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 10000 using 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); else return 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: 1000 int caseNum = 1; while(caseNum--) { //getchar(); // create m, n, k srand(time(NULL)); m = rand() % MAX_N + 1; n = rand() % MAX_N + 1; k = rand() % (m + n) + 1; // create array_1 and sort it for(i = 0; i < m; i++) array_1[i] = rand() % MAX_VAL; sort(array_1, array_1 + m); // output array_1 #ifdef DEBUG cout<<"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 it for(i = 0; i < n; i++) array_2[i] = rand() % MAX_VAL; sort(array_2, array_2 + n); // output array_2 #ifdef DEBUG cout<<"array_2:"<<endl; for(i = 0; i < n; i++) cout<<array_2[i]<<" "; cout<<endl; #endif // get the kth num int kthValue = getKth(0, m - 1, 0, n - 1, k); #ifdef DEBUG cout<<"The kth value by my algorithm: "<<kthValue<<endl; #endif // verify the result int 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 DEBUG cout<<"The real kth value is: "<<realValue<<endl; #endif if(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 DEBUG cout<<endl<<endl; #endif k++; } return 0; }