二分查找变体之二维数组二分查找

一个二维数组,每一行和每一列都是递增的,给出一个数,返回该数字的位置,如果找不到,则返回(-1,-1)

pair<int,int> BinarySearchX(int ** arr,int X,pair<int,int> const& pos,int const val)
{
    typedef pair<int,int> pairI;
    int beg =pos.first;
    int end = pos.second;
    while(beg<=end)
    {
        int mid = (beg+end)/2;
        if(val==arr[X][mid])
        {
            return pairI(X,mid);
        }
        if(val<arr[X][mid] )
        {
            end = mid-1;
        }
        else
        {
            beg = mid+1;
        }
    }
    return pairI(-1,-1);
}
pair<int,int> BinarySearchY(int ** arr,int Y,pair<int,int> const& pos,int const val)
{
    typedef pair<int,int> pairI;

    int beg =pos.first;
    int end = pos.second;
    while(beg<=end)
    {
        int mid = (beg+end)/2;
        if(val == arr[mid][Y])
        {
            return pairI(mid,Y);
        }
        if(val<arr[mid][Y])
        {
            end = mid-1;
        }
        else
        {
            beg = mid+1;
        }
    }
    return pairI(-1,-1);
}

pair<int,int> BinarySearch(int ** arr,pair<int,int> beg,pair<int,int> end,int const val)
{
    typedef pair<int,int> pairI;
    if(beg.first>end.first ||beg.second>end.second)
        return pairI(-1,-1);
    if(val<arr[beg.first][beg.second]||val>arr[end.first][end.second])
    {
        return pairI(-1,-1);
    }
    while(beg.first<=end.first&&beg.second<=end.second)
    {
        if(beg.first==end.first)
        {
            return BinarySearchX(arr,beg.first,pairI(beg.second,end.second),val);
        }
        else if(beg.second == end.second)
        {
            return BinarySearchY(arr,beg.second,pairI(beg.first,end.first),val);
        }
        if((end.first-beg.first)==1&&(end.second-beg.second)==1)
        {
            if(arr[beg.first][beg.second] == val)
                return beg;
            if(arr[end.first][end.second] == val)
                return end;
            if(arr[beg.first][beg.second+1] == val)
                return pairI(beg.first,beg.second+1);
            if(arr[beg.first+1][beg.second] == val)
                return pairI(beg.first+1,beg.second);
            return pairI(-1,-1);            
        }
        pairI mid((beg.first+end.first)/2,(beg.second+end.second)/2);
        if(val ==arr[mid.first][mid.second])
            return mid;
        
        pairI ret = BinarySearch(arr,pairI(beg.first,mid.second+1),pairI(mid.first-1,end.second),val);
        if(ret.first!=-1)
            return ret;
        ret = BinarySearch(arr,pairI(mid.first+1,beg.second),pairI(end.first,mid.second-1),val);
        if(ret.first!=-1)
            return ret;

        if(val <arr[mid.first][mid.second])
        {
            end = mid;
        }
        else
        {
            beg= mid;
        }
    }
    return pairI(-1,-1);    
}


pair<int,int> BinarySearch(int ** arr,pair<int,int>&const size,int const val)
{
    typedef pair<int,int> pairI;
    return BinarySearch(arr,pairI(0,0),pairI(size.first-1,size.second-1),val);
    
}

以下是测试代码

#include<iostream>
#include <cstdlib>
#include <ctime>
#include<algorithm>
#include <utility>
int main(int argc, char* argv[])
{
    srand(time(0));
    int const sizeX = 200;
    int const sizeY = 15000;
    typedef pair<int,int> pairI;
    int ** arr = new int *[sizeX];
    for(int i =0;i<sizeX;++i)
        arr[i] = new int[sizeY];
    arr[0][0] = rand()%20;
    for(int i =1;i<sizeY;++i)
    {
        arr[0][i] =arr[0][i-1]+rand()%10;
    }
    for(int i =1;i<sizeX;++i)
    {
        arr[i][0] = arr[i-1][0]+rand()%10;
    }
    for(int i=1;i<sizeX;++i)
    {
        for(int j=1;j<sizeY;++j)
        {
            arr[i][j] = max(arr[i-1][j],arr[i][j-1]) + rand()%10;
        }
    }
    
    for(int i=0;i<sizeX;++i)
    {
        for(int j=0;j<sizeY;++j)
        {
            cout<<setw(5)<<arr[i][j];
        }
        cout<<endl;
    }
    for(int i=0;i<sizeX;++i)
    {
        for(int j=0;j<sizeY;++j)
        {
            pairI ret = BinarySearch(arr,pairI(sizeX,sizeY),arr[i][j]);
            if(ret.first == -1||arr[ret.first][ret.second]!=arr[i][j])
            {
                cout<<"error"<<endl;
            }
            
        }        
    }
    
    return 0;
}