Question

List all the element of the following set.

A={x: x is an integer, x2 ≤ 16}​

Answer 1

Step-by-step explanation:

GEEKSFORGEEKS

Number of solutions for x < y, where a <= x <= b and c <= y <= d and x, y are integers

Given four integers a, b, c, d ( upto 10^6 ). The task is to Find the number of solutions for x < y, where a <= x <= b and c <= y <= d and x, y integers.

Examples:

Input: a = 2, b = 3, c = 3, d = 4

Output: 3

Input: a = 3, b = 5, c = 6, d = 7

Output: 6

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Let’s iterate explicitly over all possible values of x. For one such fixed value of x, the problem reduces to how many values of y are there such that c <= y <= d and x = max(c, x + 1) and y <= d. Let’s assume that c <= d, otherwise, there are no valid values of y of course. It follows, that for a fixed x, there are d – max(c, x+1) + 1 valid values of y because the number of integers in a range [R1, R2] is given by R2 – R1 + 1.

Below is the implementation of the above approach:

// C++ implementation of above approach

#include <bits/stdc++.h>

using namespace std;

// function to Find the number of solutions for x < y,

// where a <= x <= b and c <= y <= d and x, y integers.

int NumberOfSolutions(int a, int b, int c, int d)

{

// to store answer

int ans = 0;

// iterate explicitly over all possible values of x

for (int i = a; i <= b; i++)

if (d >= max(c, i + 1))

ans += d - max(c, i + 1) + 1;

// return answer

return ans;

}

// Driver code

int main()

{

int a = 2, b = 3, c = 3, d = 4;

// function call

cout << NumberOfSolutions(a, b, c, d);

return 0;

}

Output:

3

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hope my answer is correct