poj 2769 Reduced ID Numbers (同余定理)
2017-08-02 08:34
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Reduced ID Numbers
Description
T. Chur teaches various groups of students at university U. Every U-student has a unique Student Identification Number (SIN). A SIN s is an integer in the range 0 ≤ s ≤ MaxSIN with MaxSIN = 106-1. T. Chur finds this range of SINs too large for identification
within her groups. For each group, she wants to find the smallest positive integer m, such that within the group all SINs reduced modulo m are unique.
Input
On the first line of the input is a single positive integer N, telling the number of test cases (groups) to follow. Each case starts with one line containing the integer G (1 ≤ G ≤ 300): the number of students in the group. The following G lines each contain
one SIN. The SINs within a group are distinct, though not necessarily sorted.
Output
For each test case, output one line containing the smallest modulus m, such that all SINs reduced modulo m are distinct.
Sample Input
Sample Output
Source
Northwestern Europe 2005
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 10341 | Accepted: 4114 |
T. Chur teaches various groups of students at university U. Every U-student has a unique Student Identification Number (SIN). A SIN s is an integer in the range 0 ≤ s ≤ MaxSIN with MaxSIN = 106-1. T. Chur finds this range of SINs too large for identification
within her groups. For each group, she wants to find the smallest positive integer m, such that within the group all SINs reduced modulo m are unique.
Input
On the first line of the input is a single positive integer N, telling the number of test cases (groups) to follow. Each case starts with one line containing the integer G (1 ≤ G ≤ 300): the number of students in the group. The following G lines each contain
one SIN. The SINs within a group are distinct, though not necessarily sorted.
Output
For each test case, output one line containing the smallest modulus m, such that all SINs reduced modulo m are distinct.
Sample Input
2 1 124866 3 124866 111111 987651
Sample Output
1 8
Source
Northwestern Europe 2005
#include <iostream> #include<cstdio> #include<cstring> #include<cmath> using namespace std; int f[305]; int vis[100001]; int main() { int T; int n; int i,j; scanf("%d",&T); while(T--) { scanf("%d",&n); for( i=0;i<n;i++) scanf("%d",&f[i]); for( i=n;;i++) { memset(vis,0,sizeof(vis)); for( j=0;j<n;j++) { if(vis[f[j]%i]) { //find=0; break; } 4000 vis[f[j]%i]=1; } if(j>=n)break; } printf("%d\n",i); } return 0; }
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