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No Plagiarism!c52vXJ4UiXikYM8WasN1posted on PENANA Q: You have a 2-D grid of size m x n representing a box, and you have n balls. The box is open on the top and bottom sides.8964 copyright protection399PENANAbHYWUoKzNo 維尼
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.8964 copyright protection399PENANA4N9DsRFV5e 維尼
- 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 1.
- 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 -1.
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 "V" shaped pattern between two boards or if a board redirects the ball into either wall of the box.8964 copyright protection399PENANAQzwtvuQu7Q 維尼
Return an array answer of size n where answer[i] is the column that the ball falls out of at the bottom after dropping the ball from the ith column at the top, or -1 if the ball gets stuck in the box.8964 copyright protection399PENANAvTjncOFNYR 維尼
* [grid[0].length] = column number8964 copyright protection399PENANAbrgumm6BxZ 維尼
A: 8964 copyright protection399PENANAVtACEnA0eb 維尼
1. Depth First Search (DFS): 8964 copyright protection399PENANANQ5DkwpFrw 維尼
Condition 1: The ball reaches a point where it can no longer move ahead. In this case, we will return -1. Condition 2: The ball reaches the last row. In this case, we will return the column in which the ball will drop.8964 copyright protection399PENANA85pqLk17LS 維尼
*Using Recursive function8964 copyright protection399PENANAgVQDxH1MB5 維尼
class Solution {8964 copyright protection399PENANAKfImLonXOA 維尼
public int[] findBall(int[][] grid) {8964 copyright protection399PENANA9dsguTiBxP 維尼
// create new int[], for int[grid[0].length]8964 copyright protection399PENANA1wJtkfEdpL 維尼
int result[] = new int[grid[0].length];8964 copyright protection399PENANABtkv4aJrRK 維尼
// how many ball as well as how many row8964 copyright protection399PENANAH3UZd4KkzC 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection399PENANAvK9GTM4gbO 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection399PENANALKRz9cJFoS 維尼
}8964 copyright protection399PENANAxDsPikjRFI 維尼
return result;8964 copyright protection399PENANAa8xGR0GGQB 維尼
}8964 copyright protection399PENANAlPXA5xpKqd 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection399PENANAtXxNhXqRwb 維尼
// base case; ball reached the last row8964 copyright protection399PENANAGKtcpS3Aid 維尼
if (row == grid.length)8964 copyright protection399PENANAuRj3Jp1kpu 維尼
return col;8964 copyright protection399PENANAFt9BwtBLzI 維尼
int nextColumn = col + grid[row][col];8964 copyright protection399PENANASeBQRVJUS1 維尼
if (nextColumn < 0 ||8964 copyright protection399PENANAPK77pfC5XT 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection399PENANAtyqM1Hv52W 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection399PENANACUnti0JgNn 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection399PENANAs5YtHyBcyI 維尼
return -1;8964 copyright protection399PENANAp9wcJ7HLPW 維尼
}8964 copyright protection399PENANA4RTTnc0iFu 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection399PENANAMxedgfsZnb 維尼
}8964 copyright protection399PENANAIAQOkcfCk8 維尼
}8964 copyright protection399PENANATTKGzqi0zU 維尼
2. Dynamic Programming Approach:8964 copyright protection399PENANAxTvlNMqRKg 維尼
class Solution {8964 copyright protection399PENANAGC1Di3ZjXB 維尼
public int[] findBall(int[][] grid) {8964 copyright protection399PENANA29ETy8aRbD 維尼
int result[] = new int[grid[0].length];8964 copyright protection399PENANA1Oun0q1BKA 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];403Please respect copyright.PENANA6eauWB3r9E
8964 copyright protection399PENANAVNlIe8J3pt 維尼
403Please respect copyright.PENANAJYmvwqXvTd
8964 copyright protection399PENANATIMR1obB9x 維尼
for (int row = grid.length; row >= 0; row--) {8964 copyright protection399PENANAdtv3Sn5QQg 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection399PENANAYvvkpAFMOE 維尼
if (row == grid.length) {8964 copyright protection399PENANAByfulSPjTe 維尼
// for the last row 403Please respect copyright.PENANAf1UC068EJJ
8964 copyright protection399PENANA4Sj9mS5Hhy 維尼
memo[row][col] = col;8964 copyright protection399PENANAMkw1qsn9mM 維尼
continue;8964 copyright protection399PENANAwBNFZRE8dF 維尼
}8964 copyright protection399PENANAZaRmfkbaAx 維尼
// for the remaining row.8964 copyright protection399PENANAFURxVc1Z6c 維尼
int nextColumn = col + grid[row][col];8964 copyright protection399PENANAfx5Rplr7an 維尼
if (nextColumn < 0 ||8964 copyright protection399PENANA7Zt3Ld6Cxe 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection399PENANAFtmYqeA1lk 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection399PENANABghc4FNPQp 維尼
memo[row][col] = -1;8964 copyright protection399PENANA4I7Xg6Uvog 維尼
else8964 copyright protection399PENANAeVVPSvOeHf 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection399PENANAscfFwKdwcz 維尼
// reaching row 0, copy the values in all the column in the result array. 403Please respect copyright.PENANAk2qc0zM4em
8964 copyright protection399PENANAWFxB0Xbq3K 維尼
if (row == 0) {8964 copyright protection399PENANAo5FuxRqRMr 維尼
result[col] = memo[row][col];8964 copyright protection399PENANAcTBNpoFf7y 維尼
}8964 copyright protection399PENANAM7gnqYqruW 維尼
}8964 copyright protection399PENANAUkKJnx8Iq7 維尼
}8964 copyright protection399PENANAA8NS1mHiWR 維尼
return result;8964 copyright protection399PENANAvEMImNGnBR 維尼
}8964 copyright protection399PENANAt3dZGRPshA 維尼
}8964 copyright protection399PENANAmk4ega0ZTO 維尼
3. Iterative Approach, Simulation:8964 copyright protection399PENANAoQnqWBQ9b2 維尼
class Solution {8964 copyright protection399PENANA1Ow2KS2eJf 維尼
public int[] findBall(int[][] grid) {8964 copyright protection399PENANAbw687lOW6u 維尼
int result[] = new int[grid[0].length];8964 copyright protection399PENANAlBoBv7ycWg 維尼
// 1. Start by picking up a ball starting from every column col, iterating from the 0th column to the last column. Initialize the current column as col.8964 copyright protection399PENANAwVm1tRxGpk 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection399PENANAVc5JSqNHph 維尼
int currentCol = col;8964 copyright protection399PENANAvOq8rLi2C9 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection399PENANAaJ8ztXyUcd 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection399PENANAxGHG3BQsZI 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection399PENANA698naSpf4o 維尼
// stuck case 8964 copyright protection399PENANAXwQQFkUu2L 維尼
if (nextColumn < 0 ||8964 copyright protection399PENANARGRSjA8hpL 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection399PENANA0vlwfQSZXH 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection399PENANA4Ky4KY6MsX 維尼
result[col] = -1;8964 copyright protection399PENANAlP0rH1N3W5 維尼
break;8964 copyright protection399PENANAMrPDaMAKE1 維尼
}8964 copyright protection399PENANA19y8m4P0aU 維尼
// 3. Update the value of nextColumn in the result array for every row. In the end, the result will store the column number where the ball will fall after the last row. (result[col] = currentCol, return the result)8964 copyright protection399PENANABB1exTsZo1 維尼
result[col] = nextColumn;8964 copyright protection399PENANAC9xK4ZxNI8 維尼
currentCol = nextColumn;8964 copyright protection399PENANA5od7NSZ3wI 維尼
}8964 copyright protection399PENANA7ngl4Wyumd 維尼
}8964 copyright protection399PENANAZ7vtf8cJx1 維尼
return result;8964 copyright protection399PENANA5xfD4H8jBd 維尼
}8964 copyright protection399PENANANJ3WUiQwHt 維尼
}8964 copyright protection399PENANAaZ6gvzzMBp 維尼
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