Queries for decimal values of subarrays of a binary array

3

Given a binary array arr[], we to find the number represented by the subarray a[l..r]. There are multiple such queries.

Examples:

Input :  arr[] = {1, 0, 1, 0, 1, 1};
         l = 2, r = 4
         l = 4, r = 5
Output : 5
         3 
Subarray 2 to 4 is 101 which is 5 in decimal.
Subarray 4 to 5 is 11 which is 3 in decimal.

Input : arr[] = {1, 1, 1}
        l = 0, r = 2
        l = 1, r = 2
Output : 7
         3

A Simple Solution is to compute decimal value for every given range using simple binary to decimal conversion. Here each query takes O(len) time where len is length of range.

An Efficient Solution is to do per-computations, so that queries can be answered in O(1) time.
The number represented by subarray arr[l..r] is arr[l]*2^{r-l} + arr[l+1]*2^{r - l - 1}….. + arr[r]*2^{r-r}

  1. Make an array pre[] of same size as of given array where pre[i] stores the sum of arr[j]*2^{n - 1 - j} where j includes each value from i to n-1.
  2. The number represented by subarray arr[l..r] will be equal to (pre[l] – pre[r+1])/2^{n-1-r}.pre[l] – pre[r+1] is equal to arr[l]*2^{n - 1 - l} + arr[l+1]*2^{n - 1 - l - 1} +……arr[r]*2^{n - 1 - r}. So if we divide it by 2^{n - 1 - r}, we get the required answer
// C++ implementation of finding number
// represented by binary subarray
#include<bits/stdc++.h>
using namespace std;

// Fills pre[] 
void precompute(int arr[], int n, int pre[])
{
    memset(pre, 0, n*sizeof(int));
    pre[n-1] = arr[n-1]*pow(2, 0);
    for (int i=n-2; i>=0; i--)
        pre[i] = pre[i+1] + arr[i]*(1 << (n-1-i));
}

// returns the number represented by a binary
// subarray l to r
int decimalOfSubarr(int arr[], int l, int r,
                            int n, int pre[])
{
    // if r is equal to n-1 r+1 does not exist
    if (r != n-1)
       return (pre[l] - pre[r+1]) / (1 << (n-1-r));

    return pre[l] / (1 << (n-1-r));
}

// Driver Function
int main()
{
    int arr[] = {1, 0, 1, 0, 1, 1};
    int n = sizeof(arr)/sizeof(arr[0]);

    int pre[n];
    precompute(arr, n, pre);
    cout << decimalOfSubarr(arr, 2, 4, n, pre) << endl;
    cout << decimalOfSubarr(arr, 4, 5, n, pre) << endl;
    return 0;
}

Output:

5
3

This article is contributed by Ayush Jha. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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