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we are given 4 integers, where a <= b , c <= d.
We have to find Sum of Xor of all the pairs (i,j) such that ( a <= i <= b , && c <= j <= d )
int sum = 0;
for(int i=a ; i <= b; i++) {
for(int j = c; j <= d ; j++) {
sum += (i ^ j)
}
}
return sum;
How to find this sum optimally ?
For each x calculate the effect of 2^x on the answer.
The problem then becomes 32 "at position i, calculate how many zeros are in a certain interval". After getting the number of 1's and 0's just multiply them together. Then add up all the answers and you're done.