23、查找算法-插值法查找

来源：https://www.bilibili.com/video/BV1B4411H76f?p=77

一、思路

插值法查找：序列还是需要有序，思路跟二分法是一致的，但是寻找中间坐标mid的方法不同。

对于二分法mid=1/2(low+high)=low+1/2*(high-low)

插值法中mid的求法是这样的：mid=low+((finalVal-arr[low])/(arr[high]-arr[low]))(high-low)

利用目标值finalVal的大小，大体确定一下它的位置

例如：一个1-100的数组，要找1

那二分法：mid = 0+1/2(99-0)=49,从49开始找

插值法：mid=0+((1-1)/(100-1))(99-0)=0,从0开始找，这就快了

二、实现

//插值法查找
public class InsertSearch {
    public static void main(String[] args) {
        int[] arr = new int[100];
        for (int i = 0; i < 100; i++) {
            arr[i] = i+1;
        }
        System.out.println(Arrays.toString(arr));

        int a = insertSearch(arr,0,arr.length-1,100);
        System.out.println(a);
    }

    public static int insertSearch(int[] arr, int left, int right, int finalVal){
        if(left > right || finalVal < arr[0] || finalVal > arr[arr.length-1]){
            return -1;
        }
        int mid = left + ((finalVal-arr[left])/(arr[right]-arr[left]))*(right - left);
        int midVal = arr[mid];

        if(finalVal > midVal){
            return insertSearch(arr,mid+1,right,finalVal);
        }else if(finalVal < midVal){
            return insertSearch(arr,left,mid-1,finalVal);
        }else {
            return mid;
        }
    }
}

结果

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
99