D

Problem K

K Smallest Sums

You're given k arrays, each array has k integers. There are k^k ways to pick exactly one element in each array and calculate the sum of the integers. Your task is to find the k smallest sums among them.

Input

There will be several test cases. The first line of each case contains an integer k (2<=k<=750). Each of the following k lines contains k positive integers in each array. Each of these integers does not exceed 1,000,000. The input is terminated by end-of-file (EOF). The size of input file does not exceed 5MB.

Output

For each test case, print the k smallest sums, in ascending order.

Sample Input

3
1 8 5
9 2 5
10 7 6
2
1 1
1 2

Output for the Sample Input

9 10 12
2 2

---

Rujia Liu's Present 3: A Data Structure Contest Celebrating the 100th Anniversary of Tsinghua University
Special Thanks: Yiming Li
Note: Please make sure to test your program with the gift I/O files before submitting!

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <list>
#include <iomanip>
#include <cstdlib>
#include <sstream>
using namespace std;
typedef long long LL;
const int INF=0x5fffffff;
const double EXP=1e-6;
const int MS=800;
int ans[MS],a[MS],n;
struct node
{
    int s,b;
    node(int s,int b):s(s),b(b){}
    bool operator <(const node &a)const
    {
        return s>a.s;
    }
};

void merge(int *A,int *B,int *C,int n)
{
    priority_queue<node> pq;
    for(int i=0;i<n;i++)
        pq.push(node(A[i]+B[0],0));
    for(int i=0;i<n;i++)
    {
        node t=pq.top();
        pq.pop();
        C[i]=t.s;
        int b=t.b;
        if(b+1<n)
            pq.push(node(t.s-B[b]+B[b+1],b+1));
    }
}

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=0;i<n;i++)
            scanf("%d",&ans[i]);
        sort(ans,ans+n);
        for(int i=1;i<n;i++)
        {
            for(int j=0;j<n;j++)
                scanf("%d",&a[j]);
            sort(a,a+n);
            merge(ans,a,ans,n);
        }
        for(int i=0;i<n;i++)
        {
            if(i)
                printf(" ");
            printf("%d",ans[i]);
        }
        printf("
");
    }
    return 0;
}