# 7. Equal Sum Arrays With Minimum Number of Operations

You are given two arrays of integers `nums1` and `nums2`, possibly of different lengths. The values in the arrays are between `1` and `6`, inclusive.

In one operation, you can change any integer's value in **any** of the arrays to **any** value between `1` and `6`, inclusive.

Return *the minimum number of operations required to make the sum of values in* `nums1` *equal to the sum of values in* `nums2`*.* Return `-1`​​​​​ if it is not possible to make the sum of the two arrays equal.

```
Example 1:
Input: nums1 = [1,2,3,4,5,6], nums2 = [1,1,2,2,2,2]
Output: 3
Explanation: You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed.
- Change nums2[0] to 6. nums1 = [1,2,3,4,5,6], nums2 = [6,1,2,2,2,2].
- Change nums1[5] to 1. nums1 = [1,2,3,4,5,1], nums2 = [6,1,2,2,2,2].
- Change nums1[2] to 2. nums1 = [1,2,2,4,5,1], nums2 = [6,1,2,2,2,2].

Example 2:
Input: nums1 = [1,1,1,1,1,1,1], nums2 = [6]
Output: -1
Explanation: There is no way to decrease the sum of nums1 or to increase the sum of nums2 to make them equal.
Example 3:
Input: nums1 = [6,6], nums2 = [1]

Output: 3
Explanation: You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed. 
- Change nums1[0] to 2. nums1 = [2,6], nums2 = [1].
- Change nums1[1] to 2. nums1 = [2,2], nums2 = [1].
- Change nums2[0] to 4. nums1 = [2,2], nums2 = [4].
```

## Solution: (Greedy)

**1.In order to make the two sum's equal, we need either to increase to `6` the numbers in the smaller sum array or decrease to `1` the numbers in the bigger sum array**

**2. Since we want to complete the task with minimum operations, it is optimal to choose the greater between the increase and decrease. Hence this is a greedy algorithm.**

**Note:**\
**If all numbers in an array increasing to `6` still ends up with a sum less than the sum of the other array with all numbers decreasing to `1`'s, then it is impossible to make their sums equal.**

```cpp
class Solution
{
public:
    int minOperations(vector<int> &nums1, vector<int> &nums2)
    {

        sort(nums1.begin(), nums1.end(), greater<int>());
        sort(nums2.begin(), nums2.end());

        int s1 = 0, s2 = 0;
        for (int i = 0; i < nums1.size(); i++)
        {
            s1 += nums1[i];
        }

        for (int i = 0; i < nums2.size(); i++)
        {
            s2 += nums2[i];
        }

        if (s2 > s1)
        {
            return minOperations(nums2, nums1);
        }

        if (nums1.size() > 6 * nums2.size())
        {
            return -1;
        }

        int i = 0;
        int j = 0;
        int ops = 0;

        while (s1 > s2)
        {

            if (i < nums1.size() && j < nums2.size())
            {
                int d1 = nums1[i] - 1;
                int d2 = 6 - nums2[j];

                if (d1 > d2)
                {
                    s1 = s1 - d1;
                    i++;
                }
                else
                {
                    s2 = s2 + d2;
                    j++;
                }

                ops++;
            }
            else
            {
                break;
            }
        }

        while (s1 > s2)
        {
            if (i < nums1.size())
            {
                s1 = s1 - (nums1[i] - 1);
                i++;
                ops++;
            }
        }

        while (s1 > s2)
        {
            if (j < nums2.size())
            {
                s2 = s2 + (6 - nums2[j]);
                j++;
                ops++;
            }
        }
        return ops;
    }
};
```

**Time Complexity: O max(n + m)**


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://soumyajit4419.gitbook.io/ds-algo/greedy-algorithms/untitled.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.