1/11/2022 - 1706. Where Will the Ball Fall
No Plagiarism!F35rlDDKoH8VU1Yf6k7Nposted 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 protection452PENANAcBuBhYzxyz 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 protection452PENANAlKfseEJJyB 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 protection452PENANAJUbIIRMyWo 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 protection452PENANAWxKTbsffij 維尼
* [grid[0].length] = column number8964 copyright protection452PENANAO3uS4f0qZZ 維尼
A: 8964 copyright protection452PENANAZnF80aMXlQ 維尼
1. Depth First Search (DFS): 8964 copyright protection452PENANAvNH5Y0DOVy 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 protection452PENANAaPaUU0vzvY 維尼
*Using Recursive function8964 copyright protection452PENANAwSTTltXrre 維尼
class Solution {8964 copyright protection452PENANAMyCIBsK0Ib 維尼
public int[] findBall(int[][] grid) {8964 copyright protection452PENANAVY3BmuiNdX 維尼
// create new int[], for int[grid[0].length]8964 copyright protection452PENANApQsXpU6Gv4 維尼
int result[] = new int[grid[0].length];8964 copyright protection452PENANAZ0xP6TXbFY 維尼
// how many ball as well as how many row8964 copyright protection452PENANAqQy60qKSY3 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection452PENANA3xaZaMrIy1 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection452PENANAHb0cNQ54Gz 維尼
}8964 copyright protection452PENANAJCOq1yC39K 維尼
return result;8964 copyright protection452PENANAqJ2N5kqv0q 維尼
}8964 copyright protection452PENANAJAsEGhu4Gs 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection452PENANAdr5rAuUne2 維尼
// base case; ball reached the last row8964 copyright protection452PENANAwTeHPwMdin 維尼
if (row == grid.length)8964 copyright protection452PENANAKMTGxWMPWf 維尼
return col;8964 copyright protection452PENANAq1OMfDT8nL 維尼
int nextColumn = col + grid[row][col];8964 copyright protection452PENANAb7aKIXwgei 維尼
if (nextColumn < 0 ||8964 copyright protection452PENANAbxO2k1yP8T 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection452PENANAqIpzedB4fS 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection452PENANAkwB3JhQbXm 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection452PENANA8GWJGGqtPS 維尼
return -1;8964 copyright protection452PENANAqI2AHyaPYH 維尼
}8964 copyright protection452PENANAXkQtMsfKRC 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection452PENANAQAaegy7qYP 維尼
}8964 copyright protection452PENANAVxdOXnv2oP 維尼
}8964 copyright protection452PENANAeIOICJYlGR 維尼
2. Dynamic Programming Approach:8964 copyright protection452PENANAcbeAY0lqAa 維尼
class Solution {8964 copyright protection452PENANAHKM8AaU1Bo 維尼
public int[] findBall(int[][] grid) {8964 copyright protection452PENANA7OEONKR6pS 維尼
int result[] = new int[grid[0].length];8964 copyright protection452PENANAuCuuxrSQkI 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];456Please respect copyright.PENANAOVyWVd3dNR
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456Please respect copyright.PENANAiL6zndVu3g
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for (int row = grid.length; row >= 0; row--) {8964 copyright protection452PENANAob4N9JsFGN 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection452PENANAnAyWiyd4G9 維尼
if (row == grid.length) {8964 copyright protection452PENANA8Tlp4iIB28 維尼
// for the last row 456Please respect copyright.PENANAJH2EeBsAgD
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memo[row][col] = col;8964 copyright protection452PENANA3Iqhgc3ftB 維尼
continue;8964 copyright protection452PENANAGMnFfGesRl 維尼
}8964 copyright protection452PENANAkPi9ruPGx7 維尼
// for the remaining row.8964 copyright protection452PENANAIw4nuQ5bUI 維尼
int nextColumn = col + grid[row][col];8964 copyright protection452PENANASdSDAaHqn3 維尼
if (nextColumn < 0 ||8964 copyright protection452PENANAga1xYgylhp 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection452PENANAcomQbaa6mT 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection452PENANAeL9WKPiIuF 維尼
memo[row][col] = -1;8964 copyright protection452PENANAFFkIabmdtz 維尼
else8964 copyright protection452PENANA0bppz7EARo 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection452PENANAE2Gf0YKFx3 維尼
// reaching row 0, copy the values in all the column in the result array. 456Please respect copyright.PENANAfzXPjMWn3G
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if (row == 0) {8964 copyright protection452PENANAvjUnhfTbQa 維尼
result[col] = memo[row][col];8964 copyright protection452PENANAGs45Z6jLPL 維尼
}8964 copyright protection452PENANAyhsFdIff5y 維尼
}8964 copyright protection452PENANAWwZwGDgut2 維尼
}8964 copyright protection452PENANAlvJ4dEDl0T 維尼
return result;8964 copyright protection452PENANA6oVc2P2hcI 維尼
}8964 copyright protection452PENANAVXmGvixFZ8 維尼
}8964 copyright protection452PENANAmcLo3PIQAN 維尼
3. Iterative Approach, Simulation:8964 copyright protection452PENANA3i17r78DRJ 維尼
class Solution {8964 copyright protection452PENANAUituVudLHM 維尼
public int[] findBall(int[][] grid) {8964 copyright protection452PENANA3GEBW5kIw0 維尼
int result[] = new int[grid[0].length];8964 copyright protection452PENANAoFlHVXkUxB 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 protection452PENANApLyDozeYQw 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection452PENANA5SCgALMgvp 維尼
int currentCol = col;8964 copyright protection452PENANAjsWiiTfEbq 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection452PENANAWw3SQJtPo2 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection452PENANAC1JM5VWGdb 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection452PENANAzh3WNiaHeY 維尼
// stuck case 8964 copyright protection452PENANA3qqY66MXTE 維尼
if (nextColumn < 0 ||8964 copyright protection452PENANAw5Xme77FJN 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection452PENANAhqdMcPRXKm 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection452PENANAdCGwZu8gza 維尼
result[col] = -1;8964 copyright protection452PENANAbFBrAyKtR9 維尼
break;8964 copyright protection452PENANAzK3M8qW6HF 維尼
}8964 copyright protection452PENANAK5ItPQhFYI 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 protection452PENANA4aglZLsvfT 維尼
result[col] = nextColumn;8964 copyright protection452PENANASdXBuEdOJI 維尼
currentCol = nextColumn;8964 copyright protection452PENANACUp1jsqG2G 維尼
}8964 copyright protection452PENANAbZGvQ5UVzA 維尼
}8964 copyright protection452PENANA2bz4uR3180 維尼
return result;8964 copyright protection452PENANAgnTNVbUgt8 維尼
}8964 copyright protection452PENANAG24yT9lsqz 維尼
}8964 copyright protection452PENANAVW81kf5xMl 維尼
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