BS_using_recursion

BinarysearchReccursion.cpp

@@ -0,0 +1,113 @@
+// C++ implementation to search an element in a
+// sorted matrix
+#include <bits/stdc++.h>
+using namespace std;
+
+const int MAX = 100;
+
+// This function does Binary search for x in i-th
+// row. It does the search from mat[i][j_low] to
+// mat[i][j_high]
+void binarySearch(int mat[][MAX], int i, int j_low,
+								int j_high, int x)
+{
+	while (j_low <= j_high)
+	{
+		int j_mid = (j_low + j_high) / 2;
+
+		// Element found
+		if (mat[i][j_mid] == x)
+		{
+			cout << "Found at (" << i << ", "
+				<< j_mid << ")";
+			return;
+		}
+
+		else if (mat[i][j_mid] > x)
+			j_high = j_mid - 1;
+
+		else
+			j_low = j_mid + 1;
+	}
+
+	// element not found
+	cout << "Element no found";
+}
+
+// Function to perform binary search on the mid
+// values of row to get the desired pair of rows
+// where the element can be found
+void sortedMatrixSearch(int mat[][MAX], int n,
+								int m, int x)
+{
+	// Single row matrix
+	if (n == 1)
+	{
+		binarySearch(mat, 0, 0, m-1, x);
+		return;
+	}
+
+	// Do binary search in middle column.
+	// Condition to terminate the loop when the
+	// 2 desired rows are found
+	int i_low = 0;
+	int i_high = n-1;
+	int j_mid = m/2;
+	while ((i_low+1) < i_high)
+	{
+		int i_mid = (i_low + i_high) / 2;
+
+		// element found
+		if (mat[i_mid][j_mid] == x)
+		{
+			cout << "Found at (" << i_mid << ", "
+				<< j_mid << ")";
+			return;
+		}
+
+		else if (mat[i_mid][j_mid] > x)
+			i_high = i_mid;
+
+		else
+			i_low = i_mid;
+	}
+
+	// If element is present on the mid of the
+	// two rows
+	if (mat[i_low][j_mid] == x)
+		cout << "Found at (" << i_low << ","
+			<< j_mid << ")";
+	else if (mat[i_low+1][j_mid] == x)
+		cout << "Found at (" << (i_low+1)
+			<< ", " << j_mid << ")";
+
+	// search element on 1st half of 1st row
+	else if (x <= mat[i_low][j_mid-1])
+		binarySearch(mat, i_low, 0, j_mid-1, x);
+
+	// Search element on 2nd half of 1st row
+	else if (x >= mat[i_low][j_mid+1] &&
+			x <= mat[i_low][m-1])
+	binarySearch(mat, i_low, j_mid+1, m-1, x);
+
+	// Search element on 1st half of 2nd row
+	else if (x <= mat[i_low+1][j_mid-1])
+		binarySearch(mat, i_low+1, 0, j_mid-1, x);
+
+	// search element on 2nd half of 2nd row
+	else
+		binarySearch(mat, i_low+1, j_mid+1, m-1, x);
+}
+
+// Driver program to test above
+int main()
+{
+	int n = 4, m = 5, x = 8;
+	int mat[][MAX] = {{0, 6, 8, 9, 11},
+					{20, 22, 28, 29, 31},
+					{36, 38, 50, 61, 63},
+					{64, 66, 100, 122, 128}};
+
+	sortedMatrixSearch(mat, n, m, x);
+	return 0;
+}