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Author: assassint2017

Range Sum Query - Mutable/Range_Sum_Query_Mutable.cpp

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+// 如果使用常规操作，查询和更新两个操作一个是on的复杂度，另外一个是o1的复杂度，但是如果使用
+// 区间树，就可以将两个操作都变成logn的复杂度
+
+// Runtime: 32 ms, faster than 91.34% of C++ online submissions for Range Sum Query - Mutable.
+// Memory Usage: 19.7 MB, less than 8.33% of C++ online submissions for Range Sum Query - Mutable.
+
+struct cell
+{
+	cell() : start(-1), end(-1), sum(0) {}
+	int start, end;
+	int sum;
+};
+
+class NumArray
+{
+public:
+
+	// 构建区间树
+	NumArray(vector<int>& nums)
+	{
+		// 边界条件处理
+		if (nums.size() == 0) return;
+
+		// 计算数组的大小
+		int rightPtr = nums.size() - 1, layer = 1;
+		while (rightPtr)
+			rightPtr /= 2, ++layer;
+
+		// 在定义默认构造函数后，这样做之后每个新添加上的元素会按照默认构造进行初始化
+		tree.resize(pow(2, layer) - 1);
+
+        // 建立线段树
+		buildSegmentTree(0, nums.size() - 1, 0, nums);
+	}
+
+	// 更新区间树中的元素 logn的时间复杂度
+	void update(int i, int val)
+	{
+		if (tree.size() != 0)
+		{
+			int start = 0, end = tree.front().end;
+			int index = 0;
+
+			// dfs查找
+			while (start != end)
+			{
+				int mid = (start + end) / 2;
+				if (mid >= i)
+					end = mid, index = index * 2 + 1;
+				else
+					start = mid + 1, index = index * 2 + 2;
+			}
+
+			int offset = val - tree[index].sum;
+
+			// 回溯整个路径
+			while (true)
+			{
+				tree[index].sum += offset;
+				if (index == 0) break;
+
+				if (index & 1) index = index / 2;  // 奇数节点
+				else index = index / 2 - 1;  // 偶数节点                
+			}
+		}
+	}
+
+	// 查询函数 同样是logn的时间复杂度
+	int sumRange(int start, int end)
+	{
+        return (tree.size() != 0 && start <= end && start >= 0) ? query(start, end, 0) : 0;
+	}
+
+private:
+	vector<cell> tree;
+private:
+	int query(int start, int end, int index)
+	{
+		int mid = (tree[index].start + tree[index].end) / 2;
+
+		if (start == tree[index].start && end == tree[index].end)
+			return tree[index].sum;
+		else if (end <= mid)
+			return query(start, end, 2 * index + 1);
+		else if (start > mid)
+			return query(start, end, 2 * index + 2);
+		else
+			return query(start, mid, 2 * index + 1) + query(mid + 1, end, 2 * index + 2);
+	}
+
+	int buildSegmentTree(int start, int end, int index, const vector<int>& nums)
+	{
+		if (start == end)
+		{
+			tree[index].start = start;
+			tree[index].end = start;
+			tree[index].sum = nums[start];
+		}
+		else
+		{
+			int mid = (start + end) / 2;
+			int leftSum = buildSegmentTree(start, mid, 2 * index + 1, nums);
+			int rightSum = buildSegmentTree(mid + 1, end, 2 * index + 2, nums);
+
+			tree[index].start = start;
+			tree[index].end = end;
+			tree[index].sum = leftSum + rightSum;
+		}
+		return tree[index].sum;
+	}
+};