Find K-th smallest in N sorted arrays

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Divide and Conquer, 每次将问题规模缩小到 K*(N-1)/N的大小。

时间O(logN)

注意几个corner case:

1. k > (n1+n2+...+nN)

2. 只剩下一个array。

3. k < N时，从每个数组中取出前k个，然后再取最小的k个。

#include <iostream>#include <vector>#include <algorithm>#include <cstdlib>#include <climits>using namespace std;bool comp(vector<int> a1, vector<int> a2){    return a1.size() < a2.size();}int find_kth(vector<vector<int> > array, int k){    for(int i=0; i<array.size(); i++)        if(array[i].size() == 0)            array.erase(array.begin()+i);    int n = array.size();    std::sort(array.begin(), array.end(), comp);    if(n == 1)        return array[n-1][k-1];    if(k < n)    {        vector<int> result;        for(int i=0; i<n; i++)        {            for(int j=0; j<k && j<array[i].size(); j++)                result.push_back(array[i][j]);        }        std::sort(result.begin(), result.end());        return result[k-1];    }    int num = k/n;    int sum = 0;    vector<int> nums(n);    for(int i=0; i<n; i++)    {        nums[i] = min(num, (int)(array[i].size()));        sum += nums[i];        if(i < n-1) num = (k-sum)/(n-i-1);    }    if(sum < k)    {        nums[n-1] = k - (sum-nums[n-1]);    }    int min = INT_MAX, min_idx = -1;    for(int i=0; i<n; i++)    {        if(nums[i] >= 1 && array[i][nums[i]-1] < min)        {            min = array[i][nums[i]-1];            min_idx = i;        }    }    array[min_idx].erase(array[min_idx].begin(), array[min_idx].begin()+nums[min_idx]);    return find_kth(array, k-nums[min_idx]);}int find_kth2(vector<int> A, int m, vector<int> B, int n, int k){    if(m > n)        return  find_kth2(B, n, A, m, k);    if(m == 0)        return B[k-1];    if(k == 1)        return min(A[0], B[0]);            int a = min(m, k/2);    int b = k - a;    if(A[a-1] < B[b-1])    {        vector<int> AA(A.begin()+a, A.end());        return find_kth2(AA, m-a, B, n, k-a);    }    else if(A[a-1] > B[b-1])    {        vector<int> BB(B.begin()+b, B.end());        return find_kth2(A, m, BB, n-b, k-b);    }    else        return A[a-1];    }int main(){    vector<int> v1(100);    vector<int> v2(200);    vector<int> v3(300);    vector<int> v4(400);    vector<int> v5(500);    vector<int> merged(1500);    vector<vector<int> > array(5);    array[0] = v1;    array[1] = v2;    array[2] = v3;    array[3] = v4;    array[4] = v5;    int count = 0;    for(int i=0; i<array.size(); i++)    {        for(int j=0; j<array[i].size(); j++)        {            int rad = rand()%100000;            array[i][j] = rad;            merged[count] = rad;            count++;        }        std::sort(array[i].begin(), array[i].end());    }    std::sort(merged.begin(), merged.end());    /*    for(int k=0; k<array.size(); k++)    {        for(int i=0; i<array[k].size(); i++)            cout << array[k][i] << " ";        cout << endl;            }*/        //cout << find_kth(array, 1333) << endl;        int t;    for(int i=1; i<1500; i++)        if(merged[i-1] != (t = find_kth(array, i)))            cout << "error on " << i << " " << merged[i-1] << " " << t << endl;    return 0;}

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