# Trail to Minimize Effort - Google Top Interview Questions

### Problem Statement :

```You are given a two-dimensional list of integers matrix where element represents the height of a hill.

You are currently on the top left cell and want to go to the bottom right cell.

In each move, you can go up, down, left, or right.

A path's cost is defined to the largest absolute difference of heights between any two consecutive cells in the path.

Return the minimum cost of any path.

Constraints

1 ≤ n, m ≤ 250 where n and m are the number of rows and columns in matrix

Example 1
\
Input

matrix = [

[1, 5, 3],

[2, 4, 3],

[3, 5, 3]

]

Output

2

Explanation

We can take the following path [1, 2, 4, 5, 3]. The largest absolute difference of heights between any
two consecutive cells is between 2 and 4.```

### Solution :

```                        ```Solution in C++ :

int solve(vector<vector<int>>& matrix) {
int n = matrix.size(), m = matrix[0].size();
vector<int> dir{0, -1, 0, 1, 0};
vector<vector<int>> dist(n, vector<int>(m, INT_MAX));
set<pair<int, pair<int, int>>> s;

// setting the base case
dist[0][0] = 0;
s.insert({0, {0, 0}});

while (!s.empty()) {
auto [distance, cord] = *s.begin();
auto [xcord, ycord] = cord;
s.erase(s.begin());
for (int k = 0; k < 4; k++) {
int x = xcord + dir[k];
int y = ycord + dir[k + 1];
if (x >= 0 and x < n and y >= 0 and y < m) {
int maxd = max(distance, abs(matrix[x][y] - matrix[xcord][ycord]));
if (dist[x][y] > maxd) {
if (s.find({dist[x][y], {x, y}}) != s.end()) {
s.erase(s.find({dist[x][y], {x, y}}));
}
dist[x][y] = maxd;
s.insert({dist[x][y], {x, y}});
}
}
}
}
return dist[n - 1][m - 1];
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
static int M;
public int solve(int[][] matrix) {
int N = matrix.length;
M = matrix[0].length;
DisjointSetUnion dsu = new DisjointSetUnion(N * M);
ArrayList<Edge> edges = new ArrayList<Edge>();
for (int i = 0; i < N; i++) {
for (int j = 0; j < M; j++) {
if (i < N - 1)
edges.add(new Edge(i, j, 'D', Math.abs(matrix[i][j] - matrix[i + 1][j])));
if (j < M - 1)
edges.add(new Edge(i, j, 'R', Math.abs(matrix[i][j] - matrix[i][j + 1])));
}
}
Collections.sort(edges);

for (Edge e : edges) {
dsu.connect(e.a, e.b);
if (dsu.connected(0, N * M - 1))
return e.w;
}
return 0;
}

static class Edge implements Comparable<Edge> {
int a;
int b;
int w;
public Edge(int i, int j, char d, int w) {
a = i * M + j;
if (d == 'D')
b = (i + 1) * M + j;
else
b = i * M + (j + 1);
this.w = w;
}

public int compareTo(Edge e) {
return w - e.w;
}
}

static class DisjointSetUnion {
public int[] parent;
public int[] weight;
public int count;

public DisjointSetUnion(int N) {
count = N;
parent = new int[N];
for (int i = 0; i < N; i++) parent[i] = i;
weight = new int[N];
Arrays.fill(weight, 1);
}

//"find"
public int root(int p) {
if (p == parent[p])
return p;
return parent[p] = root(parent[p]);
}

//"union"
public void connect(int p, int q) {
p = root(p);
q = root(q);
if (p == q)
return;
if (weight[p] < weight[q]) {
parent[p] = q;
weight[q] += weight[p];
} else {
parent[q] = p;
weight[p] += weight[q];
}
count--;
}

public boolean connected(int p, int q) {
return root(p) == root(q);
}
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, A):
R, C = len(A), len(A[0])
DIRS = [[1, 0], [0, 1], [-1, 0], [0, -1]]

def bfs(cost):
q = [[0, 0]]
seen = set(tuple([0, 0]))
while q:
i, j = q.pop()
if i == R - 1 and j == C - 1:
return True
for di, dj in DIRS:
ni, nj = di + i, dj + j
if (
0 <= ni < R
and 0 <= nj < C
and abs(A[ni][nj] - A[i][j]) <= cost
and tuple([ni, nj]) not in seen
):
q.append([ni, nj])
return False

l = 0
r = max([max(x) for x in A])

while l < r:
m = l + r >> 1
if bfs(m):
r = m
else:
l = m + 1
return l```
```

## Simple Text Editor

In this challenge, you must implement a simple text editor. Initially, your editor contains an empty string, S. You must perform Q operations of the following 4 types: 1. append(W) - Append W string to the end of S. 2 . delete( k ) - Delete the last k characters of S. 3 .print( k ) - Print the kth character of S. 4 . undo( ) - Undo the last (not previously undone) operation of type 1 or 2,

## Poisonous Plants

There are a number of plants in a garden. Each of the plants has been treated with some amount of pesticide. After each day, if any plant has more pesticide than the plant on its left, being weaker than the left one, it dies. You are given the initial values of the pesticide in each of the plants. Determine the number of days after which no plant dies, i.e. the time after which there is no plan

## AND xor OR

Given an array of distinct elements. Let and be the smallest and the next smallest element in the interval where . . where , are the bitwise operators , and respectively. Your task is to find the maximum possible value of . Input Format First line contains integer N. Second line contains N integers, representing elements of the array A[] . Output Format Print the value

## Waiter

You are a waiter at a party. There is a pile of numbered plates. Create an empty answers array. At each iteration, i, remove each plate from the top of the stack in order. Determine if the number on the plate is evenly divisible ith the prime number. If it is, stack it in pile Bi. Otherwise, stack it in stack Ai. Store the values Bi in from top to bottom in answers. In the next iteration, do the

## Queue using Two Stacks

A queue is an abstract data type that maintains the order in which elements were added to it, allowing the oldest elements to be removed from the front and new elements to be added to the rear. This is called a First-In-First-Out (FIFO) data structure because the first element added to the queue (i.e., the one that has been waiting the longest) is always the first one to be removed. A basic que

## Castle on the Grid

You are given a square grid with some cells open (.) and some blocked (X). Your playing piece can move along any row or column until it reaches the edge of the grid or a blocked cell. Given a grid, a start and a goal, determine the minmum number of moves to get to the goal. Function Description Complete the minimumMoves function in the editor. minimumMoves has the following parameter(s):