Function Run Fun
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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
#include <iostream>using namespace std;long long w(int a,int b,int c);int main(){ int a,b,c; while(cin>>a>>b>>c&&(a!=-1||b!=-1||c!=-1)){ cout<<"w("<<a<<", "<<b<<", "<<c<<") = "<<w(a,b,c)<<endl; } return 0;}long long w(int a,int b,int c){ if(a<=0||b<=0||c<=0) return 1; long long dp[25][25][25]; int i,j,k; for(i=0;i<=20;i++){ for(j=0;j<=20;j++) for(k=0;k<=20;k++){ dp[i][j][k]=1; } } for(i=1;i<=20;i++){ for(j=1;j<=20;j++){ for(k=1;k<=20;k++){ if(i<j&&j<k) dp[i][j][k]=dp[i][j][k-1]+dp[i][j-1][k-1]-dp[i][j-1][k]; else dp[i][j][k]=dp[i-1][j][k]+dp[i-1][j-1][k]+dp[i-1][j][k-1]-dp[i-1][j-1][k-1]; } } } /* for(i=0;i<=20;i++){ for(j=0;j<=20;j++){ for(k=0;k<=20;k++){ cout<<dp[i][j][k]<<" "; } cout<<endl; } }*/ if(a>20||b>20||c>20) return dp[20][20][20]; return dp[a][b][c];}
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