Related Articles

# Find the Initial Array from given array after range sum queries

• Last Updated : 28 May, 2021

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 has 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.
Below is the implementation of the approach:

## C++

 `// C++ implementation of the approach``#include ``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

 `// 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

 `# 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#

 `// 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

 ``

## Javascript

 ``

Output:

`10 0 -10 20 50 `

Time Complexity: O(n2)
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.

## C++

 `// C++ implementation of the approach``#include ``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

 `// 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

 `# 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#

 `// 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`

Output:

`10 0 -10 20 50 `

Time Complexity: O(n)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up