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HDU--1331--Function Run Fun--记忆化搜索

2024-08-05 09:56:16   217人阅读

Function Run Fun

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2376    Accepted Submission(s): 1187


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.
 

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 1
2 2 2
10 4 6
50 50 50
-1 7 18
-1 -1 -1
 

Sample Output
w(1, 1, 1) = 2
w(2, 2, 2) = 4
w(10, 4, 6) = 523
w(50, 50, 50) = 1048576
w(-1, 7, 18) = 1
 
题意：修改给你的这个递归，使他能够处理更大的数据

解析，a,b,c被控制在1~20之间，所以用记忆化搜索的方式记忆那些数据防止重复就行了


#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
int dp[22][22][22],s=0;	//记录防止重复搜索
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])return dp[a][b][c];	//使用记忆点防止重复
    if(a<b&&b<c)return dp[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
    return 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);
}
int main (void)
{
    int a,b,c;
    while(~scanf("%d%d%d",&a,&b,&c))
    {
        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;
}

莫名其妙，就直接把记忆化的思想加进来就搞定了，当年真是白活了啊！！


HDU--1331--Function Run Fun--记忆化搜索


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