[数据结构与算法]二分查找方法及其变形问题学习记录

二分查找算法

实现代码

//迭代算法
public int bsearch(int[] a, int n, int value) {
  int low = 0;
  int high = n - 1;

  while (low <= high) {
    int mid = (low + high) / 2;
    if (a[mid] == value) {
      return mid;
    } else if (a[mid] < value) {
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }

  return -1;
}

主要注意点

1. 退出循环的条件时是low<=high，而不是low<high
2. mid的取值如果写成(low+high)/2，在数据量很大的时候会发生内存溢出的问题，一般写成low+(high-low)/2或者直接采用位计算low+((high-low)>>1)
3. low和high的更新必须写成mid-1和mid+1，如果写成low=mid或者high=mid，会造成无法跳出循环（比如当low和high相等的时候）。

二分查找算法变形问题

查找第一个等于给定值的元素

实现代码

public int binarySearch_demo1(int[] a, int n, int value){
        int low = 0;
        int high = n - 1;
        while(low <= high){
            int mid = low + ((high - low) >> 1);
            if(a[mid] > value){
                high = mid - 1;
            }else if(a[mid] < value){
                low = mid + 1;
            }else{
                if(mid == 0 || a[mid-1] != value) return a[mid];
                high = mid - 1;
            }
        }
        return -1;
    }

查找最后一个等于给定值的元素

实现代码

public int binarySearch_demo2(int[] a, int n, int value){
        int low = 0;
        int high = n - 1;
        while(low <= high){
            int mid = low + ((high - low) >> 1);
            if(a[mid] > value){
                high = mid - 1;
            }else if(a[mid] < value){
                low = mid + 1;
            }else{
                if(mid == n-1 || a[mid + 1] != value) return a[mid];
                low = mid + 1;
            }
        }
        return -1;
    }

查找第一个大于等于给定值的元素

实现代码

public int binarySearch_demo3(int[] a, int n, int value) {
        int low = 0;
        int high = n - 1;
        while (low <= high) {
            int mid = low + ((high - low) >> 1);
            if (a[mid] >= value) {
                if (mid == 0 || a[mid - 1] < value) return a[mid];
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }
        return -1;
    }

查找第一个小于等于给定值的元素

实现代码

public int binarySearch_demo4(int[] a, int n, int value) {
        int low = 0;
        int high = n - 1;
        while (low <= high) {
            int mid =  low + ((high - low) >> 1);
            if (a[mid] > value) {
                high = mid - 1;
            } else {
                if ((mid == n - 1) || (a[mid + 1] > value)) return mid;
                else low = mid + 1;
            }
        }
        return -1;
    }