Find the Initial Array from given array after range sum queries
Last Updated :
31 Mar, 2023
Given an array arr[] which is the resultant array when a number of queries are performed on the original array. The queries are of the form [l, r, x] where l is the starting index in the array, r is the ending index in the array and x is the integer elements that have to be added to all the elements in the index range [l, r]. The task is to find the original array.
Examples:
Input: arr[] = {5, 7, 8}, l[] = {0}, r[] = {1}, x[] = {2}
Output: 3 5 8
If query [0, 1, 2] is performed on the array {3, 5, 8}
The resultant array will be {5, 7, 8}
Input: arr[] = {20, 30, 20, 70, 100},
l[] = {0, 1, 3},
r[] = {2, 4, 4},
x[] = {10, 20, 30}
Output: 10 0 -10 20 50
Naive Approach: For each range starting from l to r subtract the corresponding x to get the initial array.
Algorithm
1)Define the initial array arr and its size n.
2)Define the ranges l, r, and the values x for decrementing the elements in those ranges.
3)Define the number of queries q.
4)For each query j from 0 to q-1:
For each index i from l[j] to r[j], decrement the corresponding element in the array arr by the value x[j].
5)Print the elements of the final array arr.
Below is the implementation of the approach:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Utility function to print the contents of an array
void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++) {
cout << arr[i] << " ";
}
}
// Function to find the original array
void findOrgArr(int arr[], int l[], int r[], int x[],
int n, int q)
{
for (int j = 0; j < q; j++) {
for (int i = l[j]; i <= r[j]; i++) {
// Decrement elements between
// l[j] and r[j] by x[j]
arr[i] = arr[i] - x[j];
}
}
printArr(arr, n);
}
// Driver code
int main()
{
// Final array
int arr[] = { 20, 30, 20, 70, 100 };
// Size of the array
int n = sizeof(arr) / sizeof(arr[0]);
// Queries
int l[] = { 0, 1, 3 };
int r[] = { 2, 4, 4 };
int x[] = { 10, 20, 30 };
// Number of queries
int q = sizeof(l) / sizeof(l[0]);
findOrgArr(arr, l, r, x, n, q);
return 0;
}
// Java implementation of the approach
import java.util.*;
class GFG
{
// Utility function to print the contents of an array
static void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++) {
System.out.print(arr[i]+" ");
}
}
// Function to find the original array
static void findOrgArr(int arr[], int l[], int r[], int x[],
int n, int q)
{
for (int j = 0; j < q; j++) {
for (int i = l[j]; i <= r[j]; i++) {
// Decrement elements between
// l[j] and r[j] by x[j]
arr[i] = arr[i] - x[j];
}
}
printArr(arr, n);
}
// Driver code
public static void main(String args[])
{
// Final array
int arr[] = { 20, 30, 20, 70, 100 };
// Size of the array
int n = arr.length;
// Queries
int l[] = { 0, 1, 3 };
int r[] = { 2, 4, 4 };
int x[] = { 10, 20, 30 };
// Number of queries
int q = l.length;
findOrgArr(arr, l, r, x, n, q);
}
}
// This code is contributed by
// Shashank_Sharma
# Python3 implementation of the approach
import math as mt
# Utility function to print the
# contents of an array
def printArr(arr, n):
for i in range(n):
print(arr[i], end = " ")
# Function to find the original array
def findOrgArr(arr, l, r, x, n, q):
for j in range(q):
for i in range(l[j], r[j] + 1):
# Decrement elements between
# l[j] and r[j] by x[j]
arr[i] = arr[i] - x[j]
printArr(arr, n)
# Driver code
# Final array
arr = [20, 30, 20, 70, 100]
# Size of the array
n = len(arr)
# Queries
l = [0, 1, 3]
r = [ 2, 4, 4]
x = [ 10, 20, 30 ]
# Number of queries
q = len(l)
findOrgArr(arr, l, r, x, n, q)
# This code is contributed by
# mohit kumar 29
// C# implementation of the approach
using System;
class GFG
{
// Utility function to print the
// contents of an array
static void printArr(int[] arr, int n)
{
for (int i = 0; i < n; i++)
{
Console.Write(arr[i] + " ");
}
}
// Function to find the original array
static void findOrgArr(int[] arr, int[] l,
int[] r, int[] x,
int n, int q)
{
for (int j = 0; j < q; j++)
{
for (int i = l[j]; i <= r[j]; i++)
{
// Decrement elements between
// l[j] and r[j] by x[j]
arr[i] = arr[i] - x[j];
}
}
printArr(arr, n);
}
// Driver code
public static void Main()
{
// Final array
int[] arr = { 20, 30, 20, 70, 100 };
// Size of the array
int n = arr.Length;
// Queries
int[] l = { 0, 1, 3 };
int[] r = { 2, 4, 4 };
int[] x = { 10, 20, 30 };
// Number of queries
int q = l.Length;
findOrgArr(arr, l, r, x, n, q);
}
}
// This code is contributed by
// Akanksha Rai
<?php
// PHP implementation of the approach
// Utility function to print the contents
// of an array
function printArr(&$arr, $n)
{
for ($i = 0; $i < $n; $i++)
{
echo($arr[$i]);
echo(" ");
}
}
// Function to find the original array
function findOrgArr(&$arr, &$l, &$r,
&$x, $n, $q)
{
for ($j = 0; $j < $q; $j++)
{
for ($i = $l[$j]; $i <= $r[$j]; $i++)
{
// Decrement elements between
// l[j] and r[j] by x[j]
$arr[$i] = $arr[$i] - $x[$j];
}
}
printArr($arr, $n);
}
// Driver code
// Final array
$arr = array(20, 30, 20, 70, 100);
// Size of the array
$n = sizeof($arr);
// Queries
$l = array(0, 1, 3 );
$r = array( 2, 4, 4 );
$x = array(10, 20, 30 );
// Number of queries
$q = sizeof($l);
findOrgArr($arr, $l, $r, $x, $n, $q);
// This code is contributed by Shivi_Aggarwal
?>
<script>
// Javascript implementation of the approach
// Utility function to print the contents of an array
function printArr(arr,n)
{
for (let i = 0; i < n; i++) {
document.write(arr[i]+" ");
}
}
// Function to find the original array
function findOrgArr(arr,l,r,x,n,q)
{
for (let j = 0; j < q; j++) {
for (let i = l[j]; i <= r[j]; i++) {
// Decrement elements between
// l[j] and r[j] by x[j]
arr[i] = arr[i] - x[j];
}
}
printArr(arr, n);
}
// Driver code
// Final array
let arr = [ 20, 30, 20, 70, 100 ];
// Size of the array
let n = arr.length;
// Queries
let l = [ 0, 1, 3 ];
let r = [ 2, 4, 4 ];
let x = [ 10, 20, 30 ];
// Number of queries
let q = l.length;
findOrgArr(arr, l, r, x, n, q);
// This code is contributed by patel2127
</script>
Complexity Analysis:
- Time Complexity: O(n2)
- Auxiliary Space: O(1)
Efficient Approach:
Follow the following steps to reach the initial array:
- Take an array b[] of the size of the given array and initialize all of its elements with 0.
- In array b[], for every query update b[l] = b[l] - x and b[r + 1] = b[r + 1] + x if r + 1 < n. This is because x will cancel out the effect of -x when performed the prefix sum.
- Take the prefix sum of array b[], and add it to the given array which will produce the initial array.
Implementation:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Utility function to print the contents of an array
void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++) {
cout << arr[i] << " ";
}
}
// Function to find the original array
void findOrgArr(int arr[], int l[], int r[], int x[],
int n, int q)
{
int b[n] = { 0 };
for (int i = 0; i < q; i++) {
// Decrement the element at l[i]th index by -x
b[l[i]] += -x[i];
// Increment the element at (r[i] + 1)th index
// by x if (r[i] + 1) is a valid index
if (r[i] + 1 < n)
b[r[i] + 1] += x[i];
}
for (int i = 1; i < n; i++)
// Prefix sum of array b
b[i] = b[i - 1] + b[i];
// Update the original array
for (int i = 0; i < n; i++)
arr[i] = arr[i] + b[i];
printArr(arr, n);
}
// Driver code
int main()
{
// Final array
int arr[] = { 20, 30, 20, 70, 100 };
// Size of the array
int n = sizeof(arr) / sizeof(arr[0]);
// Queries
int l[] = { 0, 1, 3 };
int r[] = { 2, 4, 4 };
int x[] = { 10, 20, 30 };
// Number of queries
int q = sizeof(l) / sizeof(l[0]);
findOrgArr(arr, l, r, x, n, q);
return 0;
}
// Java implementation of above approach
class GFG{
// Utility function to print the contents of an array
static void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
{
System.out.print(arr[i] + " ") ;
}
}
// Function to find the original array
static void findOrgArr(int arr[], int l[], int r[], int x[],
int n, int q)
{
int b[] = new int[n] ;
for (int i = 0; i < q; i++)
b[i] = 0 ;
for (int i = 0; i < q; i++)
{
// Decrement the element at l[i]th index by -x
b[l[i]] += -x[i];
// Increment the element at (r[i] + 1)th index
// by x if (r[i] + 1) is a valid index
if (r[i] + 1 < n)
b[r[i] + 1] += x[i];
}
for (int i = 1; i < n; i++)
// Prefix sum of array b
b[i] = b[i - 1] + b[i];
// Update the original array
for (int i = 0; i < n; i++)
arr[i] = arr[i] + b[i];
printArr(arr, n);
}
// Driver code
public static void main(String []args)
{
// Final array
int arr[] = { 20, 30, 20, 70, 100 };
// Size of the array
int n = arr.length ;
// Queries
int l[] = { 0, 1, 3 };
int r[] = { 2, 4, 4 };
int x[] = { 10, 20, 30 };
// Number of queries
int q = l.length ;
findOrgArr(arr, l, r, x, n, q);
}
}
// This code is contributed by aishwarya.27
# Python3 implementation of the approach
# Utility function to print the contents
# of an array
def printArr(arr, n):
for i in range(n):
print(arr[i], end = " ")
# Function to find the original array
def findOrgArr(arr, l, r, x, n, q):
b = [0 for i in range(n)]
for i in range(q):
# Decrement the element at l[i]th
# index by -x
b[l[i]] += -x[i]
# Increment the element at (r[i] + 1)th
# index by x if (r[i] + 1) is a valid index
if (r[i] + 1 < n):
b[r[i] + 1] += x[i]
for i in range(n):
# Prefix sum of array b
b[i] = b[i - 1] + b[i]
# Update the original array
for i in range(n):
arr[i] = arr[i] + b[i]
printArr(arr, n)
# Driver code
arr = [20, 30, 20, 70, 100]
# Size of the array
n = len(arr)
# Queries
l = [0, 1, 3 ]
r = [2, 4, 4 ]
x = [10, 20, 30 ]
# Number of queries
q = len(l)
findOrgArr(arr, l, r, x, n, q)
# This code Is contributed by
# Mohit kumar 29
// C# implementation of above approach
using System;
class GFG
{
// Utility function to print the
// contents of an array
static void printArr(int[] arr, int n)
{
for (int i = 0; i < n; i++)
{
Console.Write(arr[i] + " ");
}
}
// Function to find the original array
static void findOrgArr(int[] arr, int[] l,
int[] r, int[] x,
int n, int q)
{
int[] b = new int[n];
for (int i = 0; i < q; i++)
b[i] = 0 ;
for (int i = 0; i < q; i++)
{
// Decrement the element at l[i]th
// index by -x
b[l[i]] += -x[i];
// Increment the element at (r[i] + 1)th
// index by x if (r[i] + 1) is a valid index
if (r[i] + 1 < n)
b[r[i] + 1] += x[i];
}
for (int i = 1; i < n; i++)
// Prefix sum of array b
b[i] = b[i - 1] + b[i];
// Update the original array
for (int i = 0; i < n; i++)
arr[i] = arr[i] + b[i];
printArr(arr, n);
}
// Driver code
public static void Main()
{
// Final array
int[] arr = { 20, 30, 20, 70, 100 };
// Size of the array
int n = arr.Length;
// Queries
int[] l = { 0, 1, 3 };
int[] r = { 2, 4, 4 };
int[] x = { 10, 20, 30 };
// Number of queries
int q = l.Length;
findOrgArr(arr, l, r, x, n, q);
}
}
// This code is contributed
// by Akanksha Rai
<script>
// Javascript implementation of above approach
// Utility function to print the contents of an array
function printArr(arr, n)
{
console.log(arr.join(' ')) ;
}
// Function to find the original array
function findOrgArr(arr,l,r,x,n,q)
{
let b = new Array(n) ;
for (let i = 0; i < n; i++)
b[i] = 0 ;
for (let i = 0; i < q; i++)
{
// Decrement the element at l[i]th index by -x
b[l[i]] += -x[i];
// Increment the element at (r[i] + 1)th index
// by x if (r[i] + 1) is a valid index
if (r[i] + 1 < n)
b[r[i] + 1] += x[i];
}
for (let i = 1; i < n; i++)
// Prefix sum of array b
b[i] = b[i - 1] + b[i];
// Update the original array
for (let i = 0; i < n; i++)
arr[i] = arr[i] + b[i];
printArr(arr, n);
}
// Driver code
// Final array
let arr = [ 20, 30, 20, 70, 100 ];
// Size of the array
let n = arr.length ;
// Queries
let l = [ 0, 1, 3 ];
let r = [ 2, 4, 4 ];
let x = [ 10, 20, 30 ];
// Number of queries
let q = l.length ;
// Function call
findOrgArr(arr, l, r, x, n, q);
// This code is contributed by aarohirai2616.
</script>
Complexity Analysis:
- Time Complexity: O(n)
- Auxiliary Space: O(n)
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