Print modified array after performing queries to add (i – L + 1) to each element present in the range [L, R]

Given an array arr[] consisting of N 0s (1-based indexing) and another array query[], with each row of the form {L, R}, the task for each query (L, R) is to add a value of (i – L + 1) over the range [L, R] and print the array arr[] obtained after performing all the queries.

Examples:

Input: arr[] = {0, 0, 0}, query[][] = {{1, 3}, {2, 3}}
Output: 1 3 5
Explanation: Initially the array is {0, 0, 0}.
Query 1: Range of indices involved: [1, 3]. The value (i – 1 + 1) for each index i in the range is {1, 2, 3}. Adding these values modifies the array to {1, 2, 3}.
Query 2: Range of indices involved: [2, 3]. The value (i – 2 + 1) for each index i in the range is {0, 1, 2}. Adding these values modifies the array to {1, 3, 5}. 
Therefore, the modified array is {1, 3, 5}.

Input: arr[] = {0, 0, 0, 0, 0, 0, 0}, query[][] = {{1, 7}, {3, 6}, {4, 5}}
Output: 1 2 4 7 10 10 7

Naive Approach: The simplest approach to solve the given problem is to traverse the given array over the range [L, R] and add the value (i  –  L  +  1) to each element in the range for every query. After completing all the queries, print the modified array obtained arr[].

Below is the implementation of the above approach:

C++

// C++ program for the above approach

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

// Function to perform the given queries
// in the given empty array of size N
void updateQuery(vector<vector<int> > queries,
                 int N)
{
    // Initialize an array a[]
    vector<int> a(N + 1, 0);

    // Stores the size of the array
    int n = N + 1;

    int q = queries.size();

    // Traverse the queries
    for (int i = 0; i < q; i++) {

        // Starting index
        int l = queries[i][0];

        // Ending index
        int r = queries[i][1];

        // Increment each index from L to
        // R in a[] by (j - l + 1)
        for (int j = l; j <= r; j++) {
            a[j] += (j - l + 1);
        }
    }

    // Print the modified array
    for (int i = 1; i <= N; i++) {
        cout << a[i] << " ";
    }
}

// Driver Code
int main()
{
    int N = 7;
    vector<vector<int> > queries
        = { { 1, 7 }, { 3, 6 }, { 4, 5 } };

    // Function Call
    updateQuery(queries, N);

    return 0;
}

Java

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

class GFG{

// Function to perform the given queries
// in the given empty array of size N
static void updateQuery(int [][]queries, int N)
{

    // Initialize an array a[]
    ArrayList<Integer> a = new ArrayList<Integer>();
    for(int i = 0; i < N + 1; i++)
        a.add(0);

    // Stores the size of the array
    int q = 3;

    // Traverse the queries
    for(int i = 0; i < q; i++)
    {

        // Starting index
        int l = queries[i][0];

        // Ending index
        int r = queries[i][1];

        // Increment each index from L to
        // R in a[] by (j - l + 1)
        for(int j = l; j <= r; j++)
        {
            a.set(j, a.get(j)+(j - l + 1));
        }
    }

    // Print the modified array
    for(int i = 1; i < a.size(); i++)
    {
        System.out.print(a.get(i) + " ");
    }
}

// Driver code
public static void main(String[] args)
{
    int N = 7;
    int[][] queries =  { { 1, 7 },
                         { 3, 6 },
                         { 4, 5 } };

    // Function Call
    updateQuery(queries, N);
}
}

// This code is contributed by offbeat

Python3

# Python 3 program for the above approach

# Function to perform the given queries
# in the given empty array of size N
def updateQuery(queries, N):

    # Initialize an array a[]
    a = [0 for i in range(N + 1)]

    # Stores the size of the array
    n = N + 1

    q = len(queries)

    # Traverse the queries
    for i in range(q):

        # Starting index
        l = queries[i][0]

        # Ending index
        r = queries[i][1]

        # Increment each index from L to
        # R in a[] by (j - l + 1)
        for j in range(l, r + 1, 1):
            a[j] += (j - l + 1)

    # Print the modified array
    for i in range(1, N + 1, 1):
        print(a[i], end = " ")

# Driver Code
if __name__ == '__main__':
    N = 7
    queries =  [[1, 7],[3, 6],[4, 5]]

    # Function Call
    updateQuery(queries, N)

    # This code is contributed by ipg2016107.

C#

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

class GFG{

// Function to perform the given queries
// in the given empty array of size N
static void updateQuery(int [,]queries, int N)
{

    // Initialize an array a[]
    List<int> a = new List<int>();
    for(int i = 0; i < N + 1; i++)
        a.Add(0);

    // Stores the size of the array
    int q = 3;

    // Traverse the queries
    for(int i = 0; i < q; i++)
    {

        // Starting index
        int l = queries[i, 0];

        // Ending index
        int r = queries[i, 1];

        // Increment each index from L to
        // R in a[] by (j - l + 1)
        for(int j = l; j <= r; j++)
        {
            a[j] += (j - l + 1);
        }
    }

    // Print the modified array
    for(int i = 1; i < a.Count; i++)
    {
        Console.Write(a[i] + " ");
    }
}

// Driver Code
public static void Main()
{
    int N = 7;
    int[,] queries = new int[3, 2] { { 1, 7 },
                                     { 3, 6 },
                                     { 4, 5 } };

    // Function Call
    updateQuery(queries, N);
}
}

// This code is contributed by SURENDRA_GANGWAR

Javascript

<script>

// JavaScript program for the above approach


// Function to perform the given queries
// in the given empty array of size N
function updateQuery(queries, N)
{
    // Initialize an array a[]
    let a = new Array(N + 1).fill(0);

    // Stores the size of the array
    let n = N + 1;

    let q = queries.length;

    // Traverse the queries
    for (let i = 0; i < q; i++) {

        // Starting index
        let l = queries[i][0];

        // Ending index
        let r = queries[i][1];

        // Increment each index from L to
        // R in a[] by (j - l + 1)
        for (let j = l; j <= r; j++) {
            a[j] += (j - l + 1);
        }
    }

    // Print the modified array
    for (let i = 1; i <= N; i++) {
        document.write(a[i]," ");
    }
}

// Driver Code

let N = 7;
let queries = [ [ 1, 7 ], [ 3, 6 ], [ 4, 5 ] ];

// Function Call
updateQuery(queries, N);

// This code is contributed by
</script>

Output:

1 2 4 7 10 10 7

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

Efficient Approach: The above approach can be optimized by using the Prefix Sum. Follow the steps below to solve this problem:

• Initialize an array ans[] with all elements as 0 to stores the number of times the current index is affected by the queries.
• Initialize an array res[] with all elements as 0 to stores the value to be deleted after the end of a certain query range is reached.
• Traverse the given array of queries query[] and perform the following steps:
  • Add the 1 to ans[query[i][0]] and subtract 1 from ans[query[i][1] + 1].
  • Subtract (query[i][1] – query[i][0] + 1) from res[query[i][1] + 1].
• Find the prefix sum of the array ans[].
• Traverse the array res[] and update each element res[i] as res[i] + res[i – 1] + ans[i].
• After completing the above steps, print the array res[] as the modified array after performing the given queries.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

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

// Function to perform the given queries
// in the given empty array of size N
void updateQuery(vector<vector<int> > queries,
                 int N)
{
    // Stores the resultant array
    // and the difference array
    vector<int> ans(N + 2, 0),
        res(N + 2, 0);

    int q = queries.size();

    // Traverse the given queries
    for (int i = 0; i < q; i++) {

        // Starting index
        int l = queries[i][0];

        // Ending index
        int r = queries[i][1];

        // Increment l-th index by 1
        ans[l]++;

        // Decrease r-th index by 1
        ans[r + 1]--;

        // Decrease (r + 1)th index by
        // the length of each query
        res[r + 1] -= (r - l + 1);
    }

    // Find the prefix sum of ans[]
    for (int i = 1; i <= N; i++)
        ans[i] += ans[i - 1];

    // Find the final array
    for (int i = 1; i <= N; i++)
        res[i] += res[i - 1] + ans[i];

    // Printing the modified array
    for (int i = 1; i <= N; i++) {
        cout << res[i] << " ";
    }
    cout << "\n";
}

// Driver Code
int main()
{
    int N = 7;
    vector<vector<int> > queries
        = { { 1, 7 }, { 3, 6 }, { 4, 5 } };

    updateQuery(queries, N);

    return 0;
}

Java

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

  // Function to perform the given queries
  // in the given empty array of size N
  public static void
    updateQuery(ArrayList<ArrayList<Integer> > queries,
                int N)
  {

    // Stores the resultant array
    // and the difference array
    int ans[] = new int[N + 2];
    int res[] = new int[N + 2];

    for (int i = 0; i < N + 2; i++) {
      ans[i] = 0;
      res[i] = 0;
    }

    int q = queries.size();

    // Traverse the given queries
    for (int i = 0; i < q; i++) {

      // Starting index
      int l = queries.get(i).get(0);

      // Ending index
      int r = queries.get(i).get(1);

      // Increment l-th index by 1
      ans[l]++;

      // Decrease r-th index by 1
      ans[r + 1]--;

      // Decrease (r + 1)th index by
      // the length of each query
      res[r + 1] -= (r - l + 1);
    }

    // Find the prefix sum of ans[]
    for (int i = 1; i <= N; i++)
      ans[i] += ans[i - 1];

    // Find the final array
    for (int i = 1; i <= N; i++)
      res[i] += res[i - 1] + ans[i];

    // Printing the modified array
    for (int i = 1; i <= N; i++) {
      System.out.print(res[i] + " ");
    }
    System.out.println();
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 7;
    ArrayList<ArrayList<Integer> > queries
      = new ArrayList<ArrayList<Integer> >();
    ArrayList<Integer> temp1
      = new ArrayList<Integer>(Arrays.asList(1, 7));
    ArrayList<Integer> temp2
      = new ArrayList<Integer>(Arrays.asList(3, 6));
    ArrayList<Integer> temp3
      = new ArrayList<Integer>(Arrays.asList(4, 5));

    queries.add(temp1);
    queries.add(temp2);
    queries.add(temp3);

    updateQuery(queries, N);
  }
}

// This code is contributed by Taranpreet.

Python3

# Python 3 program for the above approach

# Function to perform the given queries
# in the given empty array of size N
def updateQuery(queries, N):

    # Stores the resultant array
    # and the difference array
    ans = [0] * (N + 2)
    res = [0] * (N + 2)

    q = len(queries)

    # Traverse the given queries
    for i in range(q):
        # Starting index
        l = queries[i][0]

        # Ending index
        r = queries[i][1]

        # Increment l-th index by 1
        ans[l] += 1

        # Decrease r-th index by 1
        ans[r + 1] -= 1

        # Decrease (r + 1)th index by
        # the length of each query
        res[r + 1] -= (r - l + 1)

    # Find the prefix sum of ans[]
    for i in range(1, N+1):
        ans[i] += ans[i - 1]

    # Find the final array
    for i in range(1, N+1):
        res[i] += res[i - 1] + ans[i]

    # Printing the modified array
    for i in range(1, N+1):
        print(res[i], end=" ")

    print("\n")

# Driver Code
if __name__ == '__main__':
    N = 7
    queries = [[1, 7], [3, 6], [4, 5]]

    updateQuery(queries, N)

 # This code is contributed by Anvesh Govind Saxena

C#

using System;
using System.Collections.Generic;

class GFG
{
  static void UpdateQuery(List<List<int>> queries, int N)
  {
    int[] ans = new int[N + 2];
    int[] res = new int[N + 2];

    for (int i = 0; i < N + 2; i++)
    {
      ans[i] = 0;
      res[i] = 0;
    }

    int q = queries.Count;

    for (int i = 0; i < q; i++)
    {
      int l = queries[i][0];
      int r = queries[i][1];
      ans[l]++;
      ans[r + 1]--;
      res[r + 1] -= (r - l + 1);
    }

    for (int i = 1; i <= N; i++)
      ans[i] += ans[i - 1];

    for (int i = 1; i <= N; i++)
      res[i] += res[i - 1] + ans[i];

    for (int i = 1; i <= N; i++)
    {
      Console.Write(res[i] + " ");
    }
    Console.WriteLine();
  }

  static void Main(string[] args)
  {
    int N = 7;
    List<List<int>> queries = new List<List<int>>();
    List<int> temp1 = new List<int>(new int[] { 1, 7 });
    List<int> temp2 = new List<int>(new int[] { 3, 6 });
    List<int> temp3 = new List<int>(new int[] { 4, 5 });

    queries.Add(temp1);
    queries.Add(temp2);
    queries.Add(temp3);

    UpdateQuery(queries, N);
  }
}

// This code is contributed by aadityaburujwale.

Javascript

// Javascript program for the above approach

// Function to perform the given queries
// in the given empty array of size N
function updateQuery(queries, N) {
    // Stores the resultant array
    // and the difference array
    let ans = Array(N + 2).fill(0),
        res = Array(N + 2).fill(0);

    let q = queries.length;

    // Traverse the given queries
    for (let i = 0; i < q; i++) {
        // Starting index
        let l = queries[i][0];

        // Ending index
        let r = queries[i][1];

        // Increment l-th index by 1
        ans[l]++;

        // Decrease r-th index by 1
        ans[r + 1]--;

        // Decrease (r + 1)th index by
        // the length of each query
        res[r + 1] -= r - l + 1;
    }

    // Find the prefix sum of ans[]
    for (let i = 1; i <= N; i++) ans[i] += ans[i - 1];

    // Find the final array
    for (let i = 1; i <= N; i++)
        res[i] += res[i - 1] + ans[i];

    // Printing the modified array
    console.log(res.slice(1, N + 1).join(" "));
}

// Testing the function
let N = 7;
let queries = [
    [1, 7],
    [3, 6],
    [4, 5],
];

updateQuery(queries, N);
// Contributed by prajwalkandekar123

Output

1 2 4 7 10 10 7 

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