# Cluster Management - Google Top Interview Questions

### Problem Statement :

```You are given two lists of integers cores and tasks.
Each cores[i] represents the number of cores available in server i.
And each tasks[i] represents the number of cores needed to run that task.

Each task can be run in only one server but each server can run multiple tasks.
Return whether it's possible to run all the tasks with the given cores.

Constraints

n ≤ 15 where n is the length of cores

m ≤ 15 where m is the length of tasks

Example 1

Input

cores = [8, 10]

tasks = [2, 3, 3, 3, 7]

Output

True

Explanation

We can put tasks[0], tasks[1], and tasks[2] into cores[0] and the rest of the tasks into cores[1].

Example 2

Input

cores = [1, 3]

tasks = [2, 2]

Output

False

Explanation

There's no way to run the tasks on these servers.```

### Solution :

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

bool can(int idx, vector<int>& a, vector<int>& b) {
if (idx == -1) return true;
for (int& out : b) {
if (out >= a[idx]) {
out -= a[idx];
if (can(idx - 1, a, b)) return true;
out += a[idx];
}
}
return false;
}

bool solve(vector<int>& cores, vector<int>& tasks) {
sort(tasks.begin(), tasks.end());
return can((int)tasks.size() - 1, tasks, cores);
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[] cores, int[] tasks) {
if (cores.length == 0 && tasks.length != 0)
return false;
if (cores.length == 0 && tasks.length == 0)
return true;
return backtrack(cores, tasks, 0, 0);
}

public boolean backtrack(int[] cores, int[] tasks, int taskI, int coreI) {
if (cores[coreI] < 0)
return false;
if (taskI == tasks.length)
return true;

for (int i = 0; i < cores.length; i++) {
cores[i] -= tasks[taskI];
if (backtrack(cores, tasks, taskI + 1, i))
return true;
cores[i] += tasks[taskI];
}

return false;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, cores, tasks):

# If the task requiring most cores can't be done then we don't need
# to check remaining tasks and answer will be false.
tasks.sort(reverse=True)

def canRun(task):
if task == len(tasks):  # all tasks done
return True

required_cores = tasks[task]
for i, available_cores in enumerate(cores):
# if current server can fulfill the current task requirement
# then check for next task
if available_cores >= required_cores:
cores[i] -= required_cores
if canRun(task + 1):
return True
cores[i] += required_cores

return False

return canRun(0)```
```

## Equal Stacks

ou have three stacks of cylinders where each cylinder has the same diameter, but they may vary in height. You can change the height of a stack by removing and discarding its topmost cylinder any number of times. Find the maximum possible height of the stacks such that all of the stacks are exactly the same height. This means you must remove zero or more cylinders from the top of zero or more of

## Game of Two Stacks

Alexa has two stacks of non-negative integers, stack A = [a0, a1, . . . , an-1 ] and stack B = [b0, b1, . . . , b m-1] where index 0 denotes the top of the stack. Alexa challenges Nick to play the following game: In each move, Nick can remove one integer from the top of either stack A or stack B. Nick keeps a running sum of the integers he removes from the two stacks. Nick is disqualified f

## Largest Rectangle

Skyline Real Estate Developers is planning to demolish a number of old, unoccupied buildings and construct a shopping mall in their place. Your task is to find the largest solid area in which the mall can be constructed. There are a number of buildings in a certain two-dimensional landscape. Each building has a height, given by . If you join adjacent buildings, they will form a solid rectangle

## 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