logseq_notes/pages/OJ notes/pages/Binary Search Algorithm.md

Binary Search Algorithm

2022-06-13 15:46

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Algorithms:

#algorithm #binary_search

Data structures:

#array #vector #set #multiset

Difficulty:

#CS_analysis #difficulty_easy

Related problems:

Links:

• g4g for manual implementation

• cppreference, find

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How to implement Binary search?

a: Use cpp's library

Use cpp's set's find or equal_range

b: Manual

• Tips:

  [!tip] Why mid = l + (r - l) / 2, not mid = (l + r) / 2 Avoids integer overflow when l and r is big

  [!tip] Why r = array.size() - 1 Avoids OOB when (l == r && r == array.size()) This happens if 1 is not subtracted

  1. Use a while loop: Leetcode Search-a-2D-Matrix

  2. Use recursion: from g4g:

  // C++ program to implement recursive Binary Search
  #include <bits/stdc++.h>
  using namespace std;
  
  // A recursive binary search function. It returns
  // location of x in given array arr[l..r] is present,
  // otherwise -1
  int binarySearch(int arr[], int l, int r, int x) {
  if (r >= l) {
    int mid = l + (r - l) / 2;
  
    // If the element is present at the middle
    // itself
    if (arr[mid] == x)
      return mid;
  
    // If element is smaller than mid, then
    // it can only be present in left subarray
    if (arr[mid] > x)
      return binarySearch(arr, l, mid - 1, x);
  
    // Else the element can only be present
    // in right subarray
    return binarySearch(arr, mid + 1, r, x);
  }
  
  // We reach here when element is not
  // present in array
  return -1;
  }
  
  int main(void) {
  int arr[] = {2, 3, 4, 10, 40};
  int x = 10;
  int n = sizeof(arr) / sizeof(arr[0]);
  int result = binarySearch(arr, 0, n - 1, x);
  (result == -1) ? cout << "Element is not present in array"
                 : cout << "Element is present at index " << result;
  return 0;
  }