如何求两个有序数组的第K个数

给定两个已排序数组，如何求第K个数。传统的做法就是类似归并排序的方式，时间

复杂度是O（N），这里给出一个二分法，时间复杂度是O（lgN）

 

#include <iostream>#include <algorithm>#include <ctime>//#define DEBUG#define MINV(a, b) ((a) <= (b) ? (a) : (b))#define MAXV(a, b) ((a) >= (b) ? (a) : (b))#define MAX_N 10000000#define MAX_VAL 10000using namespace std;int array_1[MAX_N] = {0, 12, 17, 19, 44, 47, 52, 52, 57, 90};int array_2[MAX_N] = {14, 20, 38, 47, 76, 77, 77, 82, 89, 89};int n, m, k;int getKth(int s1, int e1, int s2, int e2, int k){int mid_1 = (s1 + e1) / 2;int mid_2 = (s2 + e2) / 2;int pLen_1 = mid_1 - s1 + 1;int pLen_2 = mid_2 - s2 + 1;if(s1 > e1) pLen_1 = 0;if(s2 > e2) pLen_2 = 0;int pSum = pLen_1 + pLen_2;if(k < pSum){if(pLen_2 != 0 && (pLen_1 == 0 || array_1[mid_1] <= array_2[mid_2]))return getKth(s1, e1, s2, mid_2 - 1, k);elsereturn getKth(s1, mid_1 - 1, s2, e2, k);}else{if(k == pSum){if(pLen_1 == 0) return array_2[mid_2];else if(pLen_2 == 0) return array_1[mid_1];}if(pLen_1 != 0 && (pLen_2 == 0 || array_1[mid_1] <= array_2[mid_2]))return getKth(mid_1 + 1, e1, s2, e2, k - pLen_1);else return getKth(s1, e1, mid_2 + 1, e2, k - pLen_2);}}int main(){int i, j;// testing cases num: 1000int caseNum = 1;while(caseNum--){//getchar();// create m, n, ksrand(time(NULL));m = rand() % MAX_N + 1;n = rand() % MAX_N + 1;k = rand() % (m + n) + 1;// create array_1 and sort itfor(i = 0; i < m; i++)array_1[i] = rand() % MAX_VAL;sort(array_1, array_1 + m);// output array_1#ifdef DEBUGcout<<"k:"<<k<<endl;cout<<"array_1:"<<endl;for(i = 0; i < m; i++)cout<<array_1[i]<<" ";cout<<endl;#endif// create array_2 and sort itfor(i = 0; i < n; i++)array_2[i] = rand() % MAX_VAL;sort(array_2, array_2 + n);// output array_2#ifdef DEBUGcout<<"array_2:"<<endl;for(i = 0; i < n; i++)cout<<array_2[i]<<" ";cout<<endl;#endif// get the kth numint kthValue = getKth(0, m - 1, 0, n - 1, k);#ifdef DEBUGcout<<"The kth value by my algorithm: "<<kthValue<<endl;#endif// verify the resultint idex = 0;int realValue;i = j = 0;while(i < m || j < n){if(j == n || (i != m && array_1[i] <= array_2[j])){idex++;if(idex == k){realValue = array_1[i];break;}i++;continue;}if(i == m || (j != n && array_2[j] <= array_1[i])){idex++;if(idex == k){realValue = array_2[j];break;}j++;}}#ifdef DEBUGcout<<"The real kth value is: "<<realValue<<endl;#endifif(realValue == kthValue) cout<<"Result: Correct"<<endl;else{cout<<"k:"<<k<<endl;cout<<"array_1:"<<endl;for(i = 0; i < m; i++)cout<<array_1[i]<<" ";cout<<endl;cout<<"array_2:"<<endl;for(i = 0; i < n; i++)cout<<array_2[i]<<" ";cout<<endl;cout<<"The kth value by my algorithm: "<<kthValue<<endl;cout<<"The real kth value is: "<<realValue<<endl;cout<<"Resutl: Wrong"<<endl;break;}#ifdef DEBUGcout<<endl<<endl;#endifk++;}return 0;}