1/11/2022 - 1706. Where Will the Ball Fall
No Plagiarism!bLDg8FneHbA8fJp4kOqhposted 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 protection397PENANAWtrne7EB6x 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 protection397PENANAOLTbBN9I3f 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 protection397PENANADFWPXPUoK6 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 protection397PENANA1CdMDxuCgd 維尼
* [grid[0].length] = column number8964 copyright protection397PENANArIRoxTditI 維尼
A: 8964 copyright protection397PENANACP24pf0L5j 維尼
1. Depth First Search (DFS): 8964 copyright protection397PENANAgtUrtbNjUU 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 protection397PENANAJvwZycdY54 維尼
*Using Recursive function8964 copyright protection397PENANAP6HX9PB6GS 維尼
class Solution {8964 copyright protection397PENANANPOGypRz8Q 維尼
public int[] findBall(int[][] grid) {8964 copyright protection397PENANAnjNleyTMwR 維尼
// create new int[], for int[grid[0].length]8964 copyright protection397PENANAnuLYcLFG6o 維尼
int result[] = new int[grid[0].length];8964 copyright protection397PENANAMjShYCqEkO 維尼
// how many ball as well as how many row8964 copyright protection397PENANAUkkac9VPbg 維尼
for (int i = 0; i < grid[0].length; i++) {8964 copyright protection397PENANAYW6XIgHnkx 維尼
result[i] = findBallDropColumn(0, i, grid);8964 copyright protection397PENANA3ccwUX5xJG 維尼
}8964 copyright protection397PENANAZBaKHrb9nZ 維尼
return result;8964 copyright protection397PENANAgFJ61TkfPe 維尼
}8964 copyright protection397PENANAocEOW9iAYu 維尼
public int findBallDropColumn(int row, int col, int[][] grid) {8964 copyright protection397PENANAxsgK8JFVeJ 維尼
// base case; ball reached the last row8964 copyright protection397PENANA3hSgXzRkjU 維尼
if (row == grid.length)8964 copyright protection397PENANA5W3uuqkSYQ 維尼
return col;8964 copyright protection397PENANApVEjzhemgX 維尼
int nextColumn = col + grid[row][col];8964 copyright protection397PENANApkJOmyX0pm 維尼
if (nextColumn < 0 ||8964 copyright protection397PENANArMYXyYDrGy 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection397PENANAI22qCMHTur 維尼
// [1,1] & [-1,-1]drop, [1,-1] & [-1,1] stuck8964 copyright protection397PENANAC3SeZn41eM 維尼
grid[row][col] != grid[row][nextColumn]) {8964 copyright protection397PENANApYSd0NdAGO 維尼
return -1;8964 copyright protection397PENANA30OnEEW050 維尼
}8964 copyright protection397PENANAVCAikMjBXg 維尼
return findBallDropColumn(row + 1, nextColumn, grid);8964 copyright protection397PENANAQV9IGAiVE0 維尼
}8964 copyright protection397PENANAJGCTTsDRKh 維尼
}8964 copyright protection397PENANAt8SMlnC3MD 維尼
2. Dynamic Programming Approach:8964 copyright protection397PENANAbJ5S2u5JVU 維尼
class Solution {8964 copyright protection397PENANAjM8oz82KJV 維尼
public int[] findBall(int[][] grid) {8964 copyright protection397PENANAdxajBAu9KD 維尼
int result[] = new int[grid[0].length];8964 copyright protection397PENANAyc2SDbTypG 維尼
Integer memo[][] = new Integer[grid.length + 1][grid[0].length];401Please respect copyright.PENANApoouslCmHa
8964 copyright protection397PENANADfcDTcMFEy 維尼
401Please respect copyright.PENANAgCyKbNv70q
8964 copyright protection397PENANArBsdk5PBLz 維尼
for (int row = grid.length; row >= 0; row--) {8964 copyright protection397PENANAEbgDqjyoLo 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection397PENANA457MgPNxrv 維尼
if (row == grid.length) {8964 copyright protection397PENANAaalslfULvo 維尼
// for the last row 401Please respect copyright.PENANAeKSYnAhckd
8964 copyright protection397PENANAf15hs8xZwg 維尼
memo[row][col] = col;8964 copyright protection397PENANApnWumY2lal 維尼
continue;8964 copyright protection397PENANAkeePsdyaM5 維尼
}8964 copyright protection397PENANAsgvHzzXqBp 維尼
// for the remaining row.8964 copyright protection397PENANAtCA9XtiK4G 維尼
int nextColumn = col + grid[row][col];8964 copyright protection397PENANAaT19mwoT7t 維尼
if (nextColumn < 0 ||8964 copyright protection397PENANAOT0cEQNnvK 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection397PENANAAz0wKGsExJ 維尼
grid[row][col] != grid[row][nextColumn])8964 copyright protection397PENANA6A9f9P7GUt 維尼
memo[row][col] = -1;8964 copyright protection397PENANAl9q5Oyk4Uw 維尼
else8964 copyright protection397PENANARIyP1h9MEg 維尼
memo[row][col] = memo[row + 1][nextColumn];8964 copyright protection397PENANA4aNduDeujM 維尼
// reaching row 0, copy the values in all the column in the result array. 401Please respect copyright.PENANAVdHE6sPAwM
8964 copyright protection397PENANA509w9XRtZW 維尼
if (row == 0) {8964 copyright protection397PENANAWJhAb37QH0 維尼
result[col] = memo[row][col];8964 copyright protection397PENANAVqBGhYOKJr 維尼
}8964 copyright protection397PENANAr12iXZOHVu 維尼
}8964 copyright protection397PENANANm6pJXlEgf 維尼
}8964 copyright protection397PENANAo1Yn5Pei9d 維尼
return result;8964 copyright protection397PENANAHkKHPCeDEz 維尼
}8964 copyright protection397PENANAAksfuodRB0 維尼
}8964 copyright protection397PENANAM6cJWSzsSB 維尼
3. Iterative Approach, Simulation:8964 copyright protection397PENANAZpnWrK0xwL 維尼
class Solution {8964 copyright protection397PENANAlaxwG8ty7X 維尼
public int[] findBall(int[][] grid) {8964 copyright protection397PENANA15xsaP3HOU 維尼
int result[] = new int[grid[0].length];8964 copyright protection397PENANAckDD36lgGr 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 protection397PENANA94QaPo0vo4 維尼
for (int col = 0; col < grid[0].length; col++) {8964 copyright protection397PENANA0mZ22lbPwt 維尼
int currentCol = col;8964 copyright protection397PENANA8gy1tvvkuL 維尼
// 2. For every such ball, simulate its movement in every row ranging from the 0th to the nth row.8964 copyright protection397PENANASQBEBVApYX 維尼
for (int row = 0; row < grid.length; row++) {8964 copyright protection397PENANANvq09ujXYD 維尼
int nextColumn = currentCol + grid[row][currentCol];8964 copyright protection397PENANAKpONYi8Rob 維尼
// stuck case 8964 copyright protection397PENANAOJcsPkhqcS 維尼
if (nextColumn < 0 ||8964 copyright protection397PENANA43R3XCmzok 維尼
nextColumn > grid[0].length - 1 ||8964 copyright protection397PENANAewskQ8pvk4 維尼
grid[row][currentCol] != grid[row][nextColumn]) {8964 copyright protection397PENANARia6l5Iall 維尼
result[col] = -1;8964 copyright protection397PENANAGIQqtcwkYW 維尼
break;8964 copyright protection397PENANAYuqVIyh22D 維尼
}8964 copyright protection397PENANAObpoHRWTzB 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 protection397PENANAiN82RCikTb 維尼
result[col] = nextColumn;8964 copyright protection397PENANAowr5344Tzi 維尼
currentCol = nextColumn;8964 copyright protection397PENANAhymFbO3LQA 維尼
}8964 copyright protection397PENANA1EZqWdIeFc 維尼
}8964 copyright protection397PENANAVOC7tQwndq 維尼
return result;8964 copyright protection397PENANAxNdXHBJPzn 維尼
}8964 copyright protection397PENANAZxeBprSwkj 維尼
}8964 copyright protection397PENANAv3a5UQnc8T 維尼
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