New Problem "Range Sum Query 2D - Immutable"

Hao Chen · Hao Chen · commit d99a27c05812 · 2015-11-14T11:29:19.000+08:00
diff --git a/README.md b/README.md
@@ -8,6 +8,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|304|[Range Sum Query 2D - Immutable](https://leetcode.com/problems/range-sum-query-2d-immutable/) | [C++](./algorithms/cpp/rangeSumQuery2D-Immutable/RangeSumQuery2dImmutable.cpp)|Medium|
 |303|[Range Sum Query - Immutable](https://leetcode.com/problems/range-sum-query-immutable/)  | [C++](./algorithms/cpp/rangeSumQuery-Immutable/rangeSumQuery-Immutable.cpp)|Easy|
 |301|[Remove Invalid Parentheses](https://leetcode.com/problems/remove-invalid-parentheses/) | [C++](./algorithms/cpp/removeInvalidParentheses/RemoveInvalidParentheses.cpp) |Hard|
 |300|[Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)  | [C++](./algorithms/cpp/longestIncreasingSubsequence/longestIncreasingSubsequence.cpp)|Medium|
diff --git a/algorithms/cpp/rangeSumQuery2D-Immutable/RangeSumQuery2dImmutable.cpp b/algorithms/cpp/rangeSumQuery2D-Immutable/RangeSumQuery2dImmutable.cpp
@@ -0,0 +1,103 @@
+// Source : https://leetcode.com/problems/range-sum-query-2d-immutable/
+// Author : Hao Chen
+// Date   : 2015-11-14
+
+/*************************************************************************************** 
+ *
+ * Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined 
+ * by its upper left corner (row1, col1) and lower right corner (row2, col2).
+ * 
+ * The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and 
+ * (row2, col2) = (4, 3), which contains sum = 8.
+ * 
+ * Example:
+ * 
+ * Given matrix = [
+ *   [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]
+ * ]
+ * 
+ * sumRegion(2, 1, 4, 3) -> 8
+ * sumRegion(1, 1, 2, 2) -> 11
+ * sumRegion(1, 2, 2, 4) -> 12
+ * 
+ * Note:
+ * 
+ * You may assume that the matrix does not change.
+ * There are many calls to sumRegion function.
+ * You may assume that row1 ≤ row2 and col1 ≤ col2.
+ * 
+ ***************************************************************************************/
+
+
+/*
+ * 
+ * Construct a 2D array `sums[row+1][col+1]`
+ * 
+ * (**notice**: we add additional blank row `sums[0][col+1]={0}` and blank column `sums[row+1][0]={0}` 
+ * to remove the edge case checking), so, we can have the following definition 
+ * 
+ *     `sums[i+1][j+1]` represents the sum of area from `matrix[0][0]` to `matrix[i][j]`
+ * 
+ * To calculate sums, the ideas as below
+ * 
+ *     +-----+-+-------+     +--------+-----+     +-----+---------+     +-----+--------+
+ *     |     | |       |     |        |     |     |     |         |     |     |        |
+ *     |     | |       |     |        |     |     |     |         |     |     |        |
+ *     +-----+-+       |     +--------+     |     |     |         |     +-----+        |
+ *     |     | |       |  =  |              |  +  |     |         |  -  |              |
+ *     +-----+-+       |     |              |     +-----+         |     |              |
+ *     |               |     |              |     |               |     |              |
+ *     |               |     |              |     |               |     |              |
+ *     +---------------+     +--------------+     +---------------+     +--------------+
+ *     
+ *        sums[i][j]      =    sums[i-1][j]    +     sums[i][j-1]    -   sums[i-1][j-1]   +  
+ * 
+ *                             matrix[i-1][j-1]
+ * 
+ * So, we use the same idea to find the specific area's sum.
+ * 
+ * 
+ * 
+ *     +---------------+   +--------------+   +---------------+   +--------------+   +--------------+
+ *     |               |   |         |    |   |   |           |   |         |    |   |   |          |
+ *     |   (r1,c1)     |   |         |    |   |   |           |   |         |    |   |   |          |
+ *     |   +------+    |   |         |    |   |   |           |   +---------+    |   +---+          |
+ *     |   |      |    | = |         |    | - |   |           | - |      (r1,c2) | + |   (r1,c1)    |
+ *     |   |      |    |   |         |    |   |   |           |   |              |   |              |
+ *     |   +------+    |   +---------+    |   +---+           |   |              |   |              |
+ *     |        (r2,c2)|   |       (r2,c2)|   |   (r2,c1)     |   |              |   |              |
+ *     +---------------+   +--------------+   +---------------+   +--------------+   +--------------+
+ * 
+ * 
+ */
+
+class NumMatrix {
+private:
+    int row, col;
+    vector<vector<int>> sums;
+public:
+    NumMatrix(vector<vector<int>> &matrix) {
+        row = matrix.size();
+        col = row>0 ? matrix[0].size() : 0;
+        sums = vector<vector<int>>(row+1, vector<int>(col+1, 0));
+        for(int i=1; i<=row; i++) {
+            for(int j=1; j<=col; j++) {
+                sums[i][j] = sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1] + matrix[i-1][j-1];
+            }
+        }
+    }
+
+    int sumRegion(int row1, int col1, int row2, int col2) {
+        return sums[row2+1][col2+1] - sums[row2+1][col1] - sums[row1][col2+1] + sums[row1][col1];
+    }
+};
+
+
+// Your NumMatrix object will be instantiated and called as such:
+// NumMatrix numMatrix(matrix);
+// numMatrix.sumRegion(0, 1, 2, 3);
+// numMatrix.sumRegion(1, 2, 3, 4);
