leetcode_c++：Median_of _two_sorted_arrays（004）

题目

两个已经排序好的数组num1和num2，长度分别是m和n。找到两个有序数组的中位数（中间的那个数，若为偶数，则是中间的两个数的平均数）要求复杂度是O(lg(n+m))

• 算法1
  Merge两个数组，然后取得中位数

复杂度：O（n+m）

#include <iostream>#include <algorithm>#include <vector>using namespace std;const int maxn=100;class Solution{public:    double findMedianSortedArrays(int A[],int m,int B[],int n){        vector<int> C;        int pa=0,pb=0; //pointer of A[] & B[]        while (pa<m || pb<n) {            if(pa==m){                C.push_back(B[pb++]);                continue;            }            if(pb==n){                C.push_back(A[pa++]);                continue;            }            if(A[pa]>B[pb])                C.push_back(B[pb++]);            else                C.push_back(A[pa++]);        }        if((n+m)&1)  // 奇数，按位与            return C[(n+m)/2];        else            return (C[(n+m)/2-1]+C[(n+m)/2])/2.0;    }};int main(){    int n,m;    int A[maxn],B[maxn];    Solution s;    while(cin>>n){        for(int i=0;i<n;i++)            cin>>A[i];        cin>>m;        for(int i=0;i<m;i++)            cin>>B[i];        cout<<s.findMedianSortedArrays(A,n, B, m)<<endl;    }    return 0;}

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• 算法2
  求两个数组中的第k大的数
  若A[k/2-1]

#include <iostream>#include <algorithm>#include <vector>using namespace std;const int N = 0;class Solution {    private:        double findKthSortedArrays(int A[], int m, int B[], int n, int k) {            if (m < n) {                swap(n, m);                swap(A, B);            }            if (n == 0)                return A[k - 1];            if (k == 1)                return min(A[0], B[0]);            int pb = min(k / 2, n), pa = k - pb;            if (A[pa - 1] > B[pb - 1])                return findKthSortedArrays(A, m, B + pb, n - pb, k - pb);            else if (A[pa - 1] < B[pb - 1])                return findKthSortedArrays(A + pa, m - pa, B, n, k - pa);            else                return A[pa - 1];        }    public:        double findMedianSortedArrays(int A[], int m, int B[], int n) {            if ((n + m)&1)                return findKthSortedArrays(A, m, B, n, (n + m) / 2 + 1);            else                return (findKthSortedArrays(A, m, B, n, (n + m) / 2 + 1) +                        findKthSortedArrays(A, m, B, n, (n + m) / 2)) / 2.0;        }};int main() {    int n, m;    int A[100], B[100];    Solution s;    while (cin >> n) {        for (int i = 0; i < n; i++)             cin >> A[i];        cin >> m;        for (int i = 0; i < m; i++)             cin >> B[i];        cout << s.findMedianSortedArrays(A, n, B, m) << endl;    }    return 0;}

• vector版本

#include <iostream>#include <algorithm>#include <vector>using namespace std;const int N = 0;class Solution {  public:      double findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {          int m = nums1.size();          int n = nums2.size();          int value1 = KthValue(nums1, m, nums1.begin(), nums2, n, nums2.begin(), (m+n+1)/2);          double result = value1;          if (((m+n) & 1) == 0)          {              int value2 = KthValue(nums1, m, nums1.begin(), nums2, n, nums2.begin(), (m+n)/2+1);              result = ((double)value1 + (double)value2)/2;          }          return result;       }  private:      int KthValue(vector<int> &nums1, int size1, vector<int>::iterator it1, vector<int> &nums2,                   int size2, vector<int>::iterator it2, int k)      {          /*if (size1 > size2)          {              return KthValue(nums2, size2, it2, nums1, size1, it1, k);          }  */        if(size1>size2)        {            swap(size1,size2);            nums1.swap(nums2);        }        if (size1 == 0)          {              return *(it2+k-1);          }          if (k == 1)          {              return min(*it1, *it2);          }          int offset1 = min(k/2, size1);          int offset2 = k - offset1;          if (*(it1+offset1-1) <= *(it2+offset2-1))          {              return KthValue(nums1, size1-offset1, it1+offset1, nums2, offset2, it2, k-offset1);          }          else          {              return KthValue(nums1, offset1, it1, nums2, size2-offset2, it2+offset2, k-offset2);          }      }  }; int main() {    int n, m,t;   vector<int> A;   vector<int> B;    Solution s;  while(cin>>n)  {      for(int i=0;i<n;i++)      {          cin>>t;          A.push_back(t);      }      cin>>m;      for(int i=0;i<m;i++)      {          cin>>t;          B.push_back(t);      }      for(int i=0;i<n;i++)          cout<<"A= "<<A[i]<<endl;      for(int i=0;i<m;i++)          cout<<"B= "<<B[i]<<endl;      cout<<s.findMedianSortedArrays(A,B)<<endl;  }    return 0;}