关键词:
Function Run Fun
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.
1 1 1 2 2 2 10 4 6 50 50 50 -1 7 18 -1 -1 -1
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
能够通过空间换时间的方法。将计算出的值
//考查知识点:记忆化搜索 就是用数组存储。降低递归函数调用的次数和时间 //考试当天做出来了。今天又做一遍,居然有点生疏了,(⊙﹏⊙)b #include<stdio.h> int s[22][22][22]; void f() { int i,j,k; for(i=1;i<22;++i) { for(j=1;j<22;++j) { for(k=1;k<22;++k) { if(i<j&&j<k) { if(k-1==0) s[i][j][k-1]=s[i][j-1][k-1]=1; if(j-1==0) s[i][j-1][k-1]=s[i][j-1][k]=1; s[i][j][k]=s[i][j][k-1]+s[i][j-1][k-1]-s[i][j-1][k]; continue; } if(i==1) s[i-1][j][k]=s[i-1][j-1][k]=s[i-1][j][k-1]=s[i-1][j-1][k-1]=1; if(j==1) s[i-1][j-1][k]=s[i-1][j-1][k-1]=1; if(k==1) s[i-1][j][k-1]=s[i-1][j-1][k-1]=1; s[i][j][k]=s[i-1][j][k]+s[i-1][j-1][k]+s[i-1][j][k-1]-s[i-1][j-1][k-1]; } } } } int main() { int a,b,c; f(); while(~scanf("%d%d%d",&a,&b,&c),!(a==-1&&b==-1&&c==-1)) { if(a<=0||b<=0||c<=0) { printf("w(%d, %d, %d) = 1 ",a,b,c); continue; } if(a>20||b>20||c>20) { printf("w(%d, %d, %d) = %d ",a,b,c,s[20][20][20]); continue; } printf("w(%d, %d, %d) = %d ",a,b,c,s[a][b][c]); } return 0; }
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