Implemented Code For Binary Search In 2D Arrays

algorithms/CPlusPlus/Searching/binary-search-in-2d-arrays.cpp

@@ -0,0 +1,80 @@
+// C++ program to implement Binary Search in 2D Arrays
+
+// Time Complexity: log(m*n) where m is number columns and n is number of rows
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+// Floor of a array is the greatest number which is smaller than or equal to the target element
+// Search the floor number in the first column. Since the array is sorted that means the target element
+// should lie on the row which has the first element as its floor
+int Floor(vector<vector<int>> arr, int target)
+{
+    int start = 0;
+    int end = arr.size() - 1;
+    if(target < arr[start][0])
+        return arr[start][0];
+    while (start <= end)
+    {
+        int mid = start + (end - start) / 2;
+        if(target < arr[mid][0])
+            end = mid - 1; 
+        else if(target > arr[mid][0])
+            start = mid + 1;
+        else 
+            return mid; // if it is the target element return the column index
+    }
+    return end; // Since the condition in which the loop breaks is start > end that means the end will be smaller than target element
+    // whereas start will be greater than target element.
+}
+
+// Search just in a row which has its first element smaller than or equal to target element(floor)
+vector<int> BinarySearch(vector<vector<int>> arr, int target)
+{
+    int floor = Floor(arr, target);
+    int start = 0;
+    int end = arr[floor].size() - 1;
+    while(start <= end)
+    {
+        int mid = start + (end - start) / 2;
+        if(target > arr[floor][mid])
+            start = mid + 1;
+        else if(target < arr[floor][mid])
+            end = mid - 1;
+        else
+            return {floor, mid};
+    }
+    return {-1 , -1};  // If element is not found return negatives.
+}
+
+
+int main(int argc, char const *argv[])
+{
+    vector<vector<int>> arr = {
+        {1,2,3,4},
+        {5,6,7,8},
+        {9,10,11,12},
+        {13,14,15,16}
+    };
+    int target = 15;    // Element needs to be searched
+    vector<int> ans = BinarySearch(arr, target); 
+
+    cout << "[ " << ans[0] << " , " << ans[1] << " ]" << endl;  
+
+    
+    return 0;
+}
+
+/*
+Input:
+arr = [
+    [1,2,3,4],
+    [5,6,7,8],
+    [9,10,11,12],
+    [13,14,15,16]
+]
+target = 15
+
+Output: [3, 2]
+*/