POJ - 1579 Function Run Fun

Function Run Fun

POJ - 1579

AYIT-2021 609暑假集训第一周下记忆化搜索和背包

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

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：略
题型：记忆化搜索，签到题
思路：题中都有递归条件，复制粘贴上，注意用数组的时候要注意下标不能是负数

#include<stdio.h>
#include<string.h>
int dp[500][500][500];
int w(int a,int b,int c)
{if(a>=0&&b>=0&&c>=0&&dp[a][b][c])return dp[a][b][c];//注意利用记忆数组dp时a,b,c不能为负数，利用逻辑运算符的短路运算，这些条件可以写在一个括号里if(a<=0||b<=0||c<=0)return 1;else if(a>20||b>20||c>20)return dp[a][b][c]=w(20,20,20);else 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);else 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()
{int a,b,c;while(~scanf("%d%d%d",&a,&b,&c)&&(a+b+c)!=-3)printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));return 0;
}

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POJ - 1579 Function Run Fun

Function Run Fun

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