Print modified array after performing queries to add (i - L + 1) to each element present in the range [L, R]
Last Updated :
23 Jul, 2025
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 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
# 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# 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
<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>
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 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.
# 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
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 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
Time Complexity: O(N)
Auxiliary Space: O(N)
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