Ways to choose balls such that at least one ball is chosen
Given an integer N, the task is to find the ways to choose some balls out of the given N balls such that at least one ball is chosen. Since the value can be large so print the value modulo 1000000007.
Example:
Input: N = 2
Output: 3
The three ways are “*.”, “.*” and “**” where ‘*’ denotes
the chosen ball and ‘.’ denotes the ball which didn’t get chosen.
Input: N = 30000
Output: 165890098
Approach: There are N balls and each ball can either be chosen or not chosen. Total number of different configurations is 2 * 2 * 2 * … * N. We can write this as 2N. But the state where no ball is chosen has to be subtracted from the answer. So, the result will be (2N – 1) % 1000000007.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
int countWays( int n)
{
int ans = 1;
for ( int i = 0; i < n; i++) {
ans *= 2;
ans %= MOD;
}
return ((ans - 1 + MOD) % MOD);
}
int main()
{
int n = 3;
cout << countWays(n);
return 0;
}
|
Java
class GFG
{
static int MOD = 1000000007 ;
static int countWays( int n)
{
int ans = 1 ;
for ( int i = 0 ; i < n; i++)
{
ans *= 2 ;
ans %= MOD;
}
return ((ans - 1 + MOD) % MOD);
}
public static void main(String[] args)
{
int n = 3 ;
System.out.println(countWays(n));
}
}
|
Python3
MOD = 1000000007
def countWays(n):
return ((( 2 * * n) - 1 ) % MOD)
n = 3
print (countWays(n))
|
C#
using System;
class GFG
{
static int MOD = 1000000007;
static int countWays( int n)
{
int ans = 1;
for ( int i = 0; i < n; i++)
{
ans *= 2;
ans %= MOD;
}
return ((ans - 1 + MOD) % MOD);
}
public static void Main(String[] args)
{
int n = 3;
Console.WriteLine(countWays(n));
}
}
|
Javascript
<script>
MOD = 1000000007;
function countWays(n) {
var ans = 1;
for (i = 0; i < n; i++) {
ans *= 2;
ans %= MOD;
}
return ((ans - 1 + MOD) % MOD);
}
var n = 3;
document.write(countWays(n));
</script>
|
Time Complexity : O(n)
Auxiliary Space : O(1)
Last Updated :
03 Mar, 2022
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