lightoj 1179 - Josephus Problem 【约瑟夫环】
2015-11-08 12:36
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1179 - Josephus Problem
The historian Flavius Josephus relates how, in the Romano-Jewish conflict of 67 A.D., the Romans took the town of Jotapata which he was commanding. Escaping, Josephus found himself trapped in a cave with 40 companions. The Romans discovered his whereabouts
and invited him to surrender, but his companions refused to allow him to do so. He therefore suggested that they kill each other, one by one, the order to be decided by lot. Tradition has it that the means for affecting the lot was to stand in a circle, and,
beginning at some point, count round, every third person being killed in turn. The sole survivor of this process was Josephus, who then surrendered to the Romans. Which begs the question: had Josephus previously practiced quietly with 41 stones in a dark corner,
or had he calculated mathematically that he should adopt the 31st position in order to survive?
Now you are in a similar situation. There are n persons standing in a circle. The persons are numbered from 1 to n circularly. For example, 1 and n are adjacent and 1 and 2 are
also. The count starts from the first person. Each time you count up to k and the kth person is killed and removed from the circle. Then the count starts from the next person. Finally one person remains. Given n and k you
have to find the position of the last person who remains alive.
Each case contains two positive integers n (1 ≤ n ≤ 105) and k (1 ≤ k < 231).
PROBLEM SETTER: JANE ALAM JAN
很水的约瑟夫环。
推导f(n) = (f(n-1) + k) % n。
AC代码:
PDF (English) | Statistics | Forum |
Time Limit: 2 second(s) | Memory Limit: 32 MB |
and invited him to surrender, but his companions refused to allow him to do so. He therefore suggested that they kill each other, one by one, the order to be decided by lot. Tradition has it that the means for affecting the lot was to stand in a circle, and,
beginning at some point, count round, every third person being killed in turn. The sole survivor of this process was Josephus, who then surrendered to the Romans. Which begs the question: had Josephus previously practiced quietly with 41 stones in a dark corner,
or had he calculated mathematically that he should adopt the 31st position in order to survive?
Now you are in a similar situation. There are n persons standing in a circle. The persons are numbered from 1 to n circularly. For example, 1 and n are adjacent and 1 and 2 are
also. The count starts from the first person. Each time you count up to k and the kth person is killed and removed from the circle. Then the count starts from the next person. Finally one person remains. Given n and k you
have to find the position of the last person who remains alive.
Input
Input starts with an integer T (≤ 200), denoting the number of test cases.Each case contains two positive integers n (1 ≤ n ≤ 105) and k (1 ≤ k < 231).
Output
For each case, print the case number and the position of the last remaining person.Sample Input | Output for Sample Input |
6 2 1 2 2 3 1 3 2 3 3 4 6 | Case 1: 2 Case 2: 1 Case 3: 3 Case 4: 3 Case 5: 2 Case 6: 3 |
PROBLEM SETTER: JANE ALAM JAN
很水的约瑟夫环。
推导f(n) = (f(n-1) + k) % n。
AC代码:
#include <cstdio> #include <cstring> #include <cmath> #include <cstdlib> #include <algorithm> #include <queue> #include <stack> #include <map> #include <vector> #define INF 0x3f3f3f3f #define eps 1e-8 #define MAXN 500000+10 #define MAXM 50000000 #define Ri(a) scanf("%d", &a) #define Rl(a) scanf("%lld", &a) #define Rs(a) scanf("%s", a) #define Pi(a) printf("%d\n", (a)) #define Pl(a) printf("%lld\n", (a)) #define Ps(a) printf("%s\n", (a)) #define W(a) while(a--) #define CLR(a, b) memset(a, (b), sizeof(a)) #define MOD 1000000007 #define LL long long using namespace std; int main() { int t, kcase = 1; Ri(t); W(t) { int n, k; Ri(n); Ri(k); int last = 0; for(int i = 2; i <= n; i++) last = (last + k) % i; printf("Case %d: %d\n", kcase++, last+1); } return 0; }