Xoring Ninja


Problem Statement :


An XOR operation on a list is defined here as the xor () of all its elements (e.g.: ).

The  of set  is defined here as the sum of the s of all non-empty subsets of  known as . The set  can be expressed as:


For example: Given set 

The set of possible non-empty subsets is: 

The  of these non-empty subsets is then calculated as follows:
 = 

Given a list of  space-separated integers, determine and print .

For example, . There are three possible subsets, . The XOR of , of  and of . The XorSum is the sum of these:  and .

Note: The cardinality of powerset is , so the set of non-empty subsets of set  of size  contains  subsets.

Function Description

Complete the xoringNinja function in the editor below. It should return an integer that represents the XorSum of the input array, modulo .

xoringNinja has the following parameter(s):

arr: an integer array


Input Format

The first line contains an integer , the number of test cases.

Each test case consists of two lines:
- The first line contains an integer , the size of the set .
- The second line contains  space-separated integers .


Output Format

For each test case, print its  on a new line. The  line should contain the output for the  test case.



Solution :



title-img


                            Solution in C :

In  C  :






#include<stdio.h>
#define LL long long int
#define MOD 1000000007

LL power(LL a, LL b)
{
	if (b == 0)
		return 1;
	else
	{
		LL temp=(power(a,b/2))%MOD;
		if(b%2==0)   
			return (temp*temp)%MOD;
		else
			return (((temp*a)%MOD)*temp)%MOD;
	}
}

int main(){
	int t;
	scanf("%d",&t);
	while(t--){
		int n;
		scanf("%d",&n);
		int x=0;
		int i,a;
		for(i=0;i<n;i++)
		{
			scanf("%d",&a);
			x|=a;
		}
		LL ans=power(2,n-1);
		ans=(ans*x)%MOD;
		printf("%lld\n",ans);
	}
	return 0;
}
                        


                        Solution in C++ :

In  C++  :








#include <cstdio>
#include <iostream>
#include <fstream>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <string>
#include <ctime>
#include <cassert>
#include <utility>

using namespace std;

#define MAXN 100005
#define MOD 1000000007

int T, N;
int A[MAXN];
long long dp[MAXN][2];

int main() {
//	freopen("date.in", "r", stdin);
	
	cin >> T;
	while(T--) {
        cin >> N;
        for(int i = 0; i < N; i++)
            cin >> A[i];
        
        long long ans = 0;
        for(int bit = 0; bit < 32; bit++) {
            memset(dp, 0, sizeof(dp)); 
            dp[0][0] = 1;
            dp[0][1] = 0;
            for(int i = 0; i < N; i++) {
                int crt = 0;
                if(A[i] & (1 << bit))
                    crt = 1;
                for(int j = 0; j < 2; j++) {
                    int nj = j ^ crt;
                    dp[i + 1][nj] += dp[i][j];
                    dp[i + 1][j] += dp[i][j];
                    dp[i + 1][nj] %= MOD;
                    dp[i + 1][j] %= MOD;
                }
            }
            long long cnt = dp[N][1];
            ans += cnt * (1LL << bit);
            ans %= MOD;
        }
        
        cout << ans << '\n';
	}
	
	return 0;
}
                    


                        Solution in Java :

In   Java :






import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;


public class Solution {

	static Solution main;
	
	static long sp;
	
	public static void main(String[] args) {
		sp = 1000000007;
		long [] fact = new long[110001];
		long [] pow2 = new long[110001];
		pow2[0] = 1;
		fact[0] = 1;
		for(int i = 1 ; i < 110001 ; i++) {
			fact[i] = fact[i-1] * i;
			fact[i] %= sp;
			pow2[i] = 2*pow2[i-1];
			if(pow2[i]>=sp) {
				pow2[i]-=sp;
			}
		}
		main = new Solution();
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedOutputStream bos = new BufferedOutputStream(System.out);
		String eol = System.getProperty("line.separator");
		byte[] eolb = eol.getBytes();
		try {
			String str = br.readLine();
			int t = Integer.parseInt(str);
			for(int i = 0 ; i < t ; i++) {
				str = br.readLine();
				int n = Integer.parseInt(str);
				int [] ar = new int[40];
				Arrays.fill(ar, 0);
				str = br.readLine();
				int j=0;
				int s=0;
				int length = str.length();
				while(j<length) {
					while(j<length) {
						if(str.charAt(j) == ' ') {
							break;
						}else {
							j++;
						}
					}
					int x = Integer.parseInt(str.substring(s,j)) ;	
					int iter = 0;
					while(x>0) {
						if((x%2)==1) {
							ar[iter]++;
						}
						x/=2;
						iter++;
					}
					j++;
					s=j;			
				}
				long ans = 0;
				for(int a = 0 ;a < 40 ; a++) {
					int x = ar[a];
					for(int b = 1 ; b <= x; b+=2) {
						// x choose b * 2^(n-x) * 2^a
						long tempAns = fact[x];
						tempAns *= inverse(fact[b]);
						tempAns %= sp;
						tempAns *= inverse(fact[x-b]);
						tempAns %= sp;
						tempAns *= pow2[n-x+a];
						tempAns %= sp;
						ans += tempAns;
						if(ans>sp) {
							ans -= sp;
						}
					}
				}
				bos.write(new Long(ans).toString().getBytes());
				bos.write(eolb);
			}
			bos.flush();
		} catch(IOException ioe) {
			ioe.printStackTrace();
		}
	}
	
	public static long inverse(long a) {
		return getPow(a,sp-2);
	}
	
	public static long getPow(long a , long b) {
		long ans = 1;
		long pow = a;
		while(b>0) {
			if((b%2)==1) {
				ans *= pow;
				ans %= sp;
			}
			pow *= pow;
			pow %= sp;
			b/=2;
		}
		return ans;
	}

}
                    


                        Solution in Python : 
                            
In  Python3 :







import sys

def poweroftwo(n):
	val = 1
	yield val
	for i in range(n):
		val *= 2
		yield val
    

r = sys.stdin.readline
#table = list(poweroftwo(100000))
text = r()
t = int(text)
for i in range(t):
	text = r()
	n = int(text)
	text = r()
	tmp = 0
	for num in map(int,text.split()):
		tmp |= num
	#tmp *= table[n]
	for i in range(n-1):
		tmp *= 2
		if i % 20 == 0:
			tmp %= 1000000007
	print(tmp%1000000007)
                    


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