poj-1659-Frogs' Neighborhood-图论-Havel-Hakimi定理-java
2017-09-20 10:43
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Frogs' Neighborhood
Description未名湖附近共有N个大小湖泊L1, L2, ..., Ln(其中包括未名湖),每个湖泊Li里住着一只青蛙Fi(1 ≤ i ≤ N)。如果湖泊Li和Lj之间有水路相连,则青蛙Fi和Fj互称为邻居。现在已知每只青蛙的邻居数目x1, x2,..., xn,请你给出每两个湖泊之间的相连关系。Input第一行是测试数据的组数T(0 ≤ T ≤ 20)。每组数据包括两行,第一行是整数N(2 < N < 10),第二行是N个整数,x1, x2,..., xn(0 ≤ xi ≤ N)。Output对输入的每组测试数据,如果不存在可能的相连关系,输出"NO"。否则输出"YES",并用N×N的矩阵表示湖泊间的相邻关系,即如果湖泊i与湖泊j之间有水路相连,则第i行的第j个数字为1,否则为0。每两个数字之间输出一个空格。如果存在多种可能,只需给出一种符合条件的情形。相邻两组测试数据之间输出一个空行。Sample Input
Time Limit: 5000MS | Memory Limit: 10000K | |||
Total Submissions: 10020 | Accepted: 4190 | Special Judge |
3 7 4 3 1 5 4 2 1 6 4 3 1 4 2 0 6 2 3 1 1 2 1Sample Output
YES 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 NO YES 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0
解题思路:我现在开始系统的学一下图论 从基础开始 正常来说给一个图让你求出度入度很容易 但是反过来
给你每个顶点的出度入度和 让你判断是否存在这样一个图 图论给点概念叫:可图的
感觉很瘪嘴 有这样一个定理专门判断是否可图 Havel-Hakimi定理
流程就是将度的序列从大到小排好 设第一个点的度为d 然后让d=0;从序列的第二点开始数d个每个点的度减1
之后一次重复上述过程
稍微一看 你就知道这是再模拟连边的过程 用的是贪心思想 再减一的过程中出现了负数 意味着不存在这样的图
图中点的度一定大于等于0 所以直接结束输出no就可以了 以下是代码 有个优化但我没加
因为每次都要排序 然而不用次次都排 每进行两次排一次序就可以
import java.util.Arrays;import java.util.Scanner;public class Main {public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int t = scanner.nextInt(); for (int i = 0; i < t; i++) {int n = scanner.nextInt(); Node [] arr = new Node; for (int j = 0; j < arr.length; j++) {arr[j] = new Node(j, scanner.nextInt()); } int [][] shu = new int; int flag = 0; k:while (true) {Arrays.sort(arr);if(arr[0].d==0) {break;}for (int j = 1; j <= arr[0].d; j++) {arr[j].d -= 1;if (arr[j].d <0) {flag = 1;break k;}shu[arr[0].i][arr[j].i] = 1;shu[arr[j].i][arr[0].i] = 1;}arr[0].d = 0;} if (flag == 1) {System.out.println("NO");if(i!=t-1)System.out.println();}else {System.out.println("YES");for (int j = 0; j < n; j++) {for (int j2 = 0; j2 < n; j2++) {System.out.print(j2==0?shu[j][j2]:" "+shu[j][j2]);}System.out.println();}if(i!=t-1)System.out.println();} }}}class Node implements Comparable<Node> {int i ;int d ;public Node(int i,int d) { this.d = d;this.i = i;}@Ova938erridepublic int compareTo(Node o) {if (d>o.d) {return -1;}else if (d==o.d) {return 0;}return 1;}}
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