入门DP pku 1163 The Triangle

题目:

http://acm.pku.edu.cn/JudgeOnline/problem?id=1163

 

题目简单,主要是在递归的时候实现了记忆功能.而dp的实现是很容易的.重点是这2者的联系.逆向关系

 

实现了dp，递归记录路径功能!!!

 

#include <stdio.h> #include <memory> #define max 101 int tri[max][max]; int sum[max][max]; //标记从上往下数字三角形计算路线(递归跟DP中) int next[max][max]; int f(int i,int j,int n){ //计算到i,j位置的最佳路径,和保存到sum[i][j] //最佳路径上的第一位数字保存在save[i]中.(从上往下的顺序) //状态方程: //sum[i][j] = max(sum[i + 1][j],sum[i + 1][j + 1]) + tri[i][j]; if(sum[i][j]){ return sum[i][j]; } else{ if(i == n){ //递归出口 sum[i][j] = tri[i][j]; } else{ //减小规模.继续往下递归 sum[i + 1][j] = f(i + 1,j,n); sum[i + 1][j + 1] = f(i + 1,j + 1,n); if(sum[i + 1][j] >= sum[i + 1][j + 1]){ sum[i][j] = sum[i + 1][j] + tri[i][j]; next[i][j] = j; } else{ sum[i][j] = sum[i + 1][j + 1] + tri[i][j]; next[i][j] = j + 1; } } } return sum[i][j]; } int main(){ freopen("data.txt","r",stdin); int n,i,j; while(scanf("%d",&n)!=EOF){ memset(sum,0,sizeof(sum)); memset(next,0,sizeof(next)); for(i = 1;i <= n;i++) for(j = 1;j <= i;j++) scanf("%d",&tri[i][j]); printf("%d/n",f(1,1,n)); /* for(j = 1;j <= n;j++) sum[n][j] = tri[n][j]; for(i = n - 1;i >= 1;i--) for(j = 1;j <= i;j++) if(sum[i + 1][j] >= sum[i + 1][j + 1]){ sum[i][j] = sum[i + 1][j] + tri[i][j]; next[i][j] = j; } else{ sum[i][j] = sum[i + 1][j + 1] + tri[i][j]; next[i][j] = j + 1; } printf("%d/n",sum[1][1]); */ printf("%d/n",tri[1][1]); j = next[1][1]; for(i = 1;i <= n - 1;i++){ printf("%d/n",tri[i + 1][j]); j = next[i + 1][j]; } } return 0; }