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Queries for decimal values of subarrays of a binary array in C++
In this problem, we are given a binary array bin[] and Q queries each consists of two values L and R. Our task is to create a program to solve queries for decimal values of subarrays of a binary array in C++.
Problem description − Here to solve each query, we will have to find and print the decimal number which is created by the subarray starting from L to R i.e. subarray[L...R].
Let’s take an example to understand the problem,
Input
bin[] = {1, 1, 0, 0, 1, 0, 1, 0, 0, 0}
Q = 2
2 5
0 6Output
2 101
Explanation
For query 1, the subarray formed is { 0, 0, 1, 0}. It will create the binary number 0010 whose decimal conversion is 2.
For query 2, the subarray formed is { 1, 1, 0, 0, 1, 0, 1}. It will create the binary number 1100101 whose decimal conversion is 101.
Solution approach
A simple solution is by traversing the binary string from index L to index R, find the binary number which is formed, and then convert the given binarynumber to its decimal equivalent.
Program to show the implementation of our approach
Example
#include <iostream>
#include <math.h>
using namespace std;
int CalcDecimalValue(int bin[], int L, int R) {
int decimal = 0;
int j = 0;
for(int i = R; i >= L; i--){
decimal += bin[i] * pow(2, j);
j++;
}
return decimal;
}
int main() {
int bin[] = {1, 1, 0, 0, 1, 0, 1, 0, 0, 0};
int n = sizeof(bin) / sizeof(bin[0]);
int Q = 2;
int query[Q][2] = {{2, 5},{0, 6}};
for(int i = 0; i < Q; i++){
cout<<"For query "<<(i+1)<<": The decimal value of subarray is "<<CalcDecimalValue(bin, query[i] [0], query[i][1])<<"\n";
}
return 0;
}Output
For query 1: The decimal value of subarray is 2 For query 2: The decimal value of subarray is 101
Another approach to solving the problem is by using a pre-computed array. We will create a precomputed array that will store the decimal number created until the (n-i)th index value. And for solving queries, we will find the difference between the value at l and r.
The ith value of the array will be found using the binary to decimal conversion formula. Appling it from the right side, i.e. from n-1,
decimalArray[i] = bin[i]*2^(n-1-i) + bin[i+1]*2^(n-1-i+1) + … bin[n- 1]*2^(0).
Program to illustrate the working of our solution,
Example
#include <bits/stdc++.h>
using namespace std;
int decimalArray[1000];
void createDecimalArray(int bin[], int n){
memset(decimalArray, 0, n*sizeof(int));
decimalArray[n - 1] = bin[n - 1] * pow(2, 0);
for (int i = n - 2; i >= 0; i--)
decimalArray[i] = decimalArray[i + 1] + bin[i] * (pow(2,(n - 1 - i)));
}
int CalcDecimalValue(int L, int R, int n){
if (R != n - 1)
return (decimalArray[L] - decimalArray[R + 1]) / (pow(2, (n - 1 - R)));
return decimalArray[L] / (1 << (n - 1 - R));
}
int main(){
int bin[] = {1, 1, 0, 0, 1, 0, 1, 0, 0, 0};
int n = sizeof(bin) / sizeof(bin[0]);
createDecimalArray(bin, n);
int Q = 2;
int query[Q][2] = {{2, 5},{0, 6}};
for(int i = 0; i < Q; i++){
cout<<"For query "<<(i+1)<<": The decimal value of subarray is "<<CalcDecimalValue(query[i][0], query[i][1], n)<<"\n";
}
return 0;
}Output
For query 1: The decimal value of subarray is 2 For query 2: The decimal value of subarray is 101
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