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Calculate cost of visiting all array elements in increasing order

  • Difficulty Level : Hard
  • Last Updated : 10 Jun, 2021

Given an array arr[] consisting of N integers, the task is to find the total cost of visiting all the array elements in ascending order, starting from 0, if the cost of a move from index i to the index j is the absolute difference between i and j.

Examples:

Input: arr[ ] = { 4, 3, 2, 5, 1 }
Output: 11
Explanation: 
Jump from index 0 to index 4. Cost = abs(4 – 0) = 4.
Jump from index 4 to index 2. Cost = abs(4 – 2) = 2.
Jump from index 2 to index1. Cost = abs(2 – 1) = 1.
Jump from index 1 to index 0. Cost = abs(1 – 0) = 1.
Jump from index 0 to index 3. Cost = abs(0 – 3) = 3.
Therefore, the total cost of visiting all array elements in ascending order = (4 + 2 + 1 + 1 + 3 = 11).

Input: arr[ ] = { 1, 2, 3 }
Output: 2

 

Approach: The idea is to use the concept of sorting of the vector of pairs. Follow the steps below to solve the problem:



  • Initialize a pair of vector<pair<int, int> >, say v, to store the pairs of elements and their respective positions.
  • Traverse the array arr[] and push the pair {arr[i], i} in the vector v.
  • Initialize two variables, say ans = 0 and last = 0, to store the total cost required and the index of the last visited element.
  • Sort the vector of pairs in ascending order.
  • Traverse the vector v and increment ans by abs(v[i].second – last). Update last as last = arr[i].second.
  • After completing the above steps, print the answer obtained as ans.

Below is the implementation of the above approach:

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate total
// cost of visiting array
// elements in increasing order
int calculateDistance(int arr[], int N)
{
    // Stores the pair of element
    // and their positions
    vector<pair<int, int> > v;
 
    // Traverse the array arr[]
    for (int i = 0; i < N; i++)
 
        // Push the pair {arr[i], i} in v
        v.push_back({ arr[i], i });
 
    // Sort the vector in ascending order.
    sort(v.begin(), v.end());
 
    // Stores the total cost
    int ans = 0;
 
    // Stores the index of last element visited
    int last = 0;
 
    // Traverse the vector v
    for (auto j : v) {
 
        // Increment ans
        ans += abs(j.second - last);
 
        // Assign
        last = j.second;
    }
 
    // Return ans
    return ans;
}
 
// Driver Code
int main()
{
    int arr[] = { 4, 3, 2, 5, 1 };
    int N = sizeof(arr) / sizeof(arr[0]);
    cout << calculateDistance(arr, N);
}

Java




// java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
 
class GFG {
 
  // Pair class
  static class Pair {
 
    int first;
    int second;
 
    Pair(int first, int second)
    {
      this.first = first;
      this.second = second;
    }
  }
 
  // Function to calculate total
  // cost of visiting array
  // elements in increasing order
  static int calculateDistance(int arr[], int N)
  {
    // Stores the pair of element
    // and their positions
    Pair v[] = new Pair[N];
 
    // Traverse the array arr[]
    for (int i = 0; i < N; i++)
 
      // Push the pair {arr[i], i} in v
      v[i] = new Pair(arr[i], i);
 
    // Sort the vector in ascending order.
    Arrays.sort(v, (p1, p2) -> {
      if (p1.first != p2.first)
        return p1.first - p2.first;
      return p1.second - p2.second;
    });
 
    // Stores the total cost
    int ans = 0;
 
    // Stores the index of last element visited
    int last = 0;
 
    // Traverse the vector v
    for (Pair j : v) {
 
      // Increment ans
      ans += Math.abs(j.second - last);
 
      // Assign
      last = j.second;
    }
 
    // Return ans
    return ans;
  }
 
  // Driver Code
  public static void main(String[] args)
  {
    int arr[] = { 4, 3, 2, 5, 1 };
    int N = arr.length;
 
    // Function call
    System.out.println(calculateDistance(arr, N));
  }
}
 
// This code is contributed by Kingash.

Python3




# Python3 implementation of the above approach
 
# Function to calculate total
# cost of visiting array
# elements in increasing order
def calculateDistance(arr, N):
 
    # Stores the pair of element
    # and their positions
    v = []
 
    # Traverse the array arr[]
    for i in range(N):
 
        # Push the pair {arr[i], i} in v
        v.append([arr[i], i])
 
    # Sort the vector in ascending order.
    v.sort()
 
    # Stores the total cost
    ans = 0
 
    # Stores the index of last element visited
    last = 0
 
    # Traverse the vector v
    for j in v:
 
        # Increment ans
        ans += abs(j[1] - last)
 
        # Assign
        last = j[1]
 
    # Return ans
    return ans
 
# Driver Code
if __name__ == "__main__" :
 
    arr = [ 4, 3, 2, 5, 1 ]
    N = len(arr)
     
    print(calculateDistance(arr, N))
     
# This code is contributed by AnkThon

Javascript




<script>
// Javascript implementation of the above approach
 
// Function to calculate total
// cost of visiting array
// elements in increasing order
function calculateDistance(arr, N)
{
    // Stores the pair of element
    // and their positions
    var v = [];
     
    // Traverse the array arr[]
    for (var i = 0; i < N; i++)
    {
        // Push the pair {arr[i], i} in v
        v.push([ arr[i], i ]);
    }
 
    // Sort the vector in ascending order.
    v = v.sort();
 
    // Stores the total cost
    var ans = 0;
 
    // Stores the index of last element visited
    var last = 0;
 
    // Traverse the vector v
    for (var i = 0; i < N; i++)
    {
        // Increment ans
        ans += Math.abs(v[i][1] - last);
 
        // Assign
        last = v[i][1];
    }
 
    // Return ans
    return ans;
}
 
// Driver Code
var arr = [ 4, 3, 2, 5, 1 ];
var N = arr.length;
document.write(calculateDistance(arr, N));
 
// This code is contributed by Shubhamsingh10
</script>
Output: 
11

 

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

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