AND Product


Problem Statement :


Consider two non-negative long integers,  and , where . The bitwise AND of all long integers in the inclusive range between  and  can be expressed as , where  is the bitwise AND operator.

Given  pairs of long integers,  and , compute and print the bitwise AND of all natural numbers in the inclusive range between  and .

For example, if  and , the calculation is .

Function Description

Complete the andProduct in the editor below. It should return the computed value as an integer.

andProduct has the following parameter(s):

a: an integer
b: an integer
Input Format

The first line contains a single integer , the number of intervals to test.
Each of the next  lines contains two space-separated integers  and .

Output Format

For each pair of long integers, print the bitwise AND of all numbers in the inclusive range between  and  on a new line.



Solution :



title-img


                            Solution in C :

In C :




#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int main()
{
	int t;
	unsigned int a, b;
	
	scanf("%d", &t);
	
	while (t--) {
		scanf("%u%u", &a, &b);
		printf("%u\n", a);
	}
	
	return 0;
}
                        


                        Solution in C++ :

In  C++  :





#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ll;
ll a, b, o = 1;

bool all(ll x, ll a, ll b) {
	return (a&x) && (b&x) && (b - a) < x;
}

int main() {
	int T; scanf("%d", &T); for(int ks = 1; ks <= T; ++ks) {
		scanf("%llu%llu", &a, &b);
		ll bb = 0;
		for(int i = 0; i < 63; ++i) {
			ll t = o << i;
			if(all(t, a, b)) bb |= t;
		}
		printf("%llu\n", bb);
	}
	return 0;
}
                    


                        Solution in Java :

In  Java :







import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class B {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		for(int T = ni();T >= 1;T--){
			long a = nl(), b = nl();
			long ret = 0;
			for(int i = 32;i >= 0;i--){
				if((a^b)<<~i>=0){
					ret |= a&(1L<<i);
				}else{
					break;
				}
			}
			out.println(ret);
		}
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
                    


                        Solution in Python : 
                            
In  Python3 :






T = int(input())

for _ in range(T) :
    A,B = (int(_) for _ in input().split())
    i,C = -1,A^B
    while C > 0 :
        C >>= 1
        i += 1
    print(A & (2**32-2**i))
                    


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