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分治法求两个有序数组的中位数

算法步骤(基本原理是获取第k小的数)   	先取两个中间索引x_mid,y_mid;    下面来比较    如果x[x_mid]比较小,那么就看x_mid最大是第几小(记作m)    ①m

class Solution {
       public double findMedianSortedArrays(int[] nums1, int[] nums2) {
           if(nums2.length==0){
               if(nums1.length%2==0){
                   return (double) (nums1[(nums1.length-1)/2]+nums1[(nums1.length-1)/2+1])/2.0;            }else                return (double)nums1[(nums1.length-1)/2];        }else if(nums1.length==0){
               if(nums2.length%2==0){
                   return (double) (nums2[(nums2.length-1)/2]+nums2[(nums2.length-1)/2+1])/2.0;            }else                return (double)nums2[(nums2.length-1)/2];        }                int i;        if((nums1.length+nums2.length)%2==0){
               i=(nums1.length+nums2.length)/2;            return (get_Middle_num(nums1,0,nums1.length-1,nums2,0,nums2.length-1,i)     +get_Middle_num(nums1,0,nums1.length-1,nums2,0,nums2.length-1,i+1))/2.0;        }        else{
               i=(nums1.length+nums2.length)/2+1;            return (double)get_Middle_num(nums1,0,nums1.length-1,nums2,0,nums2.length-1,i);        }    }    int get_Middle_num(int x[],int left_x,int right_x,int y[],int left_y,int right_y,int k){
   */        if(left_x>right_x){
               return y[left_y+k-1];        }else if(left_y>right_y){
               return x[left_x+k-1];        }else if(k==1){
                   return x[left_x]>y[left_y]?y[left_y]:x[left_x];        }else{
               int x_mid = (left_x+right_x)/2;            int y_mid = (left_y+right_y)/2;            int num = (x_mid-left_x)+(y_mid-left_y);            //注意num+1代表含义:x_mid可以到达的最大第几小            // num+2代表含义:y_mid可以到达的最小第几小            if(x[x_mid]<=y[y_mid]){
                   //接下来我们开始锁定x左边界和y的右边界                if(num+2==k){
                       right_y=y_mid;                }else if(num+2>k)                    right_y=y_mid-1;                if(num+1
   
    k)                    right_x=x_mid-1;                if(num+1
   

算法复杂度分析:

@Test    public  void Test(){
           //[76,89,104,30823,31070,31259,31324,31714,31971,320331]        //[122,2919,2941,17754,17781,17830,17874,18019,18023,18130]        //[2634,2764,2801,30823,31070,31259,32319,32350,32408,32475,32681,32701,32764]        //[122,32605,32641,32716,32757]        int x[]={
   2634,2764,2801,30823,31070,31259,32319,32350,32408,32475,32681,32701,32764};        int y[]={
   122,32605,32641,32716,32757};        System.out.println(get_Middle_num(x,0,x.length-1,y,0,y.length-1,1));        System.out.println((x.length+y.length));    }

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