1/11/2022 - 1706. Where Will the Ball Fall
No Plagiarism!ASIyVotGwCSPNF6QJ3i2posted 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 protection400PENANAgWN5KNr5cx 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 protection400PENANA7LGi2SXkzZ 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 protection400PENANA9WSHqmRy1O 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 protection400PENANA6HcoOFIcKw 維尼
* [grid[0].length] = column number8964 copyright protection400PENANAmRIAFSgrVh 維尼
A: 8964 copyright protection400PENANA2RBcDe7Kxo 維尼
1. Depth First Search (DFS): 8964 copyright protection400PENANAmkkBazLGgh 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 protection400PENANAdHKG2n3DxO 維尼
*Using Recursive function8964 copyright protection400PENANAxiFaspQnMM 維尼
class Solution {8964 copyright protection400PENANAMyRCVaMss8 維尼
public int[] findBall(int[][] grid) {8964 copyright protection400PENANA4pqC6qQwbb 維尼
// create new int[], for int[grid[0].length]8964 copyright protection400PENANAb3iWiwlflb 維尼
int result[] = new int[grid[0].length];8964 copyright protection400PENANAMcr6ryGhUR 維尼
// how many ball as well as how many row8964 copyright protection400PENANA5rA1cxNgeO 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection400PENANAdklZ1m0pPS 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection400PENANAq8aGlu8208 維尼
}8964 copyright protection400PENANANsZKpsF9xy 維尼
return result;8964 copyright protection400PENANA26GS7ec9Nl 維尼
}8964 copyright protection400PENANAW7uBrDViNG 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection400PENANALG1jXrrfYV 維尼
// base case; ball reached the last row8964 copyright protection400PENANAuCAQcfbnj3 維尼
if (row == grid.length)8964 copyright protection400PENANAhm236hSDOh 維尼
return col;8964 copyright protection400PENANA9wwpSCWJdU 維尼
int nextColumn = col + grid[row][col];8964 copyright protection400PENANAVK3blb33dm 維尼
if (nextColumn < 0 ||8964 copyright protection400PENANATkXcMzgei3 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection400PENANAe3HM56lknx 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection400PENANA1m0pdznP1n 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection400PENANAfWtp0vEV3f 維尼
return -1;8964 copyright protection400PENANAMvInPnt4tO 維尼
}8964 copyright protection400PENANAv77z8giEC5 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection400PENANAHU7qQiCCn6 維尼
}8964 copyright protection400PENANAA2F215Ewtd 維尼
}8964 copyright protection400PENANAqDJFX2WSrc 維尼
2. Dynamic Programming Approach:8964 copyright protection400PENANAQf0oWs8Pio 維尼
class Solution {8964 copyright protection400PENANAiKw9uTPUXD 維尼
public int[] findBall(int[][] grid) {8964 copyright protection400PENANASrSaFJNtq5 維尼
int result[] = new int[grid[0].length];8964 copyright protection400PENANAj42L3Y17Qx 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];404Please respect copyright.PENANAboOdupmQli
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404Please respect copyright.PENANAmI1ZMoazp3
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for (int row = grid.length; row >= 0; row--) {8964 copyright protection400PENANAvqXxqxf388 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection400PENANAIi5xD4OIHH 維尼
if (row == grid.length) {8964 copyright protection400PENANAoojYiRIMII 維尼
// for the last row 404Please respect copyright.PENANAzUxXKzCsvs
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memo[row][col] = col;8964 copyright protection400PENANAoxOrrmxf4B 維尼
continue;8964 copyright protection400PENANAq9tn72NQJt 維尼
}8964 copyright protection400PENANAHyIWFA5pQb 維尼
// for the remaining row.8964 copyright protection400PENANAel2hjmAY2X 維尼
int nextColumn = col + grid[row][col];8964 copyright protection400PENANA1GVsqmAtwB 維尼
if (nextColumn < 0 ||8964 copyright protection400PENANAuwrY4lGxtH 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection400PENANAhsFg9ritSo 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection400PENANA1zrb2DCmcp 維尼
memo[row][col] = -1;8964 copyright protection400PENANAxD1g3IUzbF 維尼
else8964 copyright protection400PENANAztHmGerrIx 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection400PENANAZwyX3mBHhx 維尼
// reaching row 0, copy the values in all the column in the result array. 404Please respect copyright.PENANAjvNzEon3qL
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if (row == 0) {8964 copyright protection400PENANAfpf0L0CXRL 維尼
result[col] = memo[row][col];8964 copyright protection400PENANAoDjfuxqovz 維尼
}8964 copyright protection400PENANAlug32hZIQR 維尼
}8964 copyright protection400PENANAff7Io5LOu7 維尼
}8964 copyright protection400PENANA72eisZ8wHB 維尼
return result;8964 copyright protection400PENANAezY84zIz7g 維尼
}8964 copyright protection400PENANABKG0B9rWA8 維尼
}8964 copyright protection400PENANAZUDjvM5FiT 維尼
3. Iterative Approach, Simulation:8964 copyright protection400PENANAEmQcDJRILo 維尼
class Solution {8964 copyright protection400PENANA6EksYkdoQW 維尼
public int[] findBall(int[][] grid) {8964 copyright protection400PENANAHal9woJHSF 維尼
int result[] = new int[grid[0].length];8964 copyright protection400PENANAYr82NwXA5d 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 protection400PENANA1tfyqTcqhy 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection400PENANAGgUbdOSD3m 維尼
int currentCol = col;8964 copyright protection400PENANA8ooOlXoNEs 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection400PENANAXYdnJr4MMB 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection400PENANA0C2W9APmtx 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection400PENANAdkAaB06l6o 維尼
// stuck case 8964 copyright protection400PENANApjHjTw7X9E 維尼
if (nextColumn < 0 ||8964 copyright protection400PENANA0no0iTqEJ7 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection400PENANAeHZAHftFos 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection400PENANAYWfOXGFZLC 維尼
result[col] = -1;8964 copyright protection400PENANAfSEatSe0Ad 維尼
break;8964 copyright protection400PENANAE5VHRtGs2V 維尼
}8964 copyright protection400PENANAN8kB4cnMmJ 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 protection400PENANAwpaxeu9TTr 維尼
result[col] = nextColumn;8964 copyright protection400PENANAMMWync08UH 維尼
currentCol = nextColumn;8964 copyright protection400PENANA0sTRfi4KAc 維尼
}8964 copyright protection400PENANAiUb0nMbXRh 維尼
}8964 copyright protection400PENANAj8F5SeVSrs 維尼
return result;8964 copyright protection400PENANAVugvHuZhvd 維尼
}8964 copyright protection400PENANAgJ1HZbGleo 維尼
}8964 copyright protection400PENANAVzal2d0H8B 維尼
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