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No Plagiarism!a5I0tW0ss4Q0wD2GCtKDposted 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 protection428PENANAMUx8nbAcpb 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 protection428PENANAWlJFRWqb3d 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 protection428PENANAEoY83hMaoR 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 protection428PENANAmKHiGvvFj1 維尼
* [grid[0].length] = column number8964 copyright protection428PENANAqpts4wj0A4 維尼
A: 8964 copyright protection428PENANAT2idSWbSCH 維尼
1. Depth First Search (DFS): 8964 copyright protection428PENANAxUgiKrSPp0 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 protection428PENANA1rAfSKyb3E 維尼
*Using Recursive function8964 copyright protection428PENANA9s1tosS4fi 維尼
class Solution {8964 copyright protection428PENANAkwZwZ6P7vD 維尼
public int[] findBall(int[][] grid) {8964 copyright protection428PENANAn8RSQEzOCP 維尼
// create new int[], for int[grid[0].length]8964 copyright protection428PENANAy1iK0DxRcX 維尼
int result[] = new int[grid[0].length];8964 copyright protection428PENANAC1HafyUxaS 維尼
// how many ball as well as how many row8964 copyright protection428PENANAnnBQ5w8UU4 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection428PENANA8R7cHLUD5F 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection428PENANAUgW5oV7VMt 維尼
}8964 copyright protection428PENANAcxXMWQGSlt 維尼
return result;8964 copyright protection428PENANAmLOKf2S0bd 維尼
}8964 copyright protection428PENANAJ7aQBABaQQ 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection428PENANAP3NfKtGhyx 維尼
// base case; ball reached the last row8964 copyright protection428PENANAvFQPqgGWzQ 維尼
if (row == grid.length)8964 copyright protection428PENANAFXufdd5Cti 維尼
return col;8964 copyright protection428PENANAroy7Rf7LYK 維尼
int nextColumn = col + grid[row][col];8964 copyright protection428PENANA1TYLxbQN3R 維尼
if (nextColumn < 0 ||8964 copyright protection428PENANAfRW3MQndFj 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection428PENANA2BcenCohny 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection428PENANAElW84EHuvi 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection428PENANAl14GOB8Fuo 維尼
return -1;8964 copyright protection428PENANAzMpWC27UYJ 維尼
}8964 copyright protection428PENANAMirfMfjG6m 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection428PENANAJMPNhP6jSa 維尼
}8964 copyright protection428PENANA0ow7f4OjHi 維尼
}8964 copyright protection428PENANAJ5aYfYpF2n 維尼
2. Dynamic Programming Approach:8964 copyright protection428PENANAk7ZfKHSIFg 維尼
class Solution {8964 copyright protection428PENANAqImXelg7b6 維尼
public int[] findBall(int[][] grid) {8964 copyright protection428PENANApcRTOWUhPv 維尼
int result[] = new int[grid[0].length];8964 copyright protection428PENANAZa4wY1uxsK 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];432Please respect copyright.PENANAi0ZvB0uxKQ
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432Please respect copyright.PENANAmCTc3BWByw
8964 copyright protection428PENANAknCMXHbCXL 維尼
for (int row = grid.length; row >= 0; row--) {8964 copyright protection428PENANAB2MbYFlTdl 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection428PENANASm0PACN7oU 維尼
if (row == grid.length) {8964 copyright protection428PENANAXf5P7R2TeH 維尼
// for the last row 432Please respect copyright.PENANAJxZANkvRk8
8964 copyright protection428PENANAOT7sXaQaIp 維尼
memo[row][col] = col;8964 copyright protection428PENANAkeVJTqyZLQ 維尼
continue;8964 copyright protection428PENANAwPPIPkCWKU 維尼
}8964 copyright protection428PENANARiDy9I3gsc 維尼
// for the remaining row.8964 copyright protection428PENANANY36Sj14dP 維尼
int nextColumn = col + grid[row][col];8964 copyright protection428PENANAPdJLPUWubV 維尼
if (nextColumn < 0 ||8964 copyright protection428PENANAB3xrDqbWB4 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection428PENANATOlFgKED0B 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection428PENANAanWnD2sv6a 維尼
memo[row][col] = -1;8964 copyright protection428PENANAZjcK2zbtnr 維尼
else8964 copyright protection428PENANAtQhdTYf1Um 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection428PENANArdc4ksvSNp 維尼
// reaching row 0, copy the values in all the column in the result array. 432Please respect copyright.PENANAR7gELPJbY5
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if (row == 0) {8964 copyright protection428PENANAtDcmNDKTS4 維尼
result[col] = memo[row][col];8964 copyright protection428PENANAoU4ksq1wHc 維尼
}8964 copyright protection428PENANA0CBsYCf6bg 維尼
}8964 copyright protection428PENANAI7CCdKpeuj 維尼
}8964 copyright protection428PENANATKAxA3L0eF 維尼
return result;8964 copyright protection428PENANAXfdNmhaTWG 維尼
}8964 copyright protection428PENANArAfMpBq2an 維尼
}8964 copyright protection428PENANAfRn7XC7RQf 維尼
3. Iterative Approach, Simulation:8964 copyright protection428PENANABE6RtzlVlk 維尼
class Solution {8964 copyright protection428PENANAMBm4nY7X3L 維尼
public int[] findBall(int[][] grid) {8964 copyright protection428PENANA5koGrF9j1T 維尼
int result[] = new int[grid[0].length];8964 copyright protection428PENANASGCYpASzlt 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 protection428PENANAGyTkJb91Fz 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection428PENANA8g34LAyG0r 維尼
int currentCol = col;8964 copyright protection428PENANAhnRFfOfgRD 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection428PENANAAsBt1RVpsE 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection428PENANAXFsLMdmbUc 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection428PENANARpKZh15FCW 維尼
// stuck case 8964 copyright protection428PENANAHN2HDPzulf 維尼
if (nextColumn < 0 ||8964 copyright protection428PENANAvEZiHv3KTy 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection428PENANAr3JVmIGoaR 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection428PENANAIpTdUsObJ6 維尼
result[col] = -1;8964 copyright protection428PENANAc1X4atz4YZ 維尼
break;8964 copyright protection428PENANA1vvW6c5LUQ 維尼
}8964 copyright protection428PENANAK4VEslo5iw 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 protection428PENANA9Nj6mI7Kwg 維尼
result[col] = nextColumn;8964 copyright protection428PENANAS49vYizQR3 維尼
currentCol = nextColumn;8964 copyright protection428PENANANtspyjVtBs 維尼
}8964 copyright protection428PENANA4GeLpaBHAG 維尼
}8964 copyright protection428PENANAE5Zji6R7w0 維尼
return result;8964 copyright protection428PENANAWegj4iUn04 維尼
}8964 copyright protection428PENANAuOAgyllNcU 維尼
}8964 copyright protection428PENANASyBb048QZW 維尼
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