🌟 JavaScript || Professional Approach and In-Depth Explanation
Intuition\nThe problem involves finding the number of submatrices in a given matrix such that the sum of elements in the submatrix is equal to a target value. T
## Intuition\nThe problem involves finding the number of submatrices in a given matrix such that the sum of elements in the submatrix is equal to a target value. The intuition here is to use the cumulative sum to efficiently calculate the sum of elements in any submatrix. By considering all possible pairs of columns and using a hashmap to keep track of cumulative sums, we can efficiently count the submatrices meeting the target sum condition.\n\n## Approach\n1. **Cumulative Sum Precomputation:** Iterate through each row and precompute the cumulative sum for each element in that row. This step is essential for efficient computation of submatrix sums.\n   \n2. **Pair of Columns Iteration:** Use two nested loops to iterate through all possible pairs of columns (`c1` and `c2`). This defines the left and right boundaries of the submatrix.\n\n3. **HashMap for Cumulative Sums:** For each pair of columns, iterate through all rows and calculate the sum of elements in the submatrix formed by those columns. Keep track of the cumulative sum using a hashmap (`map`). \n\n4. **Counting Submatrices:** Update a counter (`count`) based on the occurrences of specific cumulative sums in the hashmap. If the difference between the current cumulative sum and the target sum exists in the hashmap, increment the counter by the corresponding frequency.\n\n5. **Update Hashmap:** Update the hashmap with the current cumulative sum\'s frequency.\n\n## Complexity\n- **Time complexity:** The cumulative sum precomputation takes $$O(rows \\times cols)$$ time. The subsequent pair of columns iteration involves iterating through each element in the matrix, resulting in $$O(rows \\times cols \\times cols)$$ time complexity. Overall, the time complexity is $$O(rows \\times cols \\times cols)$$.\n\n- **Space complexity:** The space complexity is $$O(rows \\times cols)$$ for storing the cumulative sum matrix. Additionally, the hashmap (`map`) has a space complexity of $$O(rows)$$, where each entry corresponds to a unique cumulative sum. Hence, the overall space complexity is $$O(rows \\times cols)$$.\n\n# Code\n```\nvar numSubmatrixSumTarget = function(matrix, target) {\n    const rows = matrix.length;\n    const cols = matrix[0].length;\n\n    // Precompute the cumulative sum for each row\n    for (let row = 0; row < rows; row++) {\n        for (let col = 1; col < cols; col++) {\n            matrix[row][col] += matrix[row][col - 1];\n        }\n    }\n\n    let count = 0;\n\n    // Iterate through all possible pairs of columns\n    for (let c1 = 0; c1 < cols; c1++) {\n        for (let c2 = c1; c2 < cols; c2++) {\n            const map = new Map();\n            map.set(0, 1);\n            let sum = 0;\n\n            // Iterate through all rows and calculate the sum\n            for (let row = 0; row < rows; row++) {\n                sum += matrix[row][c2] - (c1 > 0 ? matrix[row][c1 - 1] : 0);\n\n                // Check if there is a subarray with sum equal to target\n                count += map.get(sum - target) || 0;\n\n                // Update the frequency of the current sum\n                map.set(sum, (map.get(sum) || 0) + 1);\n            }\n        }\n    }\n\n    return count;\n};\n\n```
['JavaScript']