Connect Ropes Problem Statement

Given a number of ropes denoted as 'N' and an array containing the lengths of these ropes, your task is to connect the ropes into one single rope. The cost to connect two ropes is determined by the sum of their lengths. Your goal is to find the minimum cost required to connect all the ropes.

Input:

The first line of input consists of a single integer T, indicating the number of test cases to handle. Each test case includes: - The first line specifies the number of ropes, N. - The second line provides the rope lengths as N space-separated integers.

Output:

For each test case, output a single integer representing the minimum cost to connect all the ropes. Print each result on a new line.

Example:

Input:

T = 1 N = 4 Lengths = [4, 3, 2, 6]

Output:

29

Constraints:

1

Question

Connect Ropes Problem Statement

Given a number of ropes denoted as 'N' and an array containing the lengths of these ropes, your task is to connect the ropes into one single rope. The cost to connect two ropes is determined by the sum of their lengths. Your goal is to find the minimum cost required to connect all the ropes.

Input:

The first line of input consists of a single integer T, indicating the number of test cases to handle.

Each test case includes:
- The first line specifies the number of ropes, N.
- The second line provides the rope lengths as N space-separated integers.

Output:

For each test case, output a single integer representing the minimum cost to connect all the ropes. Print each result on a new line.

Example:

Input:

T = 1 
N = 4 
Lengths = [4, 3, 2, 6]

Output:

Constraints:

1 <= T <= 10
1 <= N <= 10⁴
1 <= length[i] <= 10⁴
Time Limit: 1 second

Note:

You do not need to print anything as it is already handled. Implement the provided function to compute the necessary result.

Accepted Answer

The task is to find the minimum cost required to connect all the ropes by summing their lengths.

Iterate through the ropes and connect the two shortest ropes at each step to minimize cost
Use a priority queue to efficiently find the shortest ropes
Keep track of the total cost as you connect the ropes
Example: For input [4, 3, 2, 6], connect 2 and 3 (cost 5), then connect 4 and 5 (cost 9), then connect 9 and 6 (cost 15) for a total cost of 29

Accepted Answer

import java.util.Arrays;

import java.util.Scanner;

class Ropes{

static int mincost(int[] arr,int N){

int res1=0,res2=0,A=0;

A=N-1;

for (int i=0 ; i

if(i==0){

res1+=arr[i]*arr[i+1];

}

else{

res2+=arr[i]*(A);

A--;

}

return (res1+res2) ;

}

public static void main(String[] args){

int[] arr={4,5,3,8};

Arrays.sort(arr);

int N=arr.length;

System.out.println("minimum cost:"+mincost(arr,N));

}