uva348 optimal matrix chain multiply classic interval DP

Tag:uva348    optimal matrix link     classic interval dp   

uva348 optimal matrix chain multiplication//typical interval dp//dp[i][j] represents the minimum cost of the matrix I to J chain multiplication//dp[i][j] = min (dp[i][k]+dp[k+1][j]+a[i].pl*a[k].pr*a[j].pr) ;//On the interval I to J find a K make dp[i][k]+dp[k+1][j] these two parts and in addition to the last//A[I].PL*A[K].PR*P[I].PR minimum value;//can have such a state key is; P =a[1] * a[2] * .... * A[k]//And q= a[k+1] * a[k+2] * .... * A[n] The results of these two parts are not mutually affecting,//So only the P and Q optimal method to calculate, the optimal sub-structure! Boundary dp[i][i]=0;////This is a classic interval DP topic, learned to use this method to consider the problem//Finally, there is a recursive printing, it is very wonderful. Still very happy. Hey, keep practicing. #include <algorithm> #include <bitset> #include <cassert> #include <cctype> #include <cfloat > #include <climits> #include <cmath> #include <complex> #include <cstdio> #include < cstdlib> #include <cstring> #include <ctime> #include <deque> #include <functional> #include <iostream> #include <list> #include <map> #include <numeric> #include <queue> #include <set> #include <stack> #include <vector> #define CEIL (A, B) (((a) + (b)-1)/(c)) #define Endl ' \ n ' #define GCD __gcd#defiNE highbit (x) (1ull<< (63-__builtin_clzll (x))) #define Popcount __builtin_popcountlltypedef Long Long ll;using namespace Std;const int MOD = 1000000007;const long Double PI = ACOs ( -1.L); Template<class t> inline T LCM (const T&AM P A, const t& b) {return A/GCD (A, b) *b;} Template<class t> Inline T lowbit (const t& x) {return x&-x;} Template<class t> inline T maximize (t& A, const t& b) {return a=a<b?b:a;} Template<class t> inline T Minimize (t& A, const t& b) {return a=a<b?a:b;} const int MAXN = 1008;struct node {int pl;int PR;} A[maxn];ll d[maxn][maxn];int path[maxn][maxn];int n;const ll inf = 0x4f4f4f4f4f4f4f4f;ll dp (int i,int j) {if (D[i][j]!=inf ) return d[i][j];ll& ans = d[i][j];for (int k=i;k<j;k++) {ll res = DP (i,k) +DP (k+1,j) + (LL) a[i].pl*a[k].pr*a[j].pr; if (ans>res) {ans = res;path[i][j] = k;}} return ans;} void print (int i,int j) {if (i==j) {printf ("a%d", i+1); return;} printf ("("); for (int k=i;k<j;k++) if (path[i][j]==k) {print (i,k);p rintf ("x");p rint (K+1,J); printf (")");//printf (")");} int main () {int kase = 0;//freopen ("G:\\code\\1.txt", "R", stdin), while (scanf ("%d", &n)!=eof&&n) {for (int i= 0;i<n;i++) scanf ("%d%d", &AMP;A[I].PL,&AMP;A[I].PR);//memset (d,0x4f,sizeof (d));//memset (path,0,sizeof (path)); for (int i=0;i<n;i++) for (int j=0;j<n;j++) {path[i][j]=0;d[i][j]=inf;} for (int. i=0;i<n;i++) D[I][I]=0;DP (0,n-1),//printf ("%lld\n", DP (0,n-1));p rintf ("Case%d:", ++kase);p rint (0,n-1); Puts ("");} return 0;}

uva348 optimal matrix chain multiply classic interval DP