Use dynamic programming algorithm to compute the binary coefficient C(7,5). Show all steps!
in DP for binary coefficient ,
Recurrence relaton is:
C(n,k) = C(n-1,k) + C(n-1,k-1) for n > k > 0
C(n,0) = 1, C(n,n) = 1 for n >= 0
we will make table, value of C(7,5) will be found from table
C(7,5) = C(6,5)+C(6,4) because [C(n,k) = C(n-1,k) + C(n-1,k-1) ]
c(column-wise) n(row-wise) |
0 | 1 | 2 | 3 | 4 | 5 |
0 | ||||||
1 | ||||||
2 | ||||||
3 | ||||||
4 | ||||||
5 | ||||||
6 | ||||||
7 |
Step 1: C(n,0) = 1, C(n,n) = 1 for n >= 0
c(column-wise) n(row-wise) |
0 | 1 | 2 | 3 | 4 | 5 |
0 | 1 | |||||
1 | 1 | 1 | ||||
2 | 1 | 1 | ||||
3 | 1 | 1 | ||||
4 | 1 | 1 | ||||
5 | 1 | 1 | ||||
6 | 1 | |||||
7 | 1 |
Step 2: C(n,k) = C(n-1,k) + C(n-1,k-1) for n > k > 0
c(column-wise) n(row-wise) |
0 | 1 | 2 | 3 | 4 | 5 |
0 | 1 | |||||
1 | 1 | 1 | ||||
2 | 1 | 2 | 1 | |||
3 | 1 | 3 | 3 | 1 | ||
4 | 1 | 4 | 6 | 4 | 1 | |
5 | 1 | 5 | 10 | 10 | 5 | 1 |
6 | 1 | 6 | 15 | 20 | 15 | 6 |
7 | 1 | 7 | 21 | 35 | 35 | 21 |
C(7,5) = C(6,5)+C(6,4) = 6+15 =21
Use dynamic programming algorithm to compute the binary coefficient C(7,5). Show all steps!
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