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Tower of Hanoi minimum cost DP.cpp
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Tower of Hanoi minimum cost DP.cpp
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// https://codeforces.com/contest/392/problem/B
#include<bits/stdc++.h>
///...................................*****.................................................///
/// Author : Raihan Khan Raka ( raihankhanraka@gmail.com ) ///
/// Department of Computer Science ///
/// & Engineering ///
/// Comilla University , Bangladesh. ///
///...................................*****.................................................///
/*....................................Values................................................*/
#define p5 100007
#define p6 1000007
#define PI acos(-1)
#define M 1000000007
#define inf 1LL << 62
#define white 0
#define gray 1
#define black 2
/*....................................Functions.............................................*/
#define sqr(x) x*x
#define sc scanf
#define pf printf
#define pfn printf("\n")
#define scin(x) sc("%d",&(x))
#define scin2(xx,zz) scanf("%d %d",&xx,&zz)
#define scln(x) sc("%lld",&(x))
#define scln2(xx,zz) scanf("%lld %lld",&xx,&zz)
#define min3(a,b,c) min(a,b<c?b:c)
#define max3(a,b,c) max(a,b>c?b:c)
#define all(v) v.begin(), v.end()
#define ok cout << "ok" << endl
#define mem(x,y) memset(x,y,sizeof(x))
#define clr(a) a.clear()
#define READ(f) freopen(f, "r", stdin)
#define WRITE(f) freopen(f, "w", stdout)
/*...................................Data_Types............................................*/
#define lli long long int
#define ull unsigned long long int
#define pii pair < int, int>
#define pll pair < ll, ll>
#define veci vector<int>
#define vecl vector<long long int>
#define vecp vector< pair<int,int> >
#define mapstrint map< string , int >
#define mapstrstr map< string , string >
#define mapint map< int, int >
#define uset unordered_set
#define umap unordered_map
#define pq priority_queue
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
/*.....................................Loops...............................................*/
#define rep( i , a , b ) for( i=a ; i<b ; i++)
#define rev( i , a , b ) for( i=a ; i>=b ; i--)
#define repx( i ,a,b, x) for( i=a ; i<b ; i+=x)
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//int month[]={31,28,31,30,31,30,31,31,30,31,30,31};
///------------------------------- Mudular functions----------------------------------------
/*
inline lli power(lli x, lli y){ lli temp; if( y == 0) return 1; temp = power(x, y/2); if (y%2 == 0) return temp*temp; else return x*temp*temp; }
inline lli add(lli a, lli b) {a += b; return a >= M ? a - M : a;}
inline lli sub(lli a, lli b) {a -= b; return a < 0 ? a + M : a;}
inline lli mul(lli a, lli b) {return (a * b) % M;}
lli gcd(lli x,lli y)
{
if(x==0) return y;
return gcd(y%x,x);
}
lli bigmod(lli n, lli k )
{
lli ans=1;
while(k)
{
if(k&1)
ans=(ans*n)%M;
k=k>>1;
n=(n*n)%M;
}
return ans;
}
*/
///----------------------------------Graph moves----------------------------------------
/*
int dx4[5] = {1, -1, 0, 0};
int dy4[5] = {0, 0, 1, -1};
int dx8[9] = {0, 0, 1, -1, -1, 1, -1, 1};
int dy8[9] = {-1, 1, 0, 0, 1, 1, -1, -1};
int knightx[9] = {-2, -2, -1, -1, 1, 1, 2, 2};
int knighty[9] = {-1, 1, -2, 2, -2, 2, -1, 1};
bool valid( int r , int c , int x , int y ){ if( x >= 1 && x <= r && y >= 1 && y <= c ) return 1 ; return 0 ; }
*/
using namespace std;
int cost[4][4];
lli dp[43][4][4][4];
lli towerhanoi(int n,int A,int B,int C)
{
if(n==0) return 0;
lli &ret=dp[n][A][B][C];
if(ret) return ret;
lli way1 = towerhanoi(n-1,A,C,B) + cost[A][B] + towerhanoi(n-1,C,B,A);
// move n-1 disks A-C then nth disk A-B then return n-1 disks C-A
lli way2 = towerhanoi(n-1,A,B,C) + cost[A][C] + towerhanoi(n-1,B,A,C) + cost[C][B] + towerhanoi(n-1,A,B,C);
//move n-1 disks A-B then nth disk A-C then return n-1 disks B-A then nth disk C-B then n-1 disks A-B
return ret = min(way1,way2);
}
int main()
{
int n,i,j;
rep(i , 1 , 4)
rep(j , 1 , 4)
scin(cost[i][j]);
scin(n);
lli minimoves= towerhanoi(n,1,3,2); // from,to,aux
cout << minimoves << endl;
#ifdef HOME
cerr << "Time elapsed: " << clock() / 1000 << " ms" << endl;
#endif
return 0;
}