hdu 1331(dp)
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题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1331
Function Run Fun
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 2219 Accepted Submission(s): 1123
Problem Description
We all love recursion! Don't we?
Consider a three-parameter recursive function w(a, b, c):
if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:
1
if a > 20 or b > 20 or c > 20, then w(a, b, c) returns:
w(20, 20, 20)
if a < b and b < c, then w(a, b, c) returns:
w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)
otherwise it returns:
w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)
This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.
Consider a three-parameter recursive function w(a, b, c):
if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:
1
if a > 20 or b > 20 or c > 20, then w(a, b, c) returns:
w(20, 20, 20)
if a < b and b < c, then w(a, b, c) returns:
w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)
otherwise it returns:
w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)
This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.
Input
The input for your program will be a series of integer triples, one per line, until the end-of-file flag of -1 -1 -1. Using the above technique, you are to calculate w(a, b, c) efficiently and print the result.
Output
Print the value for w(a,b,c) for each triple.
Sample Input
1 1 12 2 210 4 650 50 50-1 7 18-1 -1 -1
Sample Output
w(1, 1, 1) = 2w(2, 2, 2) = 4w(10, 4, 6) = 523w(50, 50, 50) = 1048576w(-1, 7, 18) = 1
思路:直接调用递归函数指定超时;所以用dp的思想,这样避免重复的递归调用,水过~~~~~
#include <iostream>#include <stdio.h>#include <string>#include <string.h>#include <cstdio>#include <cmath>using namespace std;int dp[30][30][30];int w(int a,int b,int c){ if(a<=0||b<=0||c<=0)return 1; if(a>20||b>20||c>20)return w(20,20,20); if(dp[a][b][c]>0)return dp[a][b][c]; if(a<b&&b<c) { dp[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c); } else { dp[a][b][c]=w(a-1,b,c)+w(a-1,b-1,c)+w(a-1,b,c-1)-w(a-1,b-1,c-1); } return dp[a][b][c];}int main(){ int a,b,c; while(scanf("%d%d%d",&a,&b,&c)!=EOF) { if(a==-1&&b==-1&&c==-1)break; memset(dp,0,sizeof(dp)); printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c)); } return 0;}
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