Learn and practice the Two Pointers and Modified Binary Search patterns to solve coding interview problems.

Speedrun the Oracle Coding Interview: Top Problems in Python

This module groups together two of the most common patterns that may be used to solve problems where the input data is linear: Two Pointers and Modified Binary Search. Both the Two Pointers and the Modified Binary Search patterns derive their power from their ability to efficiently reduce the size of the search space, that is, both exemplify the divide and conquer approach to problem-solving. After completing this module, we will have the knowledge of how to use this set of related patterns to solve a diverse range of problems.

Two Pointers & Co.

# Statement

Given a sorted integer array, `nums`, and an integer value, `target`, the array is rotated by some arbitrary number. Search and return the index of `target` in this array. If the `target` does not exist, return `-1`.

An original sorted array before rotation is given below:

digraph g {
 rankdir = "TB" 
 splines = false;
 bgcolor = transparent
 node[shape = record, fontname = "courier", fontsize="18"];
 size = "9"
 bgcolor = "transparent"
 array[label = <<table border="0" cellborder="1" cellspacing="0"> \
 
 <tr> \
 <td height="35" width="45" port="e1" bgcolor="#FFDC5C" >1</td>\ 
 <td height="35" width="45" port="e0" bgcolor="#FFDC5C" >10</td>\
 <td height="35" width="45" port="e2" bgcolor="#FFDC5C" >20</td> \ 
 <td height="35" width="45" port="e3" bgcolor="#FFDC5C" >47</td> \ 
 <td height="35" width="45" port="e4" bgcolor="#FFDC5C" >59</td> \ 
 <td height="35" width="45" port="e5" bgcolor="#FFDC5C" >63</td> \ 
 <td height="35" width="45" port="e6" bgcolor="#FFDC5C" >75</td> \ 
 <td height="35" width="45" port="e7" bgcolor="#FFDC5C" >88</td> \ 
 <td height="35" width="45" port="e8" bgcolor="#FFDC5C" >99</td> \ 
 <td height="35" width="45" port="e9" bgcolor="#FFDC5C" >107</td> \
 <td height="35" width="45" port="e10" bgcolor="#FFDC5C">120</td> \
 <td height="35" width="45" port="e11" bgcolor="#FFDC5C">133</td> \
 <td height="35" width="45" port="e12" bgcolor="#FFDC5C">155</td> \
 <td height="35" width="45" port="e13" bgcolor="#FFDC5C">162</td> \
 <td height="35" width="45" port="e14" bgcolor="#FFDC5C">176</td> \
 <td height="35" width="45" port="e15" bgcolor="#FFDC5C">188</td> \
 <td height="35" width="45" port="e16" bgcolor="#FFDC5C">199</td> \
 <td height="35" width="45" port="e17" bgcolor="#FFDC5C">200</td> \
 <td height="35" width="45" port="e18" bgcolor="#FFDC5C">210</td> \
 <td height="35" width="45" port="e19" bgcolor="#FFDC5C">222</td> \
 </tr> \
 </table>> shape=none];
 
 }

After rotating this array 6 times, it changes to:

digraph g {
 rankdir = "TB" 
 splines = false;
 bgcolor = transparent
 node[shape = record, fontname = "courier", fontsize="18"];
 size = "9"
 bgcolor = "transparent"
 array[label = <<table border="0" cellborder="1" cellspacing="0"> \
 
 <tr> \
 						<td height="35" width="45" port="e0" bgcolor="#33CFFF">176</td>\
 <td height="35" width="45" port="e0" bgcolor="#33CFFF" >188</td>\
 <td height="35" width="45" port="e2" bgcolor="#33CFFF" >199</td> \ 
 <td height="35" width="45" port="e3" bgcolor="#33CFFF" >200</td> \ 
 <td height="35" width="45" port="e4" bgcolor="#33CFFF" >210</td> \ 
 <td height="35" width="45" port="e5" bgcolor="#33CFFF" >222</td> \ 
 <td height="35" width="45" port="e6" bgcolor="#FFDC5C" >1</td> \ 
 <td height="35" width="45" port="e7" bgcolor="#FFDC5C" >10</td> \ 
 <td height="35" width="45" port="e8" bgcolor="#FFDC5C" >20</td> \ 
 <td height="35" width="45" port="e9" bgcolor="#FFDC5C" >47</td> \
 <td height="35" width="45" port="e10" bgcolor="#FFDC5C">59</td> \
 <td height="35" width="45" port="e11" bgcolor="#FFDC5C">63</td> \
 <td height="35" width="45" port="e12" bgcolor="#FFDC5C">75</td> \
 <td height="35" width="45" port="e13" bgcolor="#FFDC5C">88</td> \
 <td height="35" width="45" port="e14" bgcolor="#FFDC5C">99</td> \
 <td height="35" width="45" port="e15" bgcolor="#FFDC5C">107</td> \
 <td height="35" width="45" port="e16" bgcolor="#FFDC5C">120</td> \
 <td height="35" width="45" port="e17" bgcolor="#FFDC5C">133</td> \
 <td height="35" width="45" port="e18" bgcolor="#FFDC5C">155</td> \
 <td height="35" width="45" port="e18" bgcolor="#FFDC5C">162</td> \
 </tr> \
 </table>> shape=none];
 
 }

**Constraints**

- All values in `nums` are unique.
- The values in `nums` are sorted in ascending order.
- The array may have been rotated by some arbitrary number.
- $1 \leq$ `nums.length` $\leq 1000$
- $-10^4 \leq$ `nums[i]` $\leq 10^4$
- $-10^4 \leq$ `target` $\leq 10^4$

# Examples

What is the output if the following rotated sorted array and target are given as input?

nums = [4, 5, 6, 7, 0, 1, 2]

target = 1



What is the output if the following rotated sorted array and target are given as input?
nums = [4, 5, 6, 7, 0, 1, 2]
target = 1

What is the output if the following rotated sorted array and target are given as input?

nums = [7, 8, 9, 0, 6]

target = 1

What is the output if the following rotated sorted array and target are given as input?
nums = [7, 8, 9, 0, 6]
target = 1

What is the output if the following rotated sorted array and target are given as input?

nums = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14]

target = 25

What is the output if the following rotated sorted array and target are given as input?
nums = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14]
target = 25

Search in Rotated Sorted Array

Search in Rotated Sorted Array

Help me debug only the function Search in Rotated Sorted Array . . I don't need the corrected code.I don't want explanations or code review. Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Please help me understand why this code failed for the last failed test case. Don't give me the corrected code. . If yes, then Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Your current task is to review only the binary_search_rotated function and the other function(s) invoked in it/them. Do not review extra/helper files or functions not invoked in the solution function binary_search_rotated. Do not review the code of data structures objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. Also, Answer the following questions: Is the Modified Binary Search pattern used? Take your time and review the code.

Please provide a brief time complexity analysis of the function binary_search_rotated. While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. The Answer should be to the point and in a few lines.

Please provide a brief Space complexity analysis of the function binary_search_rotated. While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. Do not include the space used for the input parameters and the space used for just returning an output(not used as a scratch space). The Answer should be to the point and in a few lines

def evaluate_results(self) -> object:
 """
 self.__inputs is the list of inputs that are passed as input to function
 self.__actual_output is a list of outputs that is produced by the learner's code
 return : self.__edu__result object
 """

 def binary_search(nums, low, high, target):

 if (low > high):
 return -1
 mid = low + (high - low) // 2

 if nums[mid] == target:
 return mid

 if nums[low] <= nums[mid]:
 if nums[low] <= target and target < nums[mid]:
 return binary_search(nums, low, mid-1, target)
 return binary_search(nums, mid+1, high, target)
 else:
 if nums[mid] < target and target <= nums[high]:
 return binary_search(nums, mid+1, high, target)
 return binary_search(nums, low, mid-1, target)


 def binary_search_rotated(nums, target):
 return binary_search(nums, 0, len(nums)-1, target)

 expected_outputs = [] 
 expected = binary_search_rotated(self.__inputs[0], self.__inputs[1])
 actual_output = self.__actual_outputs[0]
 

 if expected == actual_output:
 expected_outputs.append(expected)
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 expected_outputs.append(expected)
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

def binary_search_rotated(nums, target):
  
  # Replace this placeholder return statement with your code
  return -1

search_in_rotated_sorted_array (1).yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [6, 7, 1, 2, 3, 4, 5]
    - 2 : 3
    output: 
    - 1 : 4
  - name: "testcase 2"
    inputs:
    - 1: [6, 7, 1, 2, 3, 4, 5]
    - 2: 6
    output:
    - 1 : 0
  - name: "testcase 3"
    inputs:
    - 1: [4, 5, 6, 1, 2, 3]
    - 2: 3
    output:
    - 1 : 5
  - name: "testcase 4"
    inputs:
    - 1: [4, 5, 6, 1, 2, 3]
    - 2: 6
    output:
    - 1 : 2
  - name: "testcase 5"
    inputs:
    - 1: [4]
    - 2: 1
    output:
    - 1 : -1



def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """

 def is_valid_1d_array(arr):
 if not isinstance(arr, list):
 return False

 return all(isinstance(elem, int) and not isinstance(elem, bool) for elem in arr)


 def is_sorted(arr):
 for i in range(len(arr) - 1):
 if arr[i] > arr[i + 1]:
 return False
 return True

 def is_sorted_rotated(arr):
 if len(arr) == 1 or is_sorted(arr) == True:
 return True
 
 right = left = []
 for i in range(len(arr)):
 if i + 1 < len(arr):
 if arr[i] > arr[i + 1]:
 left = arr[:i + 1]
 right = arr[i + 1:]

 if is_sorted(left) and is_sorted(right) and left[0] > right[len(right)-1]:
 return True
 else:
 return False

 nums = self.__inputs[0]
 target = self.__inputs[1]

 if not is_valid_1d_array(nums):
 self.store_result ("'nums' should be a valid 1D array of integers", ValidationFunction.FAIL)
 elif not 1 <= len(nums) <= 1000:
 self.store_result ("'nums' length should be in the range [1, 10000]", ValidationFunction.FAIL)
 elif not -10000 <= target <= 10000:
 self.store_result ("'target' should be in the range [-10000, 10000]", ValidationFunction.FAIL)
 elif len(nums) != len(list(set(nums))):
 self.store_result ("'nums' should have unique elements", ValidationFunction.FAIL)
 elif is_sorted_rotated(nums) == False:
 self.store_result ("'nums' should be rotated and sorted in ascending order", ValidationFunction.FAIL)
 elif any(not -10000 <= i <= 10000 for i in nums):
 self.store_result ("'nums[i]' should be in the range [-10000, 10000]", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Search in Rotated Sorted Array problem.

Two Pointers

Modified Binary Search

Conclusion

Search in Rotated Sorted Array

Statement

Examples

Understand the problem

Figure it out!

Try it yourself