POJ 1579-Function Run Fun(内存搜索)
2015-07-08 12:11
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Function Run Fun
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
Sample Output
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 16503 | Accepted: 8514 |
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
巨水。。
一開始wa了一组数据 (0,21,21)
#include <algorithm> #include <iostream> #include <cstring> #include <cstdlib> #include <string> #include <cctype> #include <vector> #include <cstdio> #include <cmath> #include <deque> #include <stack> #include <map> #include <set> #define ll long long #define maxn 116 #define pp pair<int,int> #define INF 0x3f3f3f3f #define max(x,y) ( ((x) > (y)) ? (x) : (y) ) #define min(x,y) ( ((x) > (y)) ? (y) : (x) ) using namespace std; int n,m,dp[22][22][22]; int dfs(int x,int y,int z) { if(x<=0||y<=0||z<=0) return 1; if(x>20||y>20||z>20) return dfs(20,20,20); if(dp[x][y][z]!=INF) return dp[x][y][z]; dp[x][y][z]=0; if(x<y&&y<z) dp[x][y][z]+=(dfs(x,y,z-1)+dfs(x,y-1,z-1)-dfs(x,y-1,z)); else dp[x][y][z]+=(dfs(x-1,y,z)+dfs(x-1,y-1,z)+dfs(x-1,y,z-1)-dfs(x-1,y-1,z-1)); return dp[x][y][z]; } int main() { int a,b,c; while(scanf("%d%d%d",&a,&b,&c)) { if(a==-1&&b==-1&&c==-1)break; memset(dp,INF,sizeof(dp)); printf("w(%d, %d, %d) = %d\n",a,b,c,dfs(a,b,c)); } return 0; }
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