Zoj 3537 Cake (interval dp)

This topic is the classic convex hull of the optimal triangulation, but this topic may not be convex bag, so to determine in advance whether it is convex, if it is convex bag to continue to split, Dp[i][j] is already in the order of the convex hull on the point i->j is divided into small triangles of the minimum cost, Then dp[i][j] = min (Dp[i][k]+dp[k][j]+cost[i][k]+cost[k][j]), wherein, (J >= i+ 3,i+1<=k<=j-1,cost[i][k] is the cost of a line that connects one I to K )。

Previous diagram from the blog http://blog.csdn.net/woshi250hua/article/details/7824433

The code is as follows:

#include <cstdio>#include<iostream>#include<cstring>#include<cmath>#include<cstdlib>#include<algorithm>#defineEPS 1e-8using namespaceStd;typedefLong Longll;Const intMAXN = -;Const intINF = (1<< -);intDP[MAXN][MAXN];intCOST[MAXN][MAXN];structPoint {intx, y;}; Point P[MAXN], CONVEX[MAXN];BOOLcmpConstPoint &p1,ConstPoint &p2) {    return(P1.y = = P2.y && p1.x < p2.x) | | P1.y <p2.y);}intX_multi (ConstPoint &p1,ConstPoint &AMP;P2,ConstPoint &p3) {    return((p3.x-p1.x) * (P2.Y-P1.Y)-(p2.x-p1.x) * (P3.Y-p1.y));}intSgnDoublex) {    if(Fabs (x) <EPS)return 0; returnX >0?1: -1;}voidConvex_hull (Point *p, point *convex,intNint&len)//Convex bag{sort (p, p+N, CMP); inttop =1; convex[0] = p[0]; convex[1] = p[1];  for(inti =2; I < n; i++)    {         while(Top >0&& X_multi (Convex[top-1], Convex[top], p[i]) <=0) Top--; convex[++top] =P[i]; }    intTMP =top;  for(inti = n-2; I >=0; i--)    {         while(Top > TMP && x_multi (Convex[top-1], Convex[top], p[i]) <=0) Top--; convex[++top] =P[i]; } Len=top;}intGet_cost (ConstPoint &p1,ConstPoint &AMP;P2,Const int&MoD) {    return(ABS (p1.x + p2.x) * ABS (P1.Y + p2.y))%MoD;}intMain () {intN, MoD;  while(~SCANF ("%d%d", &n, &MoD)) {         for(inti =0; I < n; i++) scanf ("%d%d", &p[i].x, &p[i].y); intLen;        Convex_hull (p, Convex, N, Len); if(Len < N)//if it's not a convex bag,Puts"I can ' t cut."); Else{memset (cost,0,sizeof(cost));  for(inti =0; I < n; i++)                 for(intj = i +2; J < N; J + +) Cost[i][j]= Cost[j][i] = Get_cost (Convex[i], convex[j], MoD);//calculate the cost of the opposite corner             for(inti =0; I < n; i++)//Initialize DP            {                 for(intj =0; J < N; J + +) Dp[i][j]=inf; Dp[i][i+1] =0; }              for(inti = n-3; I >=0; i--)//must reverse, because DP[I][J] is pushed by dp[i][k], Dp[k][j], and K is greater than I,                 for(intj = i +2; J < N; J + +)//in the same order, because K is less than J                     for(intK = i +1; K <= J-1; k++) Dp[i][j]= Min (Dp[i][j], dp[i][k] + dp[k][j] + cost[i][k] +Cost[k][j]); printf ("%d\n", dp[0][n-1]); }    }    return 0;}

View Code

Zoj 3537 Cake (interval dp)