1/11/2022 - 1706. Where Will the Ball Fall
No Plagiarism!9Vl5aousDqW4Fn9VOXKPposted 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 protection440PENANA5TtdWt6fWw 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 protection440PENANAfeTbC7djrk 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 protection440PENANATxyuxaF5tf 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 protection440PENANAKRlBKP6qZf 維尼
* [grid[0].length] = column number8964 copyright protection440PENANAeb5zyfwML6 維尼
A: 8964 copyright protection440PENANAPzkAb9z4HX 維尼
1. Depth First Search (DFS): 8964 copyright protection440PENANADOtWOqhy5z 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 protection440PENANACwLFvyyIZ4 維尼
*Using Recursive function8964 copyright protection440PENANA42N8UYkko1 維尼
class Solution {8964 copyright protection440PENANAf4PnSobTfL 維尼
public int[] findBall(int[][] grid) {8964 copyright protection440PENANAsuBgctE7r8 維尼
// create new int[], for int[grid[0].length]8964 copyright protection440PENANATCBjiZzmBm 維尼
int result[] = new int[grid[0].length];8964 copyright protection440PENANAnxsplbfptr 維尼
// how many ball as well as how many row8964 copyright protection440PENANAgC2b4NbSid 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection440PENANAeYzd9uh7Nw 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection440PENANAki6S0ZjP2Z 維尼
}8964 copyright protection440PENANAqkWhMxyBz7 維尼
return result;8964 copyright protection440PENANAGts0KZw53C 維尼
}8964 copyright protection440PENANAkNzZegP7AA 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection440PENANAexjYSCsl8D 維尼
// base case; ball reached the last row8964 copyright protection440PENANAfMLgKirGxO 維尼
if (row == grid.length)8964 copyright protection440PENANAc5639tbQp7 維尼
return col;8964 copyright protection440PENANAo6Ikb28l2s 維尼
int nextColumn = col + grid[row][col];8964 copyright protection440PENANAGQiumtd7ca 維尼
if (nextColumn < 0 ||8964 copyright protection440PENANAmR1jsNILlF 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection440PENANAafyG4FUoR4 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection440PENANA1KQLJ7lMd9 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection440PENANAN2qywR1eyi 維尼
return -1;8964 copyright protection440PENANApEpLVdymU7 維尼
}8964 copyright protection440PENANA8PIGjni3e8 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection440PENANAIngZJWLLf4 維尼
}8964 copyright protection440PENANAk6KpnO06b3 維尼
}8964 copyright protection440PENANANrBF0nT8Wj 維尼
2. Dynamic Programming Approach:8964 copyright protection440PENANA35mOTg4h7e 維尼
class Solution {8964 copyright protection440PENANAuEpO0e3BC2 維尼
public int[] findBall(int[][] grid) {8964 copyright protection440PENANAIUa9wql5cW 維尼
int result[] = new int[grid[0].length];8964 copyright protection440PENANAkQtc1SFP8J 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];444Please respect copyright.PENANAaUF8I6HhT7
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444Please respect copyright.PENANA1UO5JSgYke
8964 copyright protection440PENANABAoc7irNGS 維尼
for (int row = grid.length; row >= 0; row--) {8964 copyright protection440PENANAt1G59WKVSl 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection440PENANAd3CKZmg2kE 維尼
if (row == grid.length) {8964 copyright protection440PENANA6QHnJMVnSI 維尼
// for the last row 444Please respect copyright.PENANAwAhhh2cDNx
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memo[row][col] = col;8964 copyright protection440PENANAzvCaWIN4rq 維尼
continue;8964 copyright protection440PENANAotCPhdKoU4 維尼
}8964 copyright protection440PENANABT8HdPlcyL 維尼
// for the remaining row.8964 copyright protection440PENANAdjoSzbzywR 維尼
int nextColumn = col + grid[row][col];8964 copyright protection440PENANAXOYES4yuiV 維尼
if (nextColumn < 0 ||8964 copyright protection440PENANAPHUD7vN9xx 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection440PENANAAGICzneyqi 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection440PENANA1dHoSNaX67 維尼
memo[row][col] = -1;8964 copyright protection440PENANAJFNKksXBjn 維尼
else8964 copyright protection440PENANAZSLfUHO3wG 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection440PENANAqYlROelWtX 維尼
// reaching row 0, copy the values in all the column in the result array. 444Please respect copyright.PENANAxOx0g4kjOa
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if (row == 0) {8964 copyright protection440PENANAVwrxpXCKH4 維尼
result[col] = memo[row][col];8964 copyright protection440PENANA7GgCeBsuMK 維尼
}8964 copyright protection440PENANAdiA5ipshQ2 維尼
}8964 copyright protection440PENANANOSioez28P 維尼
}8964 copyright protection440PENANAdlPceIbIYB 維尼
return result;8964 copyright protection440PENANAnnoDGoW1kh 維尼
}8964 copyright protection440PENANAXzGlIIvafQ 維尼
}8964 copyright protection440PENANAaGBgcCk69l 維尼
3. Iterative Approach, Simulation:8964 copyright protection440PENANAM9CJmugdTa 維尼
class Solution {8964 copyright protection440PENANAvLXi9djVeQ 維尼
public int[] findBall(int[][] grid) {8964 copyright protection440PENANAcunSDLQxr9 維尼
int result[] = new int[grid[0].length];8964 copyright protection440PENANAx3gqlkSsNY 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 protection440PENANACIKJDBfH4M 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection440PENANAGFOA3nhy2L 維尼
int currentCol = col;8964 copyright protection440PENANADR9bAc3snm 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection440PENANAmt5GycBPpP 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection440PENANARbmHxXH0z8 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection440PENANAvVFTQZcewW 維尼
// stuck case 8964 copyright protection440PENANAsm7CZTjtT7 維尼
if (nextColumn < 0 ||8964 copyright protection440PENANAEsB9m3GXjP 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection440PENANAXCZRIOPRaS 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection440PENANAyUvU7odgF0 維尼
result[col] = -1;8964 copyright protection440PENANAXhbbHef47H 維尼
break;8964 copyright protection440PENANAx9TK1oBtLI 維尼
}8964 copyright protection440PENANAXQlSunmWB6 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 protection440PENANAGOZNCNZSay 維尼
result[col] = nextColumn;8964 copyright protection440PENANAt8nOYYoT76 維尼
currentCol = nextColumn;8964 copyright protection440PENANAt9fBDpFOlq 維尼
}8964 copyright protection440PENANAWXPks6r9y2 維尼
}8964 copyright protection440PENANA1fuWZtFwrw 維尼
return result;8964 copyright protection440PENANA3IwR6Du0gh 維尼
}8964 copyright protection440PENANAwQPbi16N69 維尼
}8964 copyright protection440PENANAIvlftNJXBz 維尼
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