题意:现在汉诺塔变成4个柱子的,(原本3个柱子的最小步数为 2^n-1),该怎么办啦?原来题目中有解法,(At first k >= 1 disks on towerA are fixed and the remaining n-k disks are moved from tower A totower B using the algorithm for four towers.Then the remaining kdisks from tower A are moved to tower D
using the algorithm forthree towers. At last the n - k disks from tower B are moved totower D again using the algorithm for four towers)意思是,先将k个移到b柱子上,然后b柱子不懂,将剩余的n-k个从A移到D,这就相当是3个柱子的。最后还需要将B柱子上的k个转移到D上面去。
思路:上面官方已经把思路给你了,如果还不会的话,请再次读题。
状态转移方程: dp[i] = min(dp[i],2*dp[k]+mypow(2,i-k)-1); (1<=k<n)
#include<cstdio> #include<cstring> #include<iostream> #define INF 100000000000 #define min(a1,b1) (a1)>(b1)?(b1):(a1) using namespace std; int n; long long dp[13]; long long mypow(long long a,int t) { if(t==1) return a; else if(t==0) { return 1; } else return a*mypow(a,t-1); } int main(void) { n = 12; dp[1] = 1; for(int i=2;i<=n;++i) { dp[i] = INF; for(int k=1;k<i;++k) { dp[i] = min(dp[i],2*dp[k]+mypow(2,i-k)-1); } } for(int i=1;i<=12;++i) cout<<dp[i]<<endl; return 0; }