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Consider an array of integers. A prefix sum array is a new array where the element at index `i` represents the sum of all elements from the original array up to index `i`. For a given array `arr` of size `n`, the prefix sum array is denoted as `prefixSum`, where `prefixSum[i] = arr[0] + arr[1] + ... + arr[i]`.Write a C++ program that calculates the prefix sum array for a given array and efficiently computes the sum of elements from index `l` to `r` in O(1) time using the prefix sum array.

Question

Consider an array of integers. A prefix sum array is a new array where the element at index i represents the sum of all elements from the original array up to index i. For a given array arr of size n, the prefix sum array is denoted as prefixSum, where prefixSum[i] = arr[0] + arr[1] + ... + arr[i].Write a C++ program that calculates the prefix sum array for a given array and efficiently computes the sum of elements from index l to r in O(1) time using the prefix sum array.

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Solution

Here is a C++ program that calculates the prefix sum array for a given array and efficiently computes the sum of elements from index l to r in O(1) time using the prefix sum array.

#include<iostream>
#include<vector>
using namespace std;

vector<int> prefixSumArray(vector<int>& arr) {
    int n = arr.size();
    vector<int> prefixSum(n);
    prefixSum[0] = arr[0];

    for(int i = 1; i < n; i++) {
        prefixSum[i] = prefixSum[i-1] + arr[i];
    }

    return prefixSum;
}

int sumRange(vector<int>& prefixSum, int l, int r) {
    if(l == 0) {
        return prefixSum[r];
    } else {
        return prefixSum[r] - prefixSum[l-1];
    }
}

int main() {
    vector<int> arr = {1, 2, 3, 4, 5};
    vector<int> prefixSum = prefixSumArray(arr);

    int l = 1, r = 3;
    cout << "Sum from index " << l << " to " << r << " is: " << sumRange(prefixSum, l, r) << endl;

    return 0;
}

In this program, the prefixSumArray function calculates the prefix sum array for the given array. The sumRange function computes the sum of elements from index l to r using the prefix sum array. If l is 0, it directly returns the value at index r in the prefix sum array. Otherwise, it subtracts the value at index l-1 in the prefix sum array from the value at index r. This gives the sum of elements from index l to r in the original array.

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Similar Questions

Consider an array of integers. A prefix sum array is a new array where the element at index `i` represents the sum of all elements from the original array up to index `i`. For a given array `arr` of size `n`, the prefix sum array is denoted as `prefixSum`, where `prefixSum[i] = arr[0] + arr[1] + ... + arr[i]`.Write a C++ program that calculates the prefix sum array for a given array and efficiently computes the sum of elements from index `l` to `r` in O(1) time using the prefix sum array.

prefixsumsWe have an array A of N integers. We also have Q queries, with each query consisting of two numbers, l and r.Your solution should output the sum of numbers from A[l] to A[r] (1-indexed).Constraints:1 ≤ N, Q, A[i] ≤ 1e6 for 1 ≤ i ≤ NInput:First line: N and Q, the size of the array A and the number of queries respectively.Subsequent line, N integers, the array A.Subsequent Q lines, 2 integers each, l and r.Output:For each testcase, output the answer.Sample Input:13 1111 3 14 12 14 1 8 9 1 1 5 14 41 116 81 24 116 137 101 910 136 133 73 10Sample Output:7918145143197324434960

#include<stdio.h>int main(){ int arr[100],size,i,sum=0,n; printf("Enter the size:"); scanf("%d",&size); for(i=0;i<n;i++) { printf("Enter %d elements,:\t"); scanf("%d",&arr[i]); } for(i=0;i<n;i++) { sum+=arr[i]; } printf("Sum of element=%d",sum); return 0;}

Write an efficient C program to find the sum of contiguous subarray within a one-dimensionalarray of integer which returns the largest sum.Explanation:Lets take the example of array {5,-3, 4}Possible contiguous subarray combinations are{5}, {-3}, {4}, {5,-3}, {-3,4}, {5,-3,4}The contiguous subarray {5,-3,4} has got the largest sum 6Input Constraints:First line : array size (N), where 1<= N<=100Second line : N integers of separated by spaceswhere each number Ni satisfies-10000 <= Ni <=10000Output Constraints:Single integer SUM which is the largest of sum of all possible contiguous subarray

Single File Programming QuestionProblem statementTheo, an aspiring mathematician, has presented you with a challenge. He wants you to create a program that calculates the absolute difference between the sum of two arrays.Create a program to find the absolute difference between two arrays with a function named calculateArraySum and calculateAbsoluteDifference where the array is passed as an argument.Input 10-100 -49 -87 5 6 7 0 100 37 5710-100 -75 -48 -86 -98 98 97 98 67 100Output 77ExplanationTwo arrays with 10 elements each are given as input.The first array has elements: -100, -49, -87, 5, 6, 7, 0, 100, 37, 57, and the sum of the first array is - 24.The second array has elements: -100, -75, -48, -86, -98, 98, 97, 98, 67, 100, and the sum of the second array is 53.The absolute difference of the sum is calculated by subtracting the second array from first array |-24 - 53| = 77, and the result is printed.Input format :The first line of input is an integer value 'N1', representing the number of elements in the first array.The second line of input consists of N1 space-separated integers arr1[i], representing the elements of the first array.The third line of input is an integer value 'N2', representing the number of elements in the second array.The fourth line of input consists of N2 space-separated integers arr2[i], representing the elements of the second array.Output format :The output displays a single integer the absolute difference between the sums of the elements in the two arrays.Refer to the sample output for the formatting specifications.Code constraints :In this scenario, the test cases fall under the following constraints:1 ≤ N1, N2 ≤ 10-100 ≤ arr1[i], arr2[i] ≤ 100Sample test cases :Input 1 :35 8 332 6 4Output 1 :4Input 2 :6-2 5 0 8 -1 364 -3 2 7 1 6Output 2 :4Input 3 :10-100 -49 -87 5 6 7 0 100 37 5710-100 -75 -48 -86 -98 98 97 98 67 100Output 3 :77

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