hdu5643 King's Game(约瑟夫环+线段树)
2016-03-17 13:45
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Problem Description
In order to remember history, King plans to play losephus problem in the parade gap.He calls n(1≤n≤5000) soldiers,
counterclockwise in a circle, in label 1,2,3...n.
The first round, the first person with label 1 counts
off, and the man who report number 1 is
out.
The second round, the next person of the person who is out in the last round counts off, and the man who report number 2 is
out.
The third round, the next person of the person who is out in the last round counts off, and the person who report number 3 is
out.
The N - 1 round, the next person of the person who is out in the last round counts off, and the person who report number n−1 is
out.
And the last man is survivor. Do you know the label of the survivor?
Input
The first line contains a number T(0<T≤5000),
the number of the testcases.
For each test case, there are only one line, containing one integer n,
representing the number of players.
Output
Output exactly T lines.
For each test case, print the label of the survivor.
Sample Input
2
2
3
Sample Output
2
2
Hint:
For test case #1:the man who report number $1$ is the man with label $1$, so the man with label $2$ is survivor.
For test case #1:the man who report number $1$ is the man with label $1$, so the man with label 1 is out. Again the the man with label 2 counts $1$, the man with label $3$ counts $2$, so the man who report number $2$ is the man with label $3$. At last the man with label $2$ is survivor.
题意:n个人排成一圈,每回合杀死一个人,杀死后从那个人的下一个人开始数数,第i个回合数到i的那个人被杀死,问最后剩下的人的编号是多少。
思路:这题和约瑟夫环有点像,我们设f
为总人数为n时,按照题目中的规则杀,最后剩下来的人的编号是多少。我们每次杀死一个人后就重新编号,那么f[1]=0,即当最后只剩下一个人时,他经过重新编号后新的编号为0,那么在上一轮,他的编号为t=(0+n-1)%2,倒数第二轮他的编号为(t+n-2)%3,这样可以依次类推到f
,就是答案了,所以这题只要用O(n^2)的复杂度初始化一下就行了。
这种方法有个缺陷,就是不能知道每一次杀死的人的编号是什么,如果要知道每一次杀死的人的编号,我们可以用线段树做。我们在线段树上对于每一段维护其剩余的空位数,那么我们每次计算这一次杀死的人是线段树总区间的第几个人,这样就可以知道每次的编号是多少了,如果这题用线段树,为了防超时,可以打个表。
下面的程序还要打个表再提交。
In order to remember history, King plans to play losephus problem in the parade gap.He calls n(1≤n≤5000) soldiers,
counterclockwise in a circle, in label 1,2,3...n.
The first round, the first person with label 1 counts
off, and the man who report number 1 is
out.
The second round, the next person of the person who is out in the last round counts off, and the man who report number 2 is
out.
The third round, the next person of the person who is out in the last round counts off, and the person who report number 3 is
out.
The N - 1 round, the next person of the person who is out in the last round counts off, and the person who report number n−1 is
out.
And the last man is survivor. Do you know the label of the survivor?
Input
The first line contains a number T(0<T≤5000),
the number of the testcases.
For each test case, there are only one line, containing one integer n,
representing the number of players.
Output
Output exactly T lines.
For each test case, print the label of the survivor.
Sample Input
2
2
3
Sample Output
2
2
Hint:
For test case #1:the man who report number $1$ is the man with label $1$, so the man with label $2$ is survivor.
For test case #1:the man who report number $1$ is the man with label $1$, so the man with label 1 is out. Again the the man with label 2 counts $1$, the man with label $3$ counts $2$, so the man who report number $2$ is the man with label $3$. At last the man with label $2$ is survivor.
题意:n个人排成一圈,每回合杀死一个人,杀死后从那个人的下一个人开始数数,第i个回合数到i的那个人被杀死,问最后剩下的人的编号是多少。
思路:这题和约瑟夫环有点像,我们设f
为总人数为n时,按照题目中的规则杀,最后剩下来的人的编号是多少。我们每次杀死一个人后就重新编号,那么f[1]=0,即当最后只剩下一个人时,他经过重新编号后新的编号为0,那么在上一轮,他的编号为t=(0+n-1)%2,倒数第二轮他的编号为(t+n-2)%3,这样可以依次类推到f
,就是答案了,所以这题只要用O(n^2)的复杂度初始化一下就行了。
这种方法有个缺陷,就是不能知道每一次杀死的人的编号是什么,如果要知道每一次杀死的人的编号,我们可以用线段树做。我们在线段树上对于每一段维护其剩余的空位数,那么我们每次计算这一次杀死的人是线段树总区间的第几个人,这样就可以知道每次的编号是多少了,如果这题用线段树,为了防超时,可以打个表。
#include<iostream> #include<stdio.h> #include<stdlib.h> #include<string.h> #include<math.h> #include<vector> #include<map> #include<set> #include<queue> #include<stack> #include<string> #include<bitset> #include<algorithm> using namespace std; typedef long long ll; typedef long double ldb; #define inf 99999999 #define pi acos(-1.0) #define maxn 6006 int a[maxn]; void init() { int i,j; a[1]=1; for(i=2;i<=5000;i++){ int num=0; //for(j=i-1;j>=1;j--){ for(j=1;j<=i;j++){ num=(num+i-j+1)%j; } a[i]=num+1; } } int main() { int n,m,i,j,T; init(); scanf("%d",&T); while(T--) { scanf("%d",&n); printf("%d\n",a ); } return 0; }
下面的程序还要打个表再提交。
#include<iostream> #include<stdio.h> #include<stdlib.h> #include<string.h> #include<math.h> #include<vector> #include<map> #include<set> #include<queue> #include<stack> #include<string> #include<bitset> #include<algorithm> using namespace std; typedef long long ll; typedef long double ldb; #define inf 99999999 #define pi acos(-1.0) #define maxn 5006 struct node{ int l,r,num; }b[4*maxn]; int n; void build(int l,int r,int th) { int mid; b.l=l;b .r=r; b .num=r-l+1; if(l==r)return; mid=(l+r)/2; build(l,mid,th*2); build(mid+1,r,th*2+1); } void update(int num,int cishu,int th) { int mid; if(b .l==b .r){ b .num=0; if(cishu==n)printf("%d,",b .l); return; } if(b[th*2].num>=num){ update(num,cishu,th*2); } else{ update(num-b[th*2].num,cishu,th*2+1 ); } b .num=b[th*2].num+b[th*2+1].num; } int main() { int t,m,i,j,T,k; freopen("o.txt","w",stdout); for(n=1;n<=5000;n++) { build(1,n,1); int p=1; int tot=n; for(k=1;k<=n;k++){ p=(p+k-1)%tot; //这里算这回合杀死的人的编号的空格数 if(p==0)p=tot; update(p,k,1); if(p==tot)p=1; //这里算出这回合杀死人后,下一回合第一个数数的编号,也可以看做是下一回合站第几个空位 tot--; //每次总人数减1 } } } 相关文章推荐
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