"UVA 11997 K smallest Sums" priority queue

Examples from the priority queue of the training guide.

Title Link: http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=18702

Test instructions: Given a k array of integers, each containing k elements. Taking an element together in each array, you can get the KK and the smallest k values (not the weight).

Data range: K [2, 750]

Idea: Violent enumeration of k^k is undesirable.

"First look at the simplified version of the problem: give two K-length arrays A and B, respectively, in A and B to take a number and add, you can get k^2 and, to find these and the smallest K." ”

First, A and B are sorted from small to large. Because only the smallest of the first k values, we can first assume that b[0] and a k elements of a set of elements are the smallest sum of k, and then each time the minimum value of s smin saved to the result array R, and the Smin minus B[i], plus b[i+1] after the resulting value is put back into the set S, Keep the size of s always K. The K-elements in R are the result after the K-wheel is removed-and the operation is put back. We called this process a merge of a-B. The complexity of merging once is O (KLOGK)

s requires K-times insertions and deletions, with a minimum value, so the data structure chooses the priority queue implemented by the complete binary heap.

Now from the two array, a, B to the K-group A1~ak, simply consider the A1 as a, followed by the i:2~k, each time the AI merged into the A1, so after the K 22 merge, the number of K in A1 is the result. Total complexity O (K2LOGK)

1#include <cstdio>2#include <algorithm>3#include <queue>4 using namespacestd;5 Const intMax_k =760;6 7 structelem{8     intsum, b;9Elem (intSintb): sum (s), B (b) {}Tenelem&operator= (Constelem&e) { Onesum =e.sum; Ab =e.b; -         return* This; -     } the     BOOL operator< (Constelem& e)Const{ -         returnSum > e.sum;//Small Top Pile -     } - }; +  - voidMergeintAintBintN) { +Priority_queue<elem>PQ; A      for(intI=0; i<n; i++){ atPq.push (Elem (a[i] + b[0],0)); -     } -      for(intI=0; i<n; i++){ -Elem e =pq.top (); -A[i] =e.sum; - Pq.pop (); inE.sum = e.sum-b[e.b] + b[e.b+1]; -e.b = e.b +1; to Pq.push (e); +     } - //for (int i=0; i<n; i++) { the //printf ("%d", A[i]); * //    } $ //printf ("\ n");Panax Notoginseng } -  the intK; + intA[max_k], b[max_k]; A  the intMain () + { -Freopen ("11997.txt","R", stdin); $      while(~SCANF ("%d", &k)) { $          for(intI=0; i<k; i++){ -scanf"%d", &a[i]); -         } theSort (A, A +k); -          for(intI=1; i<k; i++){Wuyi              for(intj=0; j<k; J + +){ thescanf"%d", &b[j]); -             } WuSort (b, + +k); - merge (A, b, k); About         } $printf"%d", a[0]); -          for(intI=1; i<k; i++){ -printf"%d", A[i]); -         } Aprintf"\ n"); +     } the     return 0; -}

"UVA 11997 K smallest Sums" priority queue