[1,1,1,-1,-1],[-1,-1,-1,1,1],[1,1,1,1,-1],[-1,-1,-1,-1,-1]]
<strong>Output:</strong> [1,-1,-1,-1,-1]
<strong>Explanation:</strong> This example is shown in the photo.
Ball b0 is dropped at column 0 and falls out of the box at column 1.
Ball b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1.
Ball b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0.
Ball b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0.
Ball b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[-1]]
<strong>Output:</strong> [-1]
<strong>Explanation:</strong> The ball gets stuck against the left wall.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1]]
<strong>Output:</strong> [0,1,2,3,4,-1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>grid[i][j]</code> is <code>1</code> or <code>-1</code>.</li>
</ul>

class Solution {
public:

    vector<vector<int>> a;
    vector<vector<int>> dp;
    int n,m;

    int helper(int i,int j,int pre = 0){

        if(j < 0 || j >= m){
            return -1;
        }

        if(i == n){
            return j;
        }

        if(dp[i][j] != 0){
            return dp[i][j];
        }

        int ans;

        if(a[i][j] == 1){
            if(j+1 == m || a[i][j+1] == -1){
                return -1;
            }
            ans = helper(i+1,j+1);
        }else{
            if(j-1 < 0 || a[i][j-1] == 1){
                return -1;
            }
            ans = helper(i+1,j-1);
        }

        return dp[i][j] =  ans;

    }


    vector<int> findBall(vector<vector<int>>& a1) {

        a = a1;
         n = a.size();  
         m = a[0].size();
         dp = vector<vector<int>>(n,vector<int>(m,0));


        vector<int> ans;

        for(int i = 0 ; i < m ; i++){

           int temp = helper(0,i);
           ans.push_back(temp);

        }

        return ans;
        
    }
};
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