Algorithm to calculate sum of LUCKY FACTOR in given range - c++

Question

Problem Statement :-
A number is given, N, which is given in binary notation, and it
contains atmost 1000000 bits. You have to calculate the sum of LUCKY
FACTOR in range from 1 to N (decimal notation).
Here, LUCKY FACTOR means, (after converting into binary representation) if
rightmost or leftmost 1's neighbour is either 0 or nothing(for
boundary bit).
EDITED :-
Means if rightmost one's left neighbour is 0, means it count as a
LUCKY FACTOR, simlarly in the left side also
Example,
5 == 101, LUCKY FACTOR = 2.
7 == 111, LUCKY FACTOR = 0.
13 == 1101, LUCKY FACTOR = 1.
16 == 1110, LUCKY FACTOR = 0.
0 == 0, LUCKY FACTOR = 0.
Answer must be in binary form
I am totally stuck, give me a hint.
My code
#include<stdio.h>
#include<string>
#include<string.h>
#include<vector>
//#include<iostream>
using namespace std;
vector<string> pp(10000001);
string add(string a, string b) {
if(b == "") return a;
string answer = "";
int c = 0;
int szeA = a.size() - 1;
int szeB = b.size() - 1;
while(szeA >= 0 || szeB >= 0) {
answer = (char)( ( ( ( (szeA >= 0) ? (a[szeA] - 48) : 0 ) ^ ( (szeB >= 0) ? (b[szeB] - 48) : 0 ) ) ^ (c) ) + 48 ) + answer;
c = ( ( ( (szeA >= 0) ? (a[szeA] - 48) : 0 ) & ( (szeB >= 0) ? (b[szeB] - 48) : 0 ) ) | ( ( (szeA >= 0) ? (a[szeA] - 48) : 0 ) & (c) ) | ( ( (szeB >= 0) ? (b[szeB] - 48) : 0 ) & (c) ) );
szeA--;
szeB--;
}
if(c) answer = '1' + answer;
return answer;
}
string subtract(string a, string b) {
int sze = a.size() - b.size();
while(sze--) b = '0' + b;
sze = a.size();
for(int i = 0; i < sze; i++) {
if(b[i] == '1') b[i] = '0';
else b[i] = '1';
}
if(b[sze-1] == '0') {
b[sze-1] = '1';
}
else {
int i = sze-1;
while(i >= 0 && b[i] == '1') {
b[i] = '0';
i--;
}
if(i >= 0) b[i] = '1';
else b = '1' + b;
}
b = add(a, b);
b.erase(b.begin() + 0);
//b[0] = '0';
while(b[0] == '0') b.erase(b.begin() + 0);
return b;
}
string power(int index) {
if(index < 0) return "";
string answer = "";
while(index--) {
answer = '0' + answer;
}
answer = '1' + answer;
return answer;
}
string convert(long long int val) {
int divisionStore=0;
int modStore=0;
string mainVector = "";
do {
modStore=val%2;
val=val/2;
mainVector = (char)(modStore+48) + mainVector;
}while(val!=0);
return mainVector;
}
string increment(string s) {
int sze = s.size()-1;
if(s[sze] == '0') {
s[sze] = '1';
return s;
}
while(sze >= 0 && s[sze] == '1') {
s[sze] = '0';
sze--;
}
if(sze >= 0) s[sze] = '1';
else s = '1' + s;
return s;
}
main() {
int T;
char s[1000001];
string answer;
scanf("%d", &T);
for(int t = 1; t <= T; t++) {
int num;
answer = "1";
int bitComeEver = 0;
int lastBit = 0;
scanf("%s", s);
int sze = strlen(s);
// I used below block because to avoid TLE.
if(sze > 3300) {
printf( "Case #%d\n", t);
for(int i = 0; i < sze; i++) printf("%c", '1');
printf("\n");
//continue;
}
else {
if(pp[sze-1] != "") answer = pp[sze-1];
else {
pp[sze-1] = power(sze-1);
answer = pp[sze-1];
}
answer = subtract(answer, convert(sze-1));
////////////////////////////
//cout << answer << endl;
for(int i = 1; i < sze; i++) {
if(s[i] == '1') {
if(s[1] == '0') {
num = sze-i-1;
if(num > 0) {
if( pp[num-1] == "") {
pp[num-1] = power(num-1);
}
if(pp[num+1] == "") {
pp[num+1] = power(num+1);
}
answer = add(answer, subtract(pp[num+1], pp[num-1]));
if(lastBit) answer = add(answer, "1");
//else answer = increment(answer);
//cout << "\t\t" << answer << endl;
}
else{
int inc;
if(lastBit) inc = 2; //answer = add(answer, "10");
else inc = 1; //answer = increment(answer);
if(s[i-1] == '0') lastBit = 1;
else lastBit = 0;
if(lastBit) inc += 2;
else inc += 1;
if(inc == 2) answer = add(answer, "10");
else if(inc == 3) answer = add(answer, "11");
else answer = add(answer, "100");
}
}
else {
if(num > 0) {
if(pp[num-1] != "") pp[num-1] = power(num-1);
answer = add(answer, pp[num-1]);
}
else {
int inc = 0;
if(lastBit) inc = 1; //answer = increment(answer);
if(s[i-1] == '0') lastBit = 1;
else lastBit = 0;
if(lastBit) inc += 1;
answer = add(answer, convert(inc));
}
}
if(s[i-1] == '0') lastBit = 1;
else lastBit = 0;
}
}
if(s[sze-1] == '0') {
if(lastBit) {
if(s[1] == '0') {
answer = add(answer, "10");
}
else answer = increment(answer);
}
else if(s[1] == '0'){
answer = increment(answer);
}
}
printf( "Case #%d\n", t);
for(int i = 0; i < sze; i++) printf("%c", answer[i]);
printf("\n");
}
}
return 0;
}

Answer 1

If a number has k bits, then calculate the number of such numbers having a LUCKY FACTOR of 2:
10.............01
Hence in this the 1st two and last two digits are fixed, the remaining k-4 digits can have any value. The number of such numbers = 2^(k-4).
So you can easily calculate the sum of lucky factors of such numbers = lucky_factor x 2^(k-4)
(ofcourse this is assuming k >= 4)
What's more, you do not need to calculate this number since it will be of the form 10000000.
If the number n is 11010010. Then 8 bit numbers less than n shall be of form:
10........ or 1100...... or 1101000_. If you see a pattern, then we have divided the calculation in terms of the number of 1s in the number n
.
I leave the rest for you.