Merge pull request #8 from Mooophy/master

add solution by devide and conquer

Author: pezy

014. Maximum Subarray/main.cc

@@ -6,5 +6,9 @@ int main()
     int A[] = {-2,1,-3,4,-1,2,1,-5,4}; 
     Solution s;
     std::cout << s.maxSubArray(A, 9) << std::endl;
+
+	SolutionByDivideAndConquer dac;
+	std::cout << s.maxSubArray(A, 9) << std::endl;
+
     return 0;
 } 

014. Maximum Subarray/solution.h

@@ -12,3 +12,44 @@ class Solution {
         return maxv;
     }
 };
+
+class SolutionByDivideAndConquer{
+	//O(n)
+	int find_max_crossing_subarray(int arr[], unsigned low, unsigned mid, unsigned hgh)
+	{
+		auto accumulation = 0;
+
+		auto lft_sum = accumulation = arr[mid];
+		if (mid > low)
+			for (auto i = mid - 1; i != low - 1; --i)
+				if ((accumulation += arr[i]) > lft_sum)
+					lft_sum = accumulation;
+
+		auto rht_sum = accumulation = arr[mid + 1];
+		if (hgh > mid)
+			for (auto i = mid + 2; i != hgh + 1; ++i)
+				if ((accumulation += arr[i]) > rht_sum)
+					rht_sum = accumulation;
+
+		return lft_sum + rht_sum;
+	}
+
+	//O(n lg n)
+	int divide_and_conquer(int arr[], unsigned low, unsigned hgh)
+	{
+		if (low == hgh) return arr[low];
+
+		auto mid = (low + hgh) / 2;
+		auto lft = divide_and_conquer(arr, low, mid);
+		auto rht = divide_and_conquer(arr, mid + 1, hgh);
+		auto crs = find_max_crossing_subarray(arr, low, mid, hgh);
+
+		return std::max({ lft, rht, crs });
+	}
+
+public:
+	int maxSubArray(int A[], int n)
+	{
+		return divide_and_conquer(A, 0, n - 1);
+	}
+};