Question

I wrote a solution for a question on interviewstreet, here is the problem description:

https://www.interviewstreet.com/challenges/dashboard/#problem/4e91289c38bfd

Here is the solution they have given:

https://gist.github.com/1285119

Here is the solution that I coded:

#include<iostream>
#include <string.h>
using namespace std;
#define LOOKUPTABLESIZE 10000000
int popCount[2*LOOKUPTABLESIZE];
int main()
{
int numberOfTests = 0;
cin >> numberOfTests;

for(int test = 0;test<numberOfTests;test++)
{
    int startingNumber = 0;
    int endingNumber = 0;
    cin >> startingNumber >> endingNumber;

    int numberOf1s = 0;


    for(int number=startingNumber;number<=endingNumber;number++)
    {
        if(number >-LOOKUPTABLESIZE && number < LOOKUPTABLESIZE)
        {
            if(popCount[number+LOOKUPTABLESIZE] != 0)
            {
                numberOf1s += popCount[number+LOOKUPTABLESIZE];
            }
            else
            {
                popCount[number+LOOKUPTABLESIZE] =__builtin_popcount (number);
                numberOf1s += popCount[number+LOOKUPTABLESIZE];
            }
        }
        else
        {
        numberOf1s += __builtin_popcount (number);
        }
    }
    cout << numberOf1s << endl;

}

}

Can you please point me what is wrong with my code? It can only pass 3/10 of tests. The time limit is 3 seconds.

Answer 1

What is unoptimized about this code?

The algorithm. You are looping

for(int number=startingNumber;number<=endingNumber;number++)

computing or looking up the number of 1-bits in each. That can take a while.

A good algorithm counts the number of 1-bits in all numbers 0 <= k < n in O(log n) time using a bit of math.

Here is an implementation counting 0s in decimal expansions, the modification to make it count 1-bits shouldn’t be hard.