POJ1088動態規劃+遞迴解題報告

題目連結：摸我

 

看完題目會有一些比較直觀的想法，顯然是用DP，迭代公式也比較好想，f(i,j) = max{ f(i-1,j), f(i+1,j), f(i,j-1), f(i,j-1) } + 1

在上述公式中要注意的是若且唯若周圍的點比當前點小的時候才能列入計算的運算式中。

為了讓搜尋更為迅速，我給資料增加了邊界，並且由於採用了迭代的方式，對DP數組中的數值設定了Unprocessed和Processing兩個值，只有未處理的節點才會進行迭代計算。

廢話不多說，代碼如下：

 

//POJ1088滑雪（動態規劃之）<br />#include <iostream><br />using namespace std;<br />const int RANK = 102;<br />const int MaxHeight = 20000;<br />int maxRoad;<br />int DP[RANK][RANK];<br />int Data[RANK][RANK];<br />enum State{UnProcess = -2,Processing};<br />void Initialize(int r, int c)<br />{<br />//set boundary!<br />for (int i=0;i<=c+1;++i)<br />{<br />DP[i][0] = UnProcess;<br />DP[i][r+1] = UnProcess;<br />Data[i][0] = MaxHeight;<br />Data[i][r+1] = MaxHeight;<br />}<br />for (int i = 0;i<=r+1;++i)<br />{<br />DP[0][i] = UnProcess;<br />DP[c+1][i] = UnProcess;<br />Data[0][i] = MaxHeight;<br />Data[c+1][i] = MaxHeight;<br />}<br />for (int i = 1;i<=c;++i)<br />{<br />for (int j = 1;j<=r;++j)<br />{<br />cin>>Data[i][j];<br />DP[i][j] = UnProcess;<br />}<br />}<br />}<br />int CaculateOne(int x,int y)<br />{<br />int max = 0;<br />bool flag = false;<br />if(Data[x][y] > Data[x-1][y])//up<br />{<br />if(DP[x-1][y] == UnProcess)<br />DP[x-1][y] = CaculateOne(x-1,y);<br />if(max<DP[x-1][y])<br />max = DP[x-1][y];<br />flag = true;<br />}<br />if(Data[x][y] > Data[x+1][y])//down<br />{<br />if(DP[x+1][y] == UnProcess)<br />DP[x+1][y] = CaculateOne(x+1,y);<br />if(max<DP[x+1][y])<br />max = DP[x+1][y];<br />flag = true;<br />}<br />if(Data[x][y] > Data[x][y-1])//left<br />{<br />if(DP[x][y-1] == UnProcess)<br />DP[x][y-1] = CaculateOne(x,y-1);<br />if(max<DP[x][y-1])<br />max = DP[x][y-1];<br />flag = true;<br />}<br />if(Data[x][y] > Data[x][y+1])//right<br />{<br />if(DP[x][y+1] == UnProcess)<br />DP[x][y+1] = CaculateOne(x,y+1);<br />if(max<DP[x][y+1])<br />max = DP[x][y+1];<br />flag = true;<br />}<br />if(flag)<br />return max + 1;<br />else return 1;<br />}<br />int CalculateMaxRoad(int r, int c)<br />{<br />int max = 0;<br />for (int i = 1;i<=c;++i)<br />{<br />for (int j = 1;j<=r;++j)<br />{<br />if(DP[i][j] == UnProcess)<br />{<br />DP[i][j] = Processing;<br />DP[i][j] = CaculateOne(i,j);<br />}<br />if(DP[i][j]>max)<br />max = DP[i][j];<br />}<br />}<br />return max;<br />}<br />int main()<br />{<br />int r,c;<br />while(cin>>c>>r)<br />{<br /> Initialize(r,c);<br /> cout<<CalculateMaxRoad(r,c)<<endl;<br />}<br />return 0;<br />}