[UCSD白板题] Binary Search

Problem Introduction

In this problem, you will implemented the binary search algorithm that allows searching very efficiently(even huge) lists provided that the list is sorted.

Problem Description

Task.The goal in this code problem is to implement the binary search algorithm.

Input Format.The first line of the input contains an integer \(n\) and a sequence \(a_0<a_1<\cdots<a_{n-1}\) of \(n\) pairwise distinct positive integers in increasing order. The next line contains an integer \(k\) and \(k\) positive integers \(b_0,b_1,\cdots,b_{k-1}\).

Constraints.\(1 \leq n,k \leq 10^5; 1 \leq a_i \leq 10^9\) for all \(0 \leq i < n; 1 \leq b_j \leq 10^9\) for all \(0 \leq j \leq k\).

Output Format.For all \(i\) from \(0\) to \(k-1\),output an index \(0 \leq j \leq n-1\) such that \(a_j=b_i\) or \(-1\) if there is no such index.

Sample 1.
Input:

5 1 5 8 12 13
5 8 1 23 1 11

Output:

2 0 -1 0 -1

Solution

# Uses python3
import sys

def binary_search(a, x):
    left, right = 0, len(a)
    while left < right:
        mid = left + (right - left) // 2
        if x == a[mid]:
            return mid
        elif x < a[mid]:
            right = mid
        else:
            left = mid + 1
    return -1

def linear_search(a, x):
    for i in range(len(a)):
        if a[i] == x:
            return i
    return -1

if __name__ == '__main__':
    input = sys.stdin.read()
    data = list(map(int, input.split()))
    n = data[0]
    m = data[n + 1]
    a = data[1 : n + 1]
    for x in data[n + 2:]:
        print(binary_search(a, x), end = ' ')