Binary seach

Complexity of O(nlog(n))

Binary search can be implimented either recursively or iteratively.

Recursive

// initially called with low = 0, high = N-1
  BinarySearch(A[0..N-1], value, low, high) {
      // invariants: value > A[i] for all i < low
                     value < A[i] for all i > high
      if (high < low)
          return not_found // value would be inserted at index "low"
      mid = (low + high) / 2
      if (A[mid] > value)
          return BinarySearch(A, value, low, mid-1)
      else if (A[mid] < value)
          return BinarySearch(A, value, mid+1, high)
      else
          return mid
  }

Iterative

  BinarySearch(A[0..N-1], value) {
      low = 0
      high = N - 1
      while (low <= high) {
          // invariants: value > A[i] for all i < low
                         value < A[i] for all i > high
          mid = (low + high) / 2
          if (A[mid] > value)
              high = mid - 1
          else if (A[mid] < value)
              low = mid + 1
          else
              return mid
      }
      return not_found // value would be inserted at index "low"
  }

Languages

• Rust
• C++
• C