Merge pull request #76 from harsh-4/master

Add jump search algorithm

Author: cozek

algorithms/Searching/jump_search.m

@@ -0,0 +1,56 @@
+function found_at = jump_search(input_array, search_key)
+  % Contributed by - Harshit Pant, [email protected]
+  % Reference - https://en.wikipedia.org/wiki/Jump_search
+  
+  % input_array - Holds the array in which the 'search_key' is to be searched.
+  %               It should be sorted in ascending order.
+  %               It can contain -ve numbers as well as non-integers.
+  % search_key  - The value to be searched in the 'input_array'.
+  % found_at    - The index at which 'search_key' is found in 'input_array'.
+  %               -1 is returned if 'search_key' is not found in 'input_array'.
+
+  array_length = length(input_array);
+  found_at = -1; 
+  
+  % Finding the optimum block_size to be jumped.
+  block_size = sqrt(array_length); 
+  block_size = round(block_size); 
+  
+  % low and high denote the lower 
+  % and upper bound of a certain block.
+  low = 1;
+  high = 1 + block_size;
+
+  % Finding the block where the 'search_key' is present
+  % if low >= array_length, the 'search_key' is not found 
+  % in the 'input_array', thus, -1 is returned.
+  while input_array(min(high, array_length)) < search_key
+      low = high;
+      high = high + block_size;
+      if low >= array_length
+          return;
+      endif;
+  endwhile;
+
+  % Now that the required block is found,
+  % running a linear search within the block 
+  % to find the 'search_key'
+  while input_array(low) < search_key
+      low = low + 1;
+      if low > min(high, array_length)
+          return;
+      endif;
+  endwhile;
+
+  % Checks if the 'search_key' was found within
+  % the block. If found, the index is returned.
+  % If not -1 is returned.
+  if input_array(low) == search_key
+      found_at = low;
+  endif;
+
+endfunction;
+
+% TEST: 
+% jump_search([-11.1, -3.3, -1.3, 0.1, 1.5, 3.5, 3.9,...
+% 5.5, 7.5, 9.6, 13.7, 21.3, 35.9], 7.5) == 9