Given an array of size N which is initialized with all zeros. We are given many range add queries, which should be applied to this array. We need to print final updated array as our result.
Examples:
N = 6 Arr = [0, 0, 0, 0, 0, 0] rangeUpdate1 [0, 2], add 100 Arr = [100, 100, 100, 0, 0, 0] rangeUpdate1 [1, 5], add 100 Arr = [100, 200, 200, 100, 100, 100] rangeUpdate1 [2, 3], add 100 Arr = [100, 200, 300, 200, 100, 100] Which is the final updated array.
This problem can be solved using segment tree with lazy updates in O(log N) time per query but we can do better here, as update operation is not given. We can process each query in constant time using this logic, when a query to add V is given in range [a, b] we will add V to arr[a] and –V to arr[b+1] now if we want to get the actual values of array we will convert the above array into prefix sum array. See below example to understand,
Arr = [0, 0, 0, 0, 0, 0] rangeUpdate1 [0, 2], add 100 Arr = [100, 0, 0, -100, 0, 0] rangeUpdate1 [1, 5], add 100 Arr = [100, 100, 0, -100, 0, 0, -100] rangeUpdate1 [2, 3], add 100 Arr = [100, 100, 100, -100, -100, 0, -100] Now we will convert above operation array to prefix sum array as shown below, Arr = [100, 200, 300, 200, 100, 100] Which is the final updated array.
So in effect, when we add a value V to specific index of array, It represents adding V to all elements right to this index, that is why we add –V after range to remove its effect after its range of add query.
Please note in below code, if range spans till the last index, the addition of –V is omitted to be in memory limit of the array.
C++
// C++ program to get updated array after many array range // add operation #include <bits/stdc++.h> using namespace std; // Utility method to add value val, to range [lo, hi] void add(int arr[], int N, int lo, int hi, int val) { arr[lo] += val; if (hi != N - 1) arr[hi + 1] -= val; } // Utility method to get actual array from operation array void updateArray(int arr[], int N) { // convert array into prefix sum array for (int i = 1; i < N; i++) arr[i] += arr[i - 1]; } // method to print final updated array void printArr(int arr[], int N) { updateArray(arr, N); for (int i = 0; i < N; i++) cout << arr[i] << " "; cout << endl; } // Driver code to test above methods int main() { int N = 6; int arr[N] = {0}; // Range add Queries add(arr, N, 0, 2, 100); add(arr, N, 1, 5, 100); add(arr, N, 2, 3, 100); printArr(arr, N); return 0; } |
Java
// Java program to get updated array after // many array range add operation import java.io.*; class GFG { // Utility method to add value val, // to range [lo, hi] static void add(int arr[], int N, int lo, int hi, int val) { arr[lo] += val; if (hi != N - 1) arr[hi + 1] -= val; } // Utility method to get actual array from // operation array static void updateArray(int arr[], int N) { // convert array into prefix sum array for (int i = 1; i < N; i++) arr[i] += arr[i - 1]; } // method to print final updated array static void printArr(int arr[], int N) { updateArray(arr, N); for (int i = 0; i < N; i++) System.out.print(""+arr[i]+" "); System.out.print("
"); } // Driver code to test above methods public static void main (String[] args) { int N = 6; int arr[] = new int[N]; // Range add Queries add(arr, N, 0, 2, 100); add(arr, N, 1, 5, 100); add(arr, N, 2, 3, 100); printArr(arr, N); } } // This code is contributed by Prakriti Gupta |
Python3
# Python3 program to get updated array # after many array range add operation # Utility method to add value # val, to range [lo, hi] def add(arr, N, lo, hi, val): arr[lo] += val if (hi != N - 1): arr[hi + 1] -= val # Utility method to get actual # array from operation array def updateArray(arr, N): # convert array into prefix sum array for i in range(1, N): arr[i] += arr[i - 1] # method to print final updated array def printArr(arr, N): updateArray(arr, N) for i in range(N): print(arr[i], end = " ") print() # Driver code N = 6arr = [0 for i in range(N)] # Range add Queries add(arr, N, 0, 2, 100) add(arr, N, 1, 5, 100) add(arr, N, 2, 3, 100) printArr(arr, N) # This code is contributed by Anant Agarwal. |
C#
// C# program to get updated array after // many array range add operation using System; class GFG { // Utility method to add value val, // to range [lo, hi] static void add(int []arr, int N, int lo, int hi, int val) { arr[lo] += val; if (hi != N - 1) arr[hi + 1] -= val; } // Utility method to get actual // array from operation array static void updateArray(int []arr, int N) { // convert array into // prefix sum array for (int i = 1; i < N; i++) arr[i] += arr[i - 1]; } // method to print final updated array static void printArr(int []arr, int N) { updateArray(arr, N); for (int i = 0; i < N; i++) Console.Write("" + arr[i] + " "); Console.Write("
"); } // Driver code public static void Main () { int N = 6; int []arr = new int[N]; // Range add Queries add(arr, N, 0, 2, 100); add(arr, N, 1, 5, 100); add(arr, N, 2, 3, 100); printArr(arr, N); } } // This code is contributed by Nitin Mittal. |
PHP
Output:
100 200 300 200 100 100
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