- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find n-variables from n sum equations with one missing in C++
In this problem, we are given an array sum[] consisting of a sum of (n-1) variables given as,
Sum[1] = x2 + x3 + x4 + … xn Sum[2] = x1 + x3 + x4 + … xn . . Sum[i] = x2 + x3 + x4 + … x(i-1) + x(i+1) + … + xn . . Sum[n] = x1 + x2 + x3 + … x(n-1) Our task is to find the value of x1, x2,... xn.
Let’s take an example to understand the problem,
Input
sum[] = {6, 6, 6, 6, 6, 6, 6}Output
x1 = 1, x2 = 1, x3 = 1, x4 = 1, x5 = 1, x6 = 1, x7 = 1
Explanation
arr[1] = 1 + 1 + 1 + 1 + 1 + 1 = 6
Solution Approach
Let the sum of all variables be sumX,
sumX = x1 + x2 + x3 + … + xn
So, the values of sum array are −
sum[1] = x2 + x3 + x4 + … xn = -x1 + x1 + x2 + x3 + x4 + … xn = sumX - x1
Similarly,
sum[2] = sumX - x2 sum[3] = sumX - x3 . sum[i] = sumX - xi . sum[n] = sumX - xn
Adding all the sum arrays we get,
Sum[1] + sum[2] + … sum[n] = sumX - x1 + sumX - x2 + … + sumX - xn arrSum = n*sumX - (x1 + x2 + x3 … xn) arrSum = n*SumX - (x1 + x2 + x3 … xn) arrSum = sumX*(n-1) sumX = arrSum/ (n-1)
Using this value of sumX, we can find the values of x1, x2…
So,
x1 = sumX - sum[1] x2 = sumX - sum[2] .. xi = sumX - sum[i] .. xn = sumX - sum[n]
Program to illustrate the working of our solution,
Example
#include <iostream>
using namespace std;
void calcSumVariables(int sum[], int n) {
float SUMX = 0;
for (int i = 0; i < n; i++) {
SUMX += sum[i];
}
SUMX /= (n - 1);
for (int i = 0; i < n; i++)
cout<<"\nx"<<(i + 1)<<" = "<<(SUMX - sum[i]);
}
int main(){
int sum[] = {3, 8, 6, 7, 4, 5, 9 };
int N = sizeof(sum) / sizeof(sum[0]);
cout<<"The value of variables that form the sum are ";
calcSumVariables(sum, N);
return 0;
}Output
The value of variables that form the sum are
x1 = 4 x2 = -1 x3 = 1 x4 = 0 x5 = 3 x6 = 2 x7 = -2
Updated on: 13-Mar-2021
33 Views
Advertisements