1865 - Finding Pairs With a Certain Sum.

Medium

You are given two integer arrays nums1 and nums2. You are tasked to implement a data structure that supports queries of two types:

• Add a positive integer to an element of a given index in the array nums2.

• Count the number of pairs (i, j) such that nums1[i] + nums2[j] equals a given value (0 <= i < nums1.length and 0 <= j < nums2.length).

Implement the FindSumPairs class:

• FindSumPairs(int[] nums1, int[] nums2) Initializes the FindSumPairs object with two integer arrays nums1 and nums2.

• void add(int index, int val) Adds val to nums2[index], i.e., apply nums2[index] += val.

• int count(int tot) Returns the number of pairs (i, j) such that nums1[i] + nums2[j] == tot.

Example 1:

Input "FindSumPairs", "count", "add", "count", "count", "add", "add", "count" [[1, 1, 2, 2, 2, 3, 1, 4, 5, 2, 5, 4], 7, 3, 2, 8, 4, 0, 1, 1, 1, 7]

Output: null, 8, null, 2, 1, null, null, 11

Explanation:

FindSumPairs findSumPairs = new FindSumPairs(1, 1, 2, 2, 2, 3, 1, 4, 5, 2, 5, 4);

findSumPairs.count(7); // return 8; pairs (2,2), (3,2), (4,2), (2,4), (3,4), (4,4) make 2 + 5 and pairs (5,1), (5,5) make 3 + 4

findSumPairs.add(3, 2); // now nums2 = 1,4,5, **4**`,5,4`

findSumPairs.count(8); // return 2; pairs (5,2), (5,4) make 3 + 5

findSumPairs.count(4); // return 1; pair (5,0) makes 3 + 1

findSumPairs.add(0, 1); // now nums2 = **`2` ** ,4,5,4`,5,4`

findSumPairs.add(1, 1); // now nums2 = `2`, **5** ,5,4`,5,4`

findSumPairs.count(7); // return 11; pairs (2,1), (2,2), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,4) make 2 + 5 and pairs (5,3), (5,5) make 3 + 4

Constraints:

• 1 <= nums1.length <= 1000

• <code>1 <= nums2.length <= 10⁵</code>

• <code>1 <= nums1i<= 10⁹</code>

• <code>1 <= nums2i<= 10⁵</code>

• 0 <= index < nums2.length

• <code>1 <= val <= 10⁵</code>

• <code>1 <= tot <= 10⁹</code>

• At most 1000 calls are made to add and count each.