G - And Then There Was One (約瑟夫環)
Description
Let’s play a stone removing game.
Initially, n stones are arranged on a circle and numbered 1, …, n clockwise (Figure 1). You are also given two numbers k and m. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m
Initial state |
Step 1 |
Step 2 |
Step 3 |
Step 4 |
Step 5 |
Step 6 |
Step 7 |
Final state |
Initial state: Eight stones are arranged on a circle.
Step 1: Stone 3 is removed since m = 3.
Step 2: You start from the slot that was occupied by stone 3. You skip four stones 4, 5, 6 and 7 (since k
Step 3: You skip stones 1, 2, 4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.
Steps 4–7: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.
Final State: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.
Input
The input consists of multiple datasets each of which is formatted as follows.
n k m
The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.
2 ≤ n ≤ 10000, 1 ≤ k ≤ 10000, 1 ≤ m ≤ n
The number of datasets is less than 100.
Output
For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.
Sample Input
8 5 3 100 9999 98 10000 10000 10000 0 0 0
Sample Output
1 93 2019
解題思路:正常約瑟夫環是從1號開始,如果從m號,那麽就是報數延遲到了m,那最後報數的人也會相應延遲m。
AC代碼:
1 #include<iostream> 2 #include<cstdio> 3 using namespace std; 4 int n,k,m,s; 5 int main(){ 6 while(~scanf("%d%d%d",&n,&k,&m)&&(n+k+m)){ 7 s=0; 8 for(int i=2;i<n;++i)s=(s+k)%i; 9 s=(s+m)%n;//最後報數的人延遲m 10 cout<<(s+1)<<endl; 11 } 12 return 0; 13 }
G - And Then There Was One (約瑟夫環)