AddedCherryPickupProblemSolution

Flipkart/Q3-Cherry_Pickup.cpp

@@ -0,0 +1,103 @@
+You are given an n x n grid representing a field of cherries, each cell is one of three possible integers.
+•	   0 means the cell is empty, so you can pass through,
+•	   1 means the cell contains a cherry that you can pick up and pass through, or
+•	   -1 means the cell contains a thorn that blocks your way.
+Return the maximum number of cherries you can collect by following the rules below:
+•	Starting at the position (0, 0) and reaching (n - 1, n - 1) by moving right or down through valid path cells (cells with value 0 or 1).
+•	 After reaching (n - 1, n - 1), returning to (0, 0) by moving left or up through valid path cells.
+•	When passing through a path cell containing a cherry, you pick it up, and the cell becomes an empty cell 0.
+•	If there is no valid path between (0, 0) and (n - 1, n - 1), then no cherries can be collected.
+
+
+Example 1:
+Input: grid = [[0,1,-1],[1,0,-1],[1,1,1]]
+Output: 5
+Explanation: The player started at (0, 0) and went down, down, right right to reach (2, 2).
+4 cherries were picked up during this single trip, and the matrix becomes [[0,1,-1],[0,0,-1],[0,0,0]].
+Then, the player went left, up, up, left to return home, picking up one more cherry.
+The total number of cherries picked up is 5, and this is the maximum possible.
+
+
+Example 2:
+Input: grid = [[1,1,-1],[1,-1,1],[-1,1,1]]
+Output: 0
+
+
+Constraints:
+n == grid.length
+n == grid[i].length
+1 <= n <= 50
+grid[i][j] is -1, 0, or 1.
+grid[0][0] != -1
+grid[n - 1][n - 1] != -1
+
+
+     **************************************
+     **************************************
+SOLUTION:
+
+***Algorithm:-
+Step1: Storing maximum no. of cherries collected in each cell for two paths: down-right and up-left.
+Step2: Checking if the starting cell (0, 0) and the ending cell (n - 1, n - 1) are not thorns (-1). If either of them is a thorn, return 0.
+Step3: Initializing setting dp[0][0][0] the starting cell, which can be either 0 or 1.
+Step4: Using a loop to iterate over k from 1 to 2n – 2. Using nested loops to iterate over possible cell positions (i, j) within the grid. Ensuring that i + j equals k.
+Step5: Checking if the current cell (i, k - i) or (j, k - j) contains a thorn (-1). If yes skip this cell.
+Step6: Calculating the number of cherries that can be collected at this cell. If i=j, both paths meet at this cell, and the cherry is counted only once.
+Step7: Initialize max_val=0.
+Step8: Using nested loops to iterate over possible previous cell positions (pi, pj). We can only move left or up (pi, pj could be -1) or stay at the same cell (pi, pj could be 0).
+Step9: Checking if previous cell positions (i + pi, j + pj) are within the grid bounds, and update max_val to the maximum cherries collected.
+Step10: Update dp[k % 2][i][j] with the maximum cherries collected at the current cell, max_val + cherries.
+Step11: After the loop, return the maximum cherries collected at the starting and ending cell (i.e., dp[(2 * n - 2) % 2][n - 1][n - 1]).
+
+***Code:-
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+
+using namespace std;
+
+int cherryPickup(vector<vector<int>>& grid) {
+    int n = grid.size();
+    if (grid[0][0] == -1 || grid[n - 1][n - 1] == -1) {
+        return 0;
+    }
+
+    vector<vector<vector<int>> dp(2, vector<vector<int>>(n, vector<int>(n, 0)));
+    dp[0][0][0] = grid[0][0];
+
+    for (int k = 1; k < 2 * n - 1; k++) {
+        for (int i = min(n - 1, k); i >= max(0, k - n + 1); i--) {
+            for (int j = min(n - 1, k); j >= max(0, k - n + 1); j--) {
+                if (grid[i][k - i] == -1 || grid[j][k - j] == -1) {
+                    continue;
+                }
+
+                int cherries = (i == j) ? grid[i][k - i] : grid[i][k - i] + grid[j][k - j];
+                int max_val = 0;
+
+                for (int pi : {-1, 0, -1}) {
+                    for (int pj : {-1, 0, -1}) {
+                        if (i + pi >= 0 && j + pj >= 0) {
+                            max_val = max(max_val, dp[(k - 1) % 2][i + pi][j + pj]);
+                        }
+                    }
+                }
+
+                dp[k % 2][i][j] = max_val + cherries;
+            }
+        }
+    }
+
+    return max(0, dp[(2 * n - 2) % 2][n - 1][n - 1]);
+}
+
+int main() {
+    vector<vector<int>> grid1 = {{0, 1, -1}, {1, 0, -1}, {1, 1, 1}};
+    cout << cherryPickup(grid1) << endl;  // Output: 5
+
+    vector<vector<int>> grid2 = {{1, 1, -1}, {1, -1, 1}, {-1, 1, 1}};
+    cout << cherryPickup(grid2) << endl;  // Output: 0
+
+    return 0;
+}