【暑假】[实用数据结构]UVa11997 K Smallest Sums

UVa11997 K Smallest Sums

 题目：

                                                        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

------------------------------------------------------------------------------------------------------------------------------------------------------------------

 

思路：

 先思考2个有序表（sort后）AB合成的情况。组织如下

【 表】1： A₁+B₁ <=  A₁+B₂ <=  A₁+B₃ <=......

 【表】2：A₂+B₁ <=  A₂+B₂ <=  A₂+B₃ <=......

 ......

 【表】n：A_n+B₁ <=  A_n+B₂ <=  A_n+B₃ <=......

转化为多路归并问题且有总数限制为k，因此将n个【表】合并为一个有序【表】C且表中数据数目为k。优先队列处理：初始化优先队列为n个表的第一元素，每次在队列中取出最小元素加入C并将该最小元素在【表】中的后一个元素入队。共取k个元素。

对于k个有序表的情况：两两合并。

 

于是有代码如下：

 

#include<cstdio>
#include<algorithm>
#include<queue>
#define FOR(a,b,c) for(int a=(b);a<(c);a++)
using namespace std;

const int maxn = 800 + 10;

struct Node{
    int s,b;
    bool operator <(const Node& rhs) const{ //相反定义 < 
      return s>rhs.s; 
    }
};


void merge(int* A,int* B,int*C,int n){ //合并AB数组取其前n小的和放入C 
priority_queue<Node> Q;
  FOR(i,0,n) Q.push(Node{A[i]+B[0],0});
  FOR(i,0,n){
      Node u=Q.top();Q.pop();
      C[i]=u.s;
      int b=u.b;
      if(b+1 < n) Q.push(Node{u.s-B[b]+B[b+1],b+1}); //加入A[a][b+1] 
  }    
}

int main(){
int n;
int A[maxn],B[maxn];

  while(scanf("%d",&n)==1){
      FOR(j,0,n) scanf("%d",&A[j]); sort(A,A+n);
      FOR(i,1,n){
           FOR(j,0,n) scanf("%d",&B[j]);
           sort(B,B+n);
         merge(A,B,A,n);
    }
    printf("%d",A[0]); 
    FOR(i,1,n)
      printf(" %d",A[i]);
    printf("\n");
 }
 return 0;
}