1/11/2022 - 1706. Where Will the Ball Fall
No Plagiarism!1TuaA9dR3u7D6BfzlTu0posted 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 protection418PENANAMMsQPXjq3W 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 protection418PENANA522YjoUIJE 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 protection418PENANAOhFM3F6vqM 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 protection418PENANA5KVNscMYCc 維尼
* [grid[0].length] = column number8964 copyright protection418PENANARrWzKM7z1P 維尼
A: 8964 copyright protection418PENANAt8Flbxs8iR 維尼
1. Depth First Search (DFS): 8964 copyright protection418PENANA37pk4zZvxN 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 protection418PENANAiilbcq1fFO 維尼
*Using Recursive function8964 copyright protection418PENANAAKyie3gw3z 維尼
class Solution {8964 copyright protection418PENANAx99uXI2Zfd 維尼
public int[] findBall(int[][] grid) {8964 copyright protection418PENANA0oKIUTyddf 維尼
// create new int[], for int[grid[0].length]8964 copyright protection418PENANAumIeeHkrlC 維尼
int result[] = new int[grid[0].length];8964 copyright protection418PENANA8RORXiVMyw 維尼
// how many ball as well as how many row8964 copyright protection418PENANA23zBiI1yXx 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection418PENANAwvDicUMYKi 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection418PENANAMou6cWUKsC 維尼
}8964 copyright protection418PENANA9w0DYi1eyg 維尼
return result;8964 copyright protection418PENANAjpVj4r12pt 維尼
}8964 copyright protection418PENANAWl6suRPpVe 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection418PENANAUNX2y1Z1jJ 維尼
// base case; ball reached the last row8964 copyright protection418PENANAhnukomDUry 維尼
if (row == grid.length)8964 copyright protection418PENANAorxCzw6ty8 維尼
return col;8964 copyright protection418PENANA0H5HUKXpjM 維尼
int nextColumn = col + grid[row][col];8964 copyright protection418PENANAtdV8ZNSWrZ 維尼
if (nextColumn < 0 ||8964 copyright protection418PENANAA9Tgab1YSD 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection418PENANA4Z4tRafXwy 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection418PENANAMkfEXppuYN 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection418PENANAWVFCCuJ7OU 維尼
return -1;8964 copyright protection418PENANAcLcRfr8LA2 維尼
}8964 copyright protection418PENANAlykxblXgva 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection418PENANAUeAJe0tKJg 維尼
}8964 copyright protection418PENANA8Q5mTSc9T0 維尼
}8964 copyright protection418PENANAHXvoPUBLP4 維尼
2. Dynamic Programming Approach:8964 copyright protection418PENANAVsi1FaiZJk 維尼
class Solution {8964 copyright protection418PENANAQvvViWOBai 維尼
public int[] findBall(int[][] grid) {8964 copyright protection418PENANA0FSH867Ukx 維尼
int result[] = new int[grid[0].length];8964 copyright protection418PENANAJjLEqLjfa5 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];422Please respect copyright.PENANAxGlwN3FyCN
8964 copyright protection418PENANAfBfTTbOCuB 維尼
422Please respect copyright.PENANAYzCmPkMjS0
8964 copyright protection418PENANA5pZwnakzY5 維尼
for (int row = grid.length; row >= 0; row--) {8964 copyright protection418PENANAmzdekIeHQb 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection418PENANAan4ucgcYQt 維尼
if (row == grid.length) {8964 copyright protection418PENANAEJoZZtLRVU 維尼
// for the last row 422Please respect copyright.PENANAy5KAfDSZx8
8964 copyright protection418PENANAiUKJB7VfYU 維尼
memo[row][col] = col;8964 copyright protection418PENANAyhE9NvPbv7 維尼
continue;8964 copyright protection418PENANAoYu6kmdS8h 維尼
}8964 copyright protection418PENANA6gw0S9C3Ju 維尼
// for the remaining row.8964 copyright protection418PENANAAPypYoMhgV 維尼
int nextColumn = col + grid[row][col];8964 copyright protection418PENANAffsakv8H4G 維尼
if (nextColumn < 0 ||8964 copyright protection418PENANAArV84nBYNh 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection418PENANArceXMoUyu3 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection418PENANAC7pWgIZ294 維尼
memo[row][col] = -1;8964 copyright protection418PENANA8qLcUR7BOh 維尼
else8964 copyright protection418PENANAGQ6mdQpbDM 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection418PENANA1j1L15FCoQ 維尼
// reaching row 0, copy the values in all the column in the result array. 422Please respect copyright.PENANAI7SLjyWkFk
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if (row == 0) {8964 copyright protection418PENANAGXjMnmiqvo 維尼
result[col] = memo[row][col];8964 copyright protection418PENANAGhmHnNcjRb 維尼
}8964 copyright protection418PENANAEXOHWgD9nf 維尼
}8964 copyright protection418PENANAcgK4aNzFVp 維尼
}8964 copyright protection418PENANANDk0gXP86N 維尼
return result;8964 copyright protection418PENANAusoM3nXIdH 維尼
}8964 copyright protection418PENANAXc9zGx8cfH 維尼
}8964 copyright protection418PENANAlPsa0OwsBJ 維尼
3. Iterative Approach, Simulation:8964 copyright protection418PENANAJjMe3Gr1c2 維尼
class Solution {8964 copyright protection418PENANAHolZGIudrS 維尼
public int[] findBall(int[][] grid) {8964 copyright protection418PENANAwzG5Nlgthp 維尼
int result[] = new int[grid[0].length];8964 copyright protection418PENANAN8IPo6LMZX 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 protection418PENANAVvKZQafsOg 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection418PENANA78RA5LMA6l 維尼
int currentCol = col;8964 copyright protection418PENANAufSb9WtLt9 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection418PENANA1NgJK6SmeY 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection418PENANAyDofWrK29b 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection418PENANAva4jCaTQ0s 維尼
// stuck case 8964 copyright protection418PENANAwLd28fnxyQ 維尼
if (nextColumn < 0 ||8964 copyright protection418PENANAOYjHnKNpP4 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection418PENANAeR8MnCWCkq 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection418PENANAZSejx73ybe 維尼
result[col] = -1;8964 copyright protection418PENANAZ8u2elNhWN 維尼
break;8964 copyright protection418PENANAmACDlsdYHp 維尼
}8964 copyright protection418PENANAeCWZISZx3X 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 protection418PENANADVQMgMCFig 維尼
result[col] = nextColumn;8964 copyright protection418PENANAsr4Ie8KCS7 維尼
currentCol = nextColumn;8964 copyright protection418PENANAw8i93z4Rwh 維尼
}8964 copyright protection418PENANAZ3ltTq1gBi 維尼
}8964 copyright protection418PENANAmOrGvEiam9 維尼
return result;8964 copyright protection418PENANAxN7urW1Ss0 維尼
}8964 copyright protection418PENANA54ybbJl4H7 維尼
}8964 copyright protection418PENANAJHQ4FSgFgg 維尼
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