Maximize ropes of consecutive length possible by connecting given ropes

Given an array A[ ] of size N where each array element represents the length of a rope, the task is to find the number of ropes of consecutive length that can be created by connecting given ropes starting from length 1.

Examples :

Input: N = 5, A[ ] = {1, 2, 7, 1, 1}

Output: 5 
Explanation:
Length | Ropes 
    1 | [1] 
    2 | [1, 1] 
    3 | [1, 2] 
    4 | [1, 2, 1] 
    5 | [1, 2, 1, 1]

Input N = 5, A = {1, 3, 2, 4, 2} 
Output: 12 

Approach: This problem can be solved by using the fact that if we are able to create ropes of range [1, K] lengths and there is a rope left of length L such that (L <= K+1) then we can create ropes of range [1, K+L] by adding L length rope to each rope of the range [max(1, K-L+1), K]. So to solve the problem, first, sort the array and then traverse the array and check each time if the current element is less than or equal to the maximum consecutive length we have obtained + 1. If found to be true, add that element to maximum consecutive length. Otherwise, return the answer.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find maximized count
// of ropes of consecutive length
int maxConsecutiveRopes(int ropes[], int N)
{
    // Stores the maximum count
    // of ropes of consecutive length
    int curSize = 0;

    // Sort the ropes by their length
    sort(ropes, ropes + N);

    // Traverse the array
    for (int i = 0; i < N; i++) {

        // If size of the current rope is less
        // than or equal to current maximum
        // possible size + 1, update the
        // range to curSize + ropes[i]

        if (ropes[i] <= curSize + 1) {
            curSize = curSize + ropes[i];
        }

        // If a rope of size (curSize + 1)
        // cannot be obtained
        else
            break;
    }
    return curSize;
}

// Driver Code
int main()
{
    // Input
    int N = 5;
    int ropes[] = { 1, 2, 7, 1, 1 };

    // Function Call
    cout << maxConsecutiveRopes(ropes, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG {

    // Function to find maximized count
    // of ropes of consecutive length
    static int maxConsecutiveRope(int ropes[], int N)
    {
        // Stores the maximum count
        // of ropes of consecutive length
        int curSize = 0;

        // Sort the ropes by their length
        Arrays.sort(ropes);

        // Traverse the array
        for (int i = 0; i < N; i++) {

            // If size of the current rope is less
            // than or equal to current maximum
            // possible size + 1, update the
            // range to curSize + ropes[i]

            if (ropes[i] <= curSize + 1) {
                curSize = curSize + ropes[i];
            }

            // If a rope of size (curSize + 1)
            // cannot be obtained
            else
                break;
        }
        return curSize;
    }

    // Driver code
    public static void main(String[] args)
    {
        // Input
        int N = 5;
        int ropes[] = { 1, 2, 7, 1, 1 };

        // Function Call
        System.out.println(
            maxConsecutiveRope(ropes, N));
    }
}

Python3

# Python3 program for the above approach

# Function to find maximized count
# of ropes of consecutive length
def maxConsecutiveRopes(ropes, N):

    # Stores the maximum count
    # of ropes of consecutive length
    curSize = 0

    # Sort the ropes by their length
    ropes = sorted(ropes)

    # Traverse the array
    for i in range(N):

        # If size of the current rope is less
        # than or equal to current maximum
        # possible size + 1, update the
        # range to curSize + ropes[i]
        if (ropes[i] <= curSize + 1):
            curSize = curSize + ropes[i]

        # If a rope of size (curSize + 1)
        # cannot be obtained
        else:
            break

    return curSize

# Driver Code
if __name__ == '__main__':

    # Input
    N = 5
    ropes = [ 1, 2, 7, 1, 1 ]

    # Function Call
    print (maxConsecutiveRopes(ropes, N))

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to find maximized count
// of ropes of consecutive length
static int maxConsecutiveRope(int[] ropes, int N)
{

    // Stores the maximum count
    // of ropes of consecutive length
    int curSize = 0;

    // Sort the ropes by their length
    Array.Sort(ropes);

    // Traverse the array
    for(int i = 0; i < N; i++)
    {

        // If size of the current rope is less
        // than or equal to current maximum
        // possible size + 1, update the
        // range to curSize + ropes[i]
        if (ropes[i] <= curSize + 1)
        {
            curSize = curSize + ropes[i];
        }

        // If a rope of size (curSize + 1)
        // cannot be obtained
        else
            break;
    }
    return curSize;
}

// Driver code
public static void Main ()
{

    // Input
    int N = 5;
    int[] ropes = { 1, 2, 7, 1, 1 };

    // Function Call
    Console.WriteLine(maxConsecutiveRope(ropes, N));
}
}

// This code is contributed by souravghosh0416

Javascript

<script>
// Javascript program for the above approach

// Function to find maximized count
// of ropes of consecutive length
function maxConsecutiveRopes(ropes, N)
{
    // Stores the maximum count
    // of ropes of consecutive length
    let curSize = 0;

    // Sort the ropes by their length
    ropes.sort((a, b) => a - b)

    // Traverse the array
    for (let i = 0; i < N; i++) {

        // If size of the current rope is less
        // than or equal to current maximum
        // possible size + 1, update the
        // range to curSize + ropes[i]

        if (ropes[i] <= curSize + 1) {
            curSize = curSize + ropes[i];
        }

        // If a rope of size (curSize + 1)
        // cannot be obtained
        else
            break;
    }
    return curSize;
}

// Driver Code

// Input
let N = 5;
let ropes = [ 1, 2, 7, 1, 1 ];

// Function Call
document.write(maxConsecutiveRopes(ropes, N));

// This contributed by _saurabh_jaiswal
</script>

Output:

5

Time Complexity: O(N)
Auxiliary Space: O(1)