Sync LeetCode submission Runtime - 117 ms (57.65%), Memory - 31.1 MB (8.46%)

Author: jimit105

0304-range-sum-query-2d---immutable/README.md

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+<p>Given a 2D matrix <code>matrix</code>, handle multiple queries of the following type:</p>
+
+<ul>
+	<li>Calculate the <strong>sum</strong> of the elements of <code>matrix</code> inside the rectangle defined by its <strong>upper left corner</strong> <code>(row1, col1)</code> and <strong>lower right corner</strong> <code>(row2, col2)</code>.</li>
+</ul>
+
+<p>Implement the <code>NumMatrix</code> class:</p>
+
+<ul>
+	<li><code>NumMatrix(int[][] matrix)</code> Initializes the object with the integer matrix <code>matrix</code>.</li>
+	<li><code>int sumRegion(int row1, int col1, int row2, int col2)</code> Returns the <strong>sum</strong> of the elements of <code>matrix</code> inside the rectangle defined by its <strong>upper left corner</strong> <code>(row1, col1)</code> and <strong>lower right corner</strong> <code>(row2, col2)</code>.</li>
+</ul>
+
+<p>You must design an algorithm where <code>sumRegion</code> works on <code>O(1)</code> time complexity.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/03/14/sum-grid.jpg" style="width: 415px; height: 415px;" />
+<pre>
+<strong>Input</strong>
+[&quot;NumMatrix&quot;, &quot;sumRegion&quot;, &quot;sumRegion&quot;, &quot;sumRegion&quot;]
+[[[[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
+<strong>Output</strong>
+[null, 8, 11, 12]
+
+<strong>Explanation</strong>
+NumMatrix numMatrix = new NumMatrix([[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]);
+numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
+numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
+numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle)
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>m == matrix.length</code></li>
+	<li><code>n == matrix[i].length</code></li>
+	<li><code>1 &lt;= m, n &lt;= 200</code></li>
+	<li><code>-10<sup>4</sup> &lt;= matrix[i][j] &lt;= 10<sup>4</sup></code></li>
+	<li><code>0 &lt;= row1 &lt;= row2 &lt; m</code></li>
+	<li><code>0 &lt;= col1 &lt;= col2 &lt; n</code></li>
+	<li>At most <code>10<sup>4</sup></code> calls will be made to <code>sumRegion</code>.</li>
+</ul>

0304-range-sum-query-2d---immutable/solution.py

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+# Approach 4: Caching Smarter
+
+# m = no. of rows, n = no. of cols
+# Time: O(1) per query, O(mn) for pre-computation
+# Space: O(mn)
+
+class NumMatrix:
+
+    def __init__(self, matrix: List[List[int]]):
+        if not matrix or not matrix[0]:
+            return
+
+        rows, cols = len(matrix), len(matrix[0])
+        self.dp = [[0] * (cols + 1) for _ in range(rows + 1)]
+
+        for r in range(rows):
+            for c in range(cols):
+                self.dp[r + 1][c + 1] = self.dp[r + 1][c] \
+                                        + self.dp[r][c + 1] \
+                                        - self.dp[r][c] \
+                                        + matrix[r][c]
+        
+
+    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
+        return self.dp[row2 + 1][col2 + 1] \
+            - self.dp[row1][col2 + 1] \
+            - self.dp[row2 + 1][col1] \
+            + self.dp[row1][col1]
+        
+
+
+# Your NumMatrix object will be instantiated and called as such:
+# obj = NumMatrix(matrix)
+# param_1 = obj.sumRegion(row1,col1,row2,col2)