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MinMax_Falling_Path_Sum.java
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MinMax_Falling_Path_Sum.java
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package Dynamic_Programming;
import com.sun.jdi.ArrayReference;
import java.util.Arrays;
public class MinMax_Falling_Path_Sum {
public static int minMaxHelper(int i, int j, int[][] grid, int[][] dp, int m){
// base case
if (j < 0 || j >= m) return (int)Math.pow(-10,9);
if (i == 0) return grid[i][j];
if (dp[i][j] != -1) return dp[i][j];
int up = grid[i][j] + minMaxHelper(i-1, j, grid, dp, m);
int left_up = grid[i][j] + minMaxHelper(i-1, j-1, grid, dp, m);
int right_up = grid[i][j] + minMaxHelper(i-1, j+1, grid, dp, m);
return dp[i][j] = Math.max(up, Math.max(left_up, right_up));
}
public static int minMax(int[][] grid){
int n = grid.length;
int m = grid[0].length;
int max = Integer.MIN_VALUE;
int[][] dp = new int[n][m];
for (int i=0; i<n; i++){
Arrays.fill(dp[i], -1);
}
// run loop for all the values of j
for (int j=0; j<m; j++){
int ans = minMaxHelper(n-1, j, grid, dp, m);
max = Math.max(ans, max);
}
display(dp);
return max;
}
public static void display(int[][] dp){
for (int i=0; i< dp.length; i++){
for (int j=0; j<dp[0].length; j++){
System.out.print(dp[i][j] + " ");
}
System.out.println();
}
}
public static int minMaxTab(int[][] grid){
int n = grid.length;
int m = grid[0].length;
int[][] dp = new int[n][m];
// create first row same
for (int j=0; j<m; j++){
dp[0][j] = grid[0][j];
}
// run loop for all the rows
for (int i=1; i<n; i++){
for (int j=0; j<m; j++){
int up = grid[i][j] + dp[i-1][j];
int left_up = grid[i][j];
if (j-1>=0){
left_up += dp[i-1][j-1];
}else{
left_up += Integer.MIN_VALUE;
}
int right_up = grid[i][j];
if (j+1<m){
right_up += dp[i-1][j+1];
}else{
right_up += Integer.MIN_VALUE;
}
dp[i][j] = Math.max(up, Math.max(left_up, right_up));
}
}
// check the last row to be max
int max = Integer.MIN_VALUE;
for (int j=0; j<dp[0].length; j++){
max = Math.max(max, dp[n-1][j]);
}
return max;
}
public static void main(String[] args) {
int[][] grid = {
{1,2,10,4},
{100,3,2,1},
{1,1,20,2},
{1,2,2,1}
};
int n = grid.length;
int m = grid[0].length;
System.out.println(minMax(grid));
System.out.println(minMaxTab(grid));
}
}