(DS "Algorithmic Competition Primer Classic") UVA 11997 K Smallest Sums

The main topic: There are K groups, each array to select a number, composed of k^k number. Select the smallest number of top K in this k^k number

Problem Solving Ideas:

1, if only k array, then the last number of the smallest first k should be obtained from the first two arrays of the smallest number of K and a third array

It is obtained by the rule arithmetic.

2. If there are only 3 numbers per array. Then the first two arrays (A: (A0,A1,A2) B: (both B0,b1,b2,a and B arrays are ordered) have the following result matrix:

A0+b0,a0+b1,a0+b2

A1+b0,a1+b1,a1+b2

A2+b0,a2+b1,a2+b2

In this matrix, the a0+b0 is certainly the smallest. If only 3 minimum numbers are maintained in a queue, the next occurrence of the minimum number is

A0+b1. Analysis is as follows:

By a1+b1>a1+b0, it is not possible to produce the next minimum number in A1+B1 and beyond. This logic indicates where the next possible minimum

It's a0+b1.

3, in the following of this solution, he did not work out k^k results, it is the essence of n+n may produce a minimum number of results

。

Problem KK Smallest Sums

You ' re given k-arrays, each with a k integers. There is KK 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'll be several test cases. The first line of each case is contains an integer k (2<=k<=750). Each of the following K lines contains k positive integers in each array. Each of the 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

31 8 59 2 510 7 621 11 2

Output for the Sample Input

9 10 122 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!

The code is as follows:

/* * uva_11997.cpp * * Created on:2014 December 30 * author:administrator * * #include <iostream> #include <cstdi o> #include <queue> #include <algorithm>using namespace std;const int maxn = 758;int a[maxn][maxn];struct Item{int S,b;item (int s,int b): s (s), B (b) {}bool operator < (const item& B) Const{return s > b.s;}; void merge (int* a,int* b,int* c,int N) {priority_queue<item> q;int i;for (i = 0; i < n; ++i) {Q.push (Item (a[i] + B [0],0)];} for (i = 0; i < n; ++i) {Item item = Q.top (); Q.pop (); C[i] = item.s;int B = item.b;if (B+1 < N) {Q.push (item (ITEM.S-B[B] + b[b+1],b+1)}}} int main () {int n;while (scanf ("%d", &n) = = 1) {int I;int j;for (i = 0; i < n; ++i) {for (j = 0; J < N; ++j) {scanf ( "%d", &a[i][j]);} Sort (a[i],a[i]+n);} for (i = 1; i < n; ++i) {merge (a[0],a[i],a[0],n);} printf ("%d", a[0][0]); for (i = 1; i < n; ++i) {printf ("%d", A[0][i]);} printf ("\ n");} return 0;}

(DS "Algorithmic Competition Primer Classic") UVA 11997 K Smallest Sums