New Problem"Range Sum Query - Mutable"

Author: haoel

README.md

@@ -8,6 +8,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|307|[Range Sum Query - Mutable](Range Sum Query - Mutable) | [C++](./algorithms/cpp/rangeSumQuery-Immutable/rangeSumQuery-Mutable/RangeSumQueryMutable.cpp)|Medium|
 |306|[Additive Number](https://leetcode.com/problems/additive-number/) | [C++](./algorithms/cpp/additiveNumber/AdditiveNumber.cpp)|Medium|
 |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|

algorithms/cpp/rangeSumQuery-Immutable/rangeSumQuery-Mutable/RangeSumQueryMutable.cpp

@@ -0,0 +1,75 @@
+// Source : https://leetcode.com/problems/range-sum-query-mutable/
+// Author : Hao Chen
+// Date   : 2015-11-24
+
+/*************************************************************************************** 
+ *
+ * Given an integer array nums, find the sum of the elements between indices i and j (i 
+ * ≤ j), inclusive.
+ * 
+ * The update(i, val) function modifies nums by updating the element at index i to val.
+ * 
+ * Example:
+ * 
+ * Given nums = [1, 3, 5]
+ * 
+ * sumRange(0, 2) -> 9
+ * update(1, 2)
+ * sumRange(0, 2) -> 8
+ * 
+ * Note:
+ * 
+ * The array is only modifiable by the update function.
+ * You may assume the number of calls to update and sumRange function is distributed 
+ * evenly.
+ *
+ ***************************************************************************************/
+
+
+// The following idea is using `Binary Index Tree`
+// There are two articles explaine this technique quite well:
+// 1) http://www.geeksforgeeks.org/binary-indexed-tree-or-fenwick-tree-2/
+// 2) http://cs.stackexchange.com/questions/10538/bit-what-is-the-intuition-behind-a-binary-indexed-tree-and-how-was-it-thought-a
+
+class NumArray {
+private:
+    int _sz;
+    vector<int> _nums;
+    vector<int> _sums;    
+public:
+    NumArray(vector<int> &nums)  {
+        _sz = nums.size();
+        _nums.resize(_sz+1, 0);
+        _sums.resize(_sz+1, 0);
+        for(int i=0; i< _sz; i++) {
+            update(i, nums[i]);          
+        }
+    }
+
+    void update(int i, int val) {
+        int oldv = _nums[i+1];
+        for(int idx = i+1; idx <= _sz; idx += (idx & (-idx))  ) {
+            _sums[idx] = _sums[idx] - oldv + val;
+        }
+        _nums[i+1] = val;
+    }
+
+    int sumRange(int i, int j) {
+        return sumRange(j+1) - sumRange(i);
+    }
+    
+    int sumRange(int i) {
+        int ret = 0;
+        for(int idx=i; idx>0; idx -= (idx & (-idx)) ) {
+            ret += _sums[idx];
+        }
+        return ret;
+    }
+};
+
+
+// Your NumArray object will be instantiated and called as such:
+// NumArray numArray(nums);
+// numArray.sumRange(0, 1);
+// numArray.update(1, 10);
+// numArray.sumRange(1, 2);