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 101int 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;}