题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4849
Wow! Such City!
Time Limit: 15000/8000 MS (Java/Others) Memory Limit: 102400/102400 K (Java/Others)
Total Submission(s): 1486 Accepted Submission(s): 511
Problem Description
Doge, tired of being a popular image on internet, is considering moving to another city for a new way of life.
In his country there are N (2 ≤N≤ 1000) cities labeled 0 . . . N - 1. He is currently in city 0. Meanwhile, for each pair of cities, there exists a road connecting them, costing Ci,j(a positive integer) for traveling from city i to city
j. Please note that Ci,j may not equal to Cj,i for any given i ≠ j.
Doge is carefully examining the cities: in fact he will divide cities (his current city 0 is NOT included) into M (2 ≤ M ≤ 106) categories as follow: If the minimal cost from his current city (labeled 0) to the city i is Di, city
i belongs to category numbered Di mod M.Doge wants to know the “minimal” category (a category with minimal number) which contains at least one city.
For example, for a country with 4 cities (labeled 0 . . . 3, note that city 0 is not considered), Doge wants to divide them into 3 categories. Suppose category 0 contains no city, category 1 contains city 2 and 3, while category 2 contains city 1, Doge consider
category 1 as the minimal one.
Could you please help Doge solve this problem?
Note:
Ci,j is generated in the following way:
Given integers X0, X1, Y0, Y1, (1 ≤ X0, X1, Y0, Y1≤ 1234567), for k ≥ 2 we have
Xk = (12345 + Xk-1 * 23456 + Xk-2 * 34567 + Xk-1 * Xk-2 * 45678) mod 5837501
Yk = (56789 + Yk-1 * 67890 + Yk-2 * 78901 + Yk-1 * Yk-2 * 89012) mod 9860381
The for k ≥ 0 we have
Zk = (Xk * 90123 + Yk ) mod 8475871 + 1
Finally for 0 ≤ i, j ≤ N - 1 we have
Ci,j = Zi*n+j for i ≠ j
Ci,j = 0 for i = j
Input
There are several test cases. Please process till EOF.
For each test case, there is only one line containing 6 integers N,M,X0,X1,Y0,Y1.See the description for more details.
Output
For each test case, output a single line containing a single integer: the number of minimal category.
Sample Input
3 10 1 2 3 4 4 20 2 3 4 5
Sample Output
1 10 For the first test case, we have 0 1 2 3 4 5 6 7 8 X 1 2 185180 788997 1483212 4659423 4123738 2178800 219267 Y 3 4 1633196 7845564 2071599 4562697 3523912 317737 1167849 Z 90127 180251 1620338 2064506 625135 5664774 5647950 8282552 4912390 the cost matrix C is 0 180251 1620338 2064506 0 5664774 5647950 8282552 0 Hint So the minimal cost from city 0 to city 1 is 180251, while the distance to city 2 is 1620338. Given M = 10, city 1 and city 2 belong to category 1 and 8 respectively. Since only category 1 and 8 contain at least one city, the minimal one of them, category 1, is the desired answer to Doge’s question.
Source
题目大意: 给你一个计算公式,要你根据所给的公式算出N个顶点的图的任意两点间的距离(即权值),然后求出0号点到所有其他点的最短距离,最后输出这些最短距离中%m最小的值即可。
特别注意:1、取模
2、权值注意超出int范围要用lld
3、数组开到n*n+n
详见代码。
#include <iostream> #include <cstdio> #include <cstring> #include <queue> using namespace std; typedef long long ll; ll inf=0x3f3f3f3f; ll x[1010*1010+1010],y[1010*1010+1010],z[1010*1010+1010]; int Map[1010][1010]; int ans[1010],vis[1010]; int n,m; void init() { //memset(vis,0,sizeof(vis)); for(int i=2; i<(n-1)*n+n; i++) { x[i]=(12345+x[i-1]*23456%5837501+x[i-2]*34567%5837501+(x[i-1]*x[i-2]%5837501)*45678%5837501)%5837501; y[i]=(56789+y[i-1]*67890%9860381+y[i-2]*78901%9860381+(y[i-1]*y[i-2]%9860381)*89012%9860381)%9860381; } for(int k=0; k<(n-1)*n+n; k++) { z[k]= (x[k]*90123%8475871+y[k])%8475871+1; } for(int i=0; i<n; i++) { for(int j=0; j<n; j++) { if(i==j) { Map[i][j]=0; } else { Map[i][j]= z[i*n+j]; } } } } void spfa() { for (int i=0; i<n; i++) { ans[i]=inf; vis[i]=0; } queue<int>q; vis[0]=1; ans[0]=0; q.push(0); while (!q.empty()) { int s=q.front(); q.pop(); vis[s]=0; for (int i=0; i<n; i++) { if (ans[i]>Map[s][i]+ans[s]) { ans[i]=Map[s][i]+ans[s]; if (!vis[i]) { q.push(i); vis[i]=1; } } } } } int main() { while (~scanf("%d%d%lld%lld%lld%lld",&n,&m,&x[0],&x[1],&y[0],&y[1])) { init(); spfa(); int Min=ans[1]%m; for (int i=2; i<n; i++) { if (Min>ans[i]%m) Min=ans[i]%m; } printf ("%d\n",Min); } return 0; }