Trying to do some practice and I ran across this problem...
Given two int arrays A and B, and an int c, return the total number of pairs (a, b) where a is from A and b is from B, and a + b is <= c
Came up with brute force solution immediately, but can't seem to connect the dots in order to do this in better time complexity. I tried sorting the arrays first, and trying to find some type of pattern but that didn't get me anywhere. I thought about cases where one array had negative numbers. In this case, I cant just look at a value from A or B and check if it itself is less than c, because there may be a negative value in the other array that when added together gives me a result of <= c. Any insight, or ideas, or clues would be appreciated.
import java.util.*;
public class CountPairs {
public static void main(String args[]){
int arrayA[] = {32,45,9,4};
int arrayB[] = {43,457,54,90};
Scanner scan = new Scanner(System.in);
System.out.println("Choose the value that you want to find pairs <= ");
int c = scan.nextInt();
System.out.println("The total number of pairs are : " + pairs(arrayA, arrayB, c));
}
public static int pairs(int A[], int B[], int n) {
int count = 0;
for (int i = 0; i < A.length; i++) {
for (int j = 0; j < B.length; j++) {
int total = A[i] + B[j];
if(total <= n)
count++;
}
}
return count;
}
}
We can solve this in O(m log m + n log m) = O(log m (m + n)) time where m is the cardinality of the smaller array; n, the larger. First, sort the smaller array:
A = {32,45,9,4};
B = {43,457,54,90};
=> A = {4,9,32,45}
Now for each b in B, use a binary search on A to find the index of the greatest a less than or equal to (c - b). Add (index + 1) to the accumulating result. For example:
c = 100:
43 => 100 - 43 = 57 => largest a <= c-b = 45, index 3 => add 4 to result
457 => 100 - 457 = -357 => largest a <= c-b = None
54 => 100 - 54 = 46 => largest a <= c-b = 45, index 3 => add 4 to result
90 => 100 - 90 = 10 => largest a <= c-b = 9, index 1 => add 2 to result
result = 4 + 4 + 2 = 10
corresponding with the following pairs:
(43,4),(43,9),(43,32),(43,45),(54,4),(54,9),(54,32),(54,45),(90,4),(9,9)