Easiest Sol with Detailed Explanation
\n# Approach\nisRegion Function:\n\nThe isRegion function checks if a 3x3 subgrid starting at position (x, y) forms a region based on the given threshold (t).\n
\n# Approach\n**isRegion Function:\n**\nThe isRegion function checks if a 3x3 subgrid starting at position (x, y) forms a region based on the given threshold (t).\nIt iterates through the subgrid and compares the intensity difference between adjacent pixels (right and below) with the threshold.\nIf any of the conditions are violated, the function returns false, indicating that the subgrid is not a valid region. Otherwise, it returns true.\n\n**findAvg Function:\n**\nThe findAvg function calculates the average intensity of a 3x3 subgrid starting at position (x, y).\nIt maintains a sum variable to accumulate the intensities and a count variable to keep track of the number of valid pixels.\nIt iterates through the subgrid, checks if each pixel is within the image boundaries, updates the sum and count accordingly, and returns the rounded-down average intensity.\n\n**fill Function:\n**\nThe fill function updates the result matrix (ans) with the average intensity values for a region.\nIt iterates through the 3x3 subgrid starting at position (x, y), updates the running sum and count matrices (sum and count), and calculates the new average intensity for each pixel in the region.\nThe updated average intensity values are then assigned to the corresponding positions in the result matrix.\n\n**Main Loop:\n**\nThe main loop iterates through the image, considering each 3x3 subgrid as a potential region.\nIf a subgrid is identified as a valid region using the isRegion function, the average intensity is calculated with the findAvg function.\nThe fill function is called to update the result matrix with the calculated average intensity values.\nFinal Update:\n\nAfter processing all potential regions, the result matrix is checked for pixels that were not part of any region. If a pixel was not part of a region, its original intensity is retained in the result matrix.\nThis approach ensures that each pixel in the result matrix is assigned the correct average intensity based on the identified regions in the image, rounding down as required. The use of additional matrices (sum and count) helps efficiently maintain running sums and counts during the processing of regions.\n\n# Complexity\n- Time complexity:\nO(n^2)\n- Space complexity:\nO(n^2)\n# Code\n```\nclass Solution {\nprivate:\n    bool isRegion(vector<vector<int>>& img, int x, int y, int t){\n        for(int i=x; i<x+3; i++){\n            for(int j=y; j<y+3; j++){\n                // Check the pixel to the right\n                if(j<y+2 && abs(img[i][j] - img[i][j+1]) > t){\n                    return false;\n                } \n                // Check the pixel below\n                if(i<x+2 && abs(img[i][j] - img[i+1][j]) > t){\n                    return false;\n                } \n            }\n        }\n        return true;\n    }\n\n    int findAvg(vector<vector<int>>& img, int x, int y){\n        int sum = 0;\n        int count = 0;\n\n        for(int i=x; i<x+3; i++){\n            for(int j=y; j<y+3; j++){\n                if(i >= 0 && i < n && j >= 0 && j < m) {\n                    sum += img[i][j];\n                    count++;\n                }\n            }\n        }\n\n        return (count > 0) ? (sum / count) : -1;\n    }\n\n    void fill(vector<vector<int>> &ans, vector<vector<int>> &sum, vector<vector<int>> &count, int x, int y, int avg){\n        for(int i=x; i<x+3; i++){\n            for(int j=y; j<y+3; j++){\n                sum[i][j] += avg;\n                count[i][j]++;\n                ans[i][j] = sum[i][j] / count[i][j];\n            }\n        }\n    }\n\npublic:\n    int n, m;\n\n    vector<vector<int>> resultGrid(vector<vector<int>>& img, int t) {\n        n = img.size();\n        m = img[0].size();\n\n        vector<vector<int>> ans(n, vector<int>(m, -1));\n        vector<vector<int>> sum(n, vector<int>(m, 0));\n        vector<vector<int>> count(n, vector<int>(m, 0));\n\n        for(int i=0; i<n-2; i++){\n            for(int j=0; j<m-2; j++){\n                \n                if(isRegion(img, i, j, t)){\n                    int avg = findAvg(img, i, j);\n                    \n                    fill(ans, sum, count, i, j, avg);\n                }\n            }\n        }\n\n        for(int i=0; i<n; i++){\n            for(int j=0; j<m; j++){\n                if(ans[i][j] == -1){\n                    ans[i][j] = img[i][j];\n                }\n            }\n        }\n\n        return ans;\n    }\n};\n\n```
['C++']