# 1865. Finding Pairs With a Certain Sum

## Description

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

1. Add a positive integer to an element of a given index in the array nums2.
2. 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
[[[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
• 1 <= nums2.length <= 105
• 1 <= nums1[i] <= 109
• 1 <= nums2[i] <= 105
• 0 <= index < nums2.length
• 1 <= val <= 105
• 1 <= tot <= 109
• At most 1000 calls are made to add and count each.

## Solutions

• class FindSumPairs {
private int[] nums1;
private int[] nums2;
private Map<Integer, Integer> cnt = new HashMap<>();

public FindSumPairs(int[] nums1, int[] nums2) {
this.nums1 = nums1;
this.nums2 = nums2;
for (int v : nums2) {
cnt.put(v, cnt.getOrDefault(v, 0) + 1);
}
}

public void add(int index, int val) {
int old = nums2[index];
cnt.put(old, cnt.get(old) - 1);
cnt.put(old + val, cnt.getOrDefault(old + val, 0) + 1);
nums2[index] += val;
}

public int count(int tot) {
int ans = 0;
for (int v : nums1) {
ans += cnt.getOrDefault(tot - v, 0);
}
return ans;
}
}

/**
* Your FindSumPairs object will be instantiated and called as such:
* FindSumPairs obj = new FindSumPairs(nums1, nums2);
* int param_2 = obj.count(tot);
*/

• class FindSumPairs {
public:
FindSumPairs(vector<int>& nums1, vector<int>& nums2) {
this->nums1 = nums1;
this->nums2 = nums2;
for (int& v : nums2) {
++cnt[v];
}
}

void add(int index, int val) {
int old = nums2[index];
--cnt[old];
++cnt[old + val];
nums2[index] += val;
}

int count(int tot) {
int ans = 0;
for (int& v : nums1) {
ans += cnt[tot - v];
}
return ans;
}

private:
vector<int> nums1;
vector<int> nums2;
unordered_map<int, int> cnt;
};

/**
* Your FindSumPairs object will be instantiated and called as such:
* FindSumPairs* obj = new FindSumPairs(nums1, nums2);
* int param_2 = obj->count(tot);
*/

• class FindSumPairs:
def __init__(self, nums1: List[int], nums2: List[int]):
self.nums1 = nums1
self.nums2 = nums2
self.cnt = Counter(nums2)

def add(self, index: int, val: int) -> None:
old = self.nums2[index]
self.cnt[old] -= 1
self.cnt[old + val] += 1
self.nums2[index] += val

def count(self, tot: int) -> int:
return sum(self.cnt[tot - v] for v in self.nums1)

# Your FindSumPairs object will be instantiated and called as such:
# obj = FindSumPairs(nums1, nums2)
# param_2 = obj.count(tot)


• type FindSumPairs struct {
nums1 []int
nums2 []int
cnt   map[int]int
}

func Constructor(nums1 []int, nums2 []int) FindSumPairs {
cnt := map[int]int{}
for _, v := range nums2 {
cnt[v]++
}
return FindSumPairs{nums1, nums2, cnt}
}

func (this *FindSumPairs) Add(index int, val int) {
old := this.nums2[index]
this.cnt[old]--
this.cnt[old+val]++
this.nums2[index] += val
}

func (this *FindSumPairs) Count(tot int) (ans int) {
for _, v := range this.nums1 {
ans += this.cnt[tot-v]
}
return
}

/**
* Your FindSumPairs object will be instantiated and called as such:
* obj := Constructor(nums1, nums2);