二分查找

概念

二分查找只对有序数组有效，他是通过将数组一分为二，然后根据中心点与目标的大小比较排除掉另一半，到最后就能找到目标了

伪代码

binary_search:
  left <- 0
  right <- n-1
  while left <= right then
    mid <- left+(right-left)//2
    if arr[mid] < target then
      left = mid + 1
    else if arr[mid] > target then
      right = mid - 1
    else 
      return mid
  return -1

时间复杂度是 O(logn)

代码实现

C

#include <stdio.h>

static int binary_search(int arr[], size_t n, int target)
{
    size_t left = 0, right = n - 1;
    size_t mid;
    while (left <= right) {
        mid = left + (right - left) / 2;
        if (arr[mid] < target)
            left = mid + 1;
        else if (arr[mid] > target)
            right = mid - 1;
        else
            return mid;
    }
    return -1;
}

static void print(int arr[], size_t size)
{
    for (size_t i = 0; i < size; i++)
        printf(" %d", arr[i]);
    printf("\n");
}

int main(void)
{
    int arr[] = {-1, 2, 3, 4, 6, 7, 9};
    size_t size = sizeof(arr) / sizeof(arr[0]);
    print(arr, size);

    printf("target: %d\nindex: %d\n", 6, binary_search(arr, size, 6));
    printf("target: %d\nindex: %d\n", 5, binary_search(arr, size, 5));

    return 0;
}

Lua

local function binary_search(arr, target)
    local left, right = 1, #arr
    local mid
    while left <= right do
        mid = left + math.floor((right - left) / 2)
        if arr[mid] < target then
            left = mid + 1
        elseif arr[mid] > target then
            right = mid - 1
        else
            return mid
        end
    end
    return -1
end

local function run()
    local arr = {-1, 2, 3, 4, 6, 7, 9};
    for _, v in ipairs(arr) do
        io.write(" " .. tostring(v))
    end
    io.write("\n")

    print(string.format("target: %d\nindex: %d", 4, binary_search(arr, 4)))
    print(string.format("target: %d\nindex: %d", -2, binary_search(arr, -2)))
end

run()