How to find the unique digits in a given range of an array efficiently?

Question

Given an array (not sorted) and few range queries. For each query I need to find the number of unique digits within the given range. Here is the naive approach I came up with.

#include<cstdio>
#include<iostream>
using namespace std;

int main()
{
    int n; scanf("%d",&n); //Size of the array
    int a[n+1]; a[0]=0;

    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);

    int q; scanf("%d",&q); //Number of queries

    while(q--)
    {
        int x,y; scanf("%d %d",&x,&y); //Range of each query
        int bit[n+1];
        for(int i=0;i<=n;i++)
            bit[i]=0;

        for(int i=1;i<=n;i++)
        {
            for(int j=i-1;j>0;j--)
            {
                bit[i]=a[i];
                if(bit[j]==a[i])
                {
                    bit[j]=0;
                    break;
                }
            }
        }
        int cnt=0;
        for(int i=x;i<=y;i++)
        {
            if(bit[i])
                cnt++;
        }
        printf("%d\n",cnt);
    }
    return 0;

}

What is the most efficient way to do this operation? I think this can be done using Binary Indexed tree but couldn't come up with the solution.

No! The array is not sorted. [Now mentioned it in the question] — Wasim Thabraze, Jan 17 '15 at 05:52
possible duplicate of [SPOJ DQUERY : TLE Even With BIT?](http://stackoverflow.com/questions/27656135/spoj-dquery-tle-even-with-bit) — kraskevich, Jan 17 '15 at 10:49
@ILoveCoding Doesn't look like a duplicate. That is unique elements in a subsequence, and this is unique elements in a range. — Imran, Jan 17 '15 at 11:19
@Imran That question it poorly written. If you read more attentively, you will see that is a about ranges. — kraskevich, Jan 17 '15 at 12:22
Oh wow you are right. I wondered how you could possible have found that question, then I saw that you wrote the accepted answer! — Imran, Jan 17 '15 at 12:26

Imran · Answer 1 · 2015-01-17T11:39:59.157

If the number of range queries is small compared to the size of the array, say O(k) vs O(n) where k << n, then:

Put all range endpoints in a balanced binary tree O(klogk)
Make one pass over the array and count unique elements in each subrange. Use a hash table to remember which elements we have already seen. O(n)
Do an in-order traversal between range endpoints for each range query and sum subrange totals. O(k^2) worst case / O(klogk) for reasonable queries.

How to find the unique digits in a given range of an array efficiently?

1 Answers1