Changing Bits


Problem Statement :


Let a and b be binary numbers of length n (MSB to the left). The following commands may be performed:

set_a idx x: Set  to , where  and  is  least significant bit of .
set_b idx x: Set  to , where  and  is  least significant bit of .
get_c idx: Print , where  and .
Given , and a list of commands, create a string made of the results of each  call, the only command that produces output. For example,  and  so the length of the numbers is . Print an answer string that contains the results of all commands on one line. A series of commands and their results follow:

Starting
ans = '' (empty string)
a b
000 111
set_a 1 1
010 111
set_b 0 1
010 111
get_c 3
a + b = 1001
ans = '1'
010 111
get_c 4
a + b = 01001
ans = '10'

Note: When the command is get_c 4,  had to be padded to the left with a  to be long enough to return a value.

Function Description

Complete the changeBits function in the editor below. For each get_c command, it should print either a 0 or a 1 without a newline until all commands have been processed. At that point, add a newline.

changeBits has the following parameters:
- a, b: two integers represented as binary strings
- queries[queries[0]-queries[n-1]]: an array of query strings in the format described

Input Format

The first line of input contains two space-separated integers,  and , the length of the binary representations of  and , and the number of commands, respectively.
The second and third lines each contain a string representation of  and .
The following  lines each contain a command string  as described above.


Output Format

For each query of the type , output a single digit 0 or 1. Output must be placed on a single line.


Solution :



title-img


                            Solution in C :

In  C  :






#define MAX_NUM ((unsigned int)-1)
#define WORD_SIZE 32
#define DATA_TYPE unsigned int
#include <stdio.h>
int main()
{
    DATA_TYPE A[3500] = {0}, B[3500] = {0}, C[3500] = {0};
    unsigned int CARRY[3500] = {0};
    int N, Q, N2;
    int idx, x, lowest_modified_idx=0;
    int i, j, rem;
    char cmd[10];
    char bit_string[100001];
    scanf("%d %d", &N, &Q);
    scanf("%s", bit_string);
    N2 = N/WORD_SIZE;
    rem = N % WORD_SIZE;

    for ( i = 0 ; i < N2 ; ++i )
        for ( j = 0 ; j < WORD_SIZE ; ++j )
            if ( bit_string[N - 1 - (i*WORD_SIZE + j)] == '1' )
                A[i] |= 1ULL << j;
    if ( rem )
        for ( j = 0 ; j < rem ; ++j )
            if ( bit_string[ rem - j - 1 ] == '1' )
                A[N2] |= 1ULL << j;
        
    
    scanf("%s", bit_string);

    for ( i = 0 ; i < N2 ; ++i )
        for ( j = 0 ; j < WORD_SIZE ; ++j )
            if ( bit_string[N - 1 - (i*WORD_SIZE + j)] == '1' )
                B[i] |= 1ULL << j;
    if ( rem )
        for ( j = 0 ; j < rem ; ++j )
            if ( bit_string[ rem - j - 1 ] == '1' )
                B[N2] |= 1ULL << j;    
    
    for ( ; Q ; --Q )
    {
        scanf("%s %d", cmd, &idx);
        switch(cmd[4])
        {
        case 'a':
            scanf("%d", &x);
            if ( x == 1 )
                A[idx/WORD_SIZE] |= (1ULL << (idx%WORD_SIZE));
            else
                A[idx/WORD_SIZE] &= ~(1ULL << (idx%WORD_SIZE));
            if ( idx < lowest_modified_idx )
              lowest_modified_idx = idx;
            break;
        case 'b':
            scanf("%d", &x);
            if ( x == 1 )
                B[idx/WORD_SIZE] |= (1ULL << (idx%WORD_SIZE));
            else
                B[idx/WORD_SIZE] &= ~(1ULL << (idx%WORD_SIZE));
            if ( idx < lowest_modified_idx )
              lowest_modified_idx = idx;
            break;
            
        case 'c':
            if ( idx >= lowest_modified_idx )
            { for ( i = lowest_modified_idx/WORD_SIZE ; i <= idx/WORD_SIZE ; ++i )
              {
                  CARRY[i+1] = 0;
                  if ( MAX_NUM - A[i] < B[i])
                     CARRY[i+1] = 1;
                  else if (A[i] < B[i] )
                  {    if ( MAX_NUM - A[i] - CARRY[i] < B[i] )
                          CARRY[i+1] = 1;
                  }
                  else if ( MAX_NUM - B[i] - CARRY[i] < A[i] )
                  {    CARRY[i+1] = 1;
                  }
                  C[i] = A[i] + B[i] + CARRY[i];
              }
              lowest_modified_idx = idx;
            }
            printf("%d", (C[idx/WORD_SIZE] & (1ULL << (idx%WORD_SIZE)))?1:0);
            break;
//        case 'd':
//            for ( j = rem ; j >= 0 ; --j )
//              printf("%d", (C[N/WORD_SIZE] & (1<<(j)))?1:0);
//              
//            for ( i = N/WORD_SIZE - 1 ; i >= 0; --i )
//              for ( j = WORD_SIZE-1;  j >= 0 ; --j )
//                printf("%d", (C[i] & (1<<j))?1:0);
//            printf("\n");
//            break;
        }
    }
}
                        

                        Solution in C++ :

In  C++  :







#include <iostream>
#include <cstring>
#include <cstdio>

using namespace std;

const int maxn = 100010;
int a[maxn], b[maxn], c[maxn];
int n, q;
char ss[maxn*5];
int l[maxn*2], r[maxn*2], s[maxn*2], tn;

int build(int ll, int rr)
{
	if(ll>=rr)
		return -1;
	int ret = tn++;
	if(ll + 1 == rr)
	{
		l[ret] = r[ret] = -1;
		s[ret] = c[ll];
		return ret;
	}
	int mid = (ll + rr) / 2;
	l[ret] = build(ll, mid);
	r[ret] = build(mid, rr);
	s[ret] = (s[l[ret]] == s[r[ret]] ? s[l[ret]] : 2);
	return ret;
}

void init() {
	scanf("%d%d", &n, &q);
	//printf("%d %d\n", n, q);
	memset(c, 0, sizeof(c));
	scanf("%s", ss);
	//printf("%s\n", ss);
	for(int i=0; i<n; ++i) {
		a[i] = c[i] = ss[n - i - 1] - '0';
	}
	scanf("%s", ss);
	//printf("%s\n", ss);
	for(int i=0; i<n; ++i) {
		b[i] = ss[n - 1 - i] - '0';
		c[i] += ss[n - 1 - i] - '0';
		if(c[i] >= 2)
		{
			c[i] -= 2;
			c[i+1] ++;
		}
	}
	a[n] = b[n] = 0;
	//memset(a, 0, sizeof(a));
	//memset(b, 0, sizeof(b));
	//memset(c, 0, sizeof(c));
	n++;
	tn = 0;
	build(0, n);
}

void push_down(int id) {
	if(s[id] == 2)
		return;
	if(l[id] < 0)
		return;
	s[l[id]] = s[r[id]] = s[id];
}

int findright(int id, int ll, int rr, int i, int bit)
{
	if(rr <= i)
		return -1;
	if(s[id] == bit)
		return i < ll ? ll : i;
	if(s[id] == (bit ^ 1))
		return -1;
	push_down(id);
	int mid = (ll + rr) / 2;
	int t = findright(l[id], ll, mid, i, bit);
	if(t >= 0)
		return t;
	return findright(r[id], mid, rr, i, bit);
}

void change(int id, int ll, int rr, int bl, int br, int bit)
{
	if(br <= ll || rr <= bl)
		return;
	if(bl <= ll && rr <= br)
	{
		s[id] = bit;
		return;
	}
	push_down(id);
	int mid = (ll + rr) / 2;
	change(l[id], ll, mid, bl, br, bit);
	change(r[id], mid, rr, bl, br, bit);
	if(s[l[id]] == s[r[id]])
		s[id] = s[l[id]];
	else
		s[id] = 2;
}

int getbit(int id, int ll, int rr, int i)
{
	if(i<ll || i>=rr)
		return 0;
	if(s[id] < 2)
		return s[id];
	int mid = (ll + rr) / 2;
	if(i < mid)
		return getbit(l[id], ll, mid, i);
	else
		return getbit(r[id], mid, rr, i);
}

void work() {
	int i, bit;
	int pn = 0;
	char cmd[10];
	while(q--) {
		scanf("%s", cmd);
		//printf("%s ", cmd);
		if(cmd[4]=='a' || cmd[4] == 'b')
		{
			scanf("%d%d", &i, &bit);
			//printf("%d %d\n", i, bit);
			if(cmd[4] == 'a' && a[i] == bit)
				continue;
			if(cmd[4] == 'b' && b[i] == bit)
				continue;
			if(cmd[4] == 'a') a[i] = bit;
			else b[i] = bit;
			int lmb = findright(0, 0, n, i, bit ^ 1);
			if(lmb == -1)
				lmb = n;
			change(0, 0, n, i, lmb, bit ^ 1);
			change(0, 0, n, lmb, lmb + 1, bit);
		}
		else
		{
			scanf("%d", &i);
			//printf("%d\n", i);
			ss[pn++] = getbit(0, 0, n, i) + '0';
			//printf("%c\n", ss[pn-1]);
		}
	}
	ss[pn] = 0;
	printf("%s\n", ss);
}

int main() {
	init();
	work();
}
                    

                        Solution in Java :

In  Java :








import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

class ChangingBitsDataSet {
	
	private static int ADDRESS_BITS = 6;
	private static int MASK = (1 << ADDRESS_BITS) - 1;
	
	private static void setBit(long[] data, int index, int value) {
		int highi = index >>> ADDRESS_BITS;
		int lowi = index & MASK;
		long mask = 1L << lowi;
		if (value == 0) {
			data[highi] &= ~mask;
		}
		else {
			data[highi] |= mask;			
		}
	}
	
	private long[] a;
	private long[] b;
	private long[] sum;
	
	public ChangingBitsDataSet(int length, String aString, String bString) {
		a = new long[1 + (length >>> ADDRESS_BITS)];
		b = new long[1 + (length >>> ADDRESS_BITS)];
		sum = new long[1 + (length >>> ADDRESS_BITS)];
		int carryFlag = 0;
		for (int i = length - 1, bitIndex = 0; i >= 0; i--, bitIndex++) {
			int aBit = aString.charAt(i) - '0';
			int bBit = bString.charAt(i) - '0';
			int s = aBit + bBit + carryFlag;
			int sumBit = s & 1;
			carryFlag = (s & 2) >>> 1;
			setBit(a, bitIndex, aBit);
			setBit(b, bitIndex, bBit);
			setBit(sum, bitIndex, sumBit);
		}
		setBit(sum, length, carryFlag);
	}

	private void add(int index) {
		int highi = index >>> ADDRESS_BITS;
		int lowi = index & MASK;
		long block = sum[highi];
		if ((~block >>> lowi) == 0L) {
			block ^= -1L << lowi;
			sum[highi++] = block;
			while (sum[highi] == -1L) {
				sum[highi++] = 0L;
			}
			block = sum[highi];
			lowi = 0;
		}
		while (((block >>> lowi) & 1) == 1) {
			block ^= 1L << lowi;
			lowi++;
		}
		block ^= 1L << lowi;
		sum[highi] = block;
	}
	
	private void sub(int index) {
		int highi = index >>> ADDRESS_BITS;
		int lowi = index & MASK;
		long block = sum[highi];
		if ((block >>> lowi) == 0L) {
			block ^= -1L << lowi;
			sum[highi++] = block;
			while (sum[highi] == 0L) {
				sum[highi++] = -1L;
			}
			block = sum[highi];
			lowi = 0;
		}
		while (((block >>> lowi) & 1) == 0) {
			block ^= 1L << lowi;
			lowi++;
		}
		block ^= 1L << lowi;
		sum[highi] = block;
	}
	
	private void set(long[] data, int index, int value) {
		int highi = index >>> ADDRESS_BITS;
		int lowi = index & MASK;
		int oldValue = (int) (data[highi] >>> lowi) & 1;
		if (oldValue == 0 & value == 1) {
			data[highi] ^= 1L << lowi;
			add(index);
		}
		else if (oldValue == 1 & value == 0) {
			data[highi] ^= 1L << lowi;
			sub(index);
		}
	}
	
	public void setA(int index, int value) {
		set(a, index, value);
	}
	
	public void setB(int index, int value) {
		set(b, index, value);
	}
	
	public int getC(int index) {
		int highi = index >>> ADDRESS_BITS;
		int lowi = index & MASK;
		return (int)(sum[highi] >>> lowi) & 1;
	}
}

public class Solution {
	static private String OPERATION_SET_A = "set_a";
	static private String OPERATION_SET_B = "set_b";
	static private String OPERATION_GET_C = "get_c";
	
	static public void main(String[] args) {
		try {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 64 << 10);
			StringTokenizer tokenizer = new StringTokenizer(br.readLine());
			int n = Integer.parseInt(tokenizer.nextToken());
			int q = Integer.parseInt(tokenizer.nextToken());
			String a = br.readLine();
			String b = br.readLine();
			ChangingBitsDataSet dataset = new ChangingBitsDataSet(n, a, b);
			StringBuilder result = new StringBuilder(n);
			for (int i = 0; i < q; i++) {
				tokenizer = new StringTokenizer(br.readLine());
				String operation = tokenizer.nextToken();
				if (OPERATION_SET_A.equals(operation)) {
					dataset.setA(Integer.parseInt(tokenizer.nextToken()), Integer.parseInt(tokenizer.nextToken()));
				}
				else if (OPERATION_SET_B.equals(operation)){
					dataset.setB(Integer.parseInt(tokenizer.nextToken()), Integer.parseInt(tokenizer.nextToken()));					
				}
				else if (OPERATION_GET_C.equals(operation)){
					result.append(dataset.getC(Integer.parseInt(tokenizer.nextToken())));
				}
			}
			System.out.println(result);
		}
		catch (Exception e) {
			System.err.println("Error:" + e.getMessage());
		}
	}
}
                    

                        Solution in Python : 
                            
In  Python3 :








n_bit, line_count = [int(i) for i in input().split()]
a = int(input(), 2)
b = int(input(), 2)

for i in range(line_count):
    inp = input().split()
    x = int(inp[1])
    
    if inp[0] == "get_c":
        print(( (a+b) & (1 << x ) ) >> x, end="")
    
    elif inp[0] == "set_a":
        if inp[2] == "1":
            a = a | ( 1 << x )
        else:
            a = a & ~( 1 << x )
    
    else:
        if inp[2] == "1":
            b = b | ( 1 << x )
        else:
            b = b & ~( 1 << x )
                    

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