# 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 :

```                            ```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.util.StringTokenizer;

class ChangingBitsDataSet {

private static int ADDRESS_BITS = 6;

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) {
}
else {
}
}

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);
}

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;
}
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 {
int n = Integer.parseInt(tokenizer.nextToken());
int q = Integer.parseInt(tokenizer.nextToken());
ChangingBitsDataSet dataset = new ChangingBitsDataSet(n, a, b);
StringBuilder result = new StringBuilder(n);
for (int i = 0; i < q; i++) {
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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