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 :



title-img 




                        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)


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