Given four characters (a, b, c, d) with distinct frequencies in a text. Suppose that a and b are the two characters having the lowest frequencies. Which of the following sets of code is a possible Huffman code for this text?
Which one of the following statements about the Maximum Finding problem is true?
For the result of accessing the keys 5 and 8 in order in the splay tree in the following figure, which one of the following statements is FALSE?
Suppose that the replacement selection technique is used in external sorting to construct the initial runs. A priority queue of size 5 is used by the internal memory. Given input sequence {5, 19, 25, 45, 30, 24, 15, 60, 16, 27, 1}. Which of the following runs will be generated?
Which one of the following statements is FALSE about a skew heap?
Max-cut problem: Given an undirected graph with positive integer edge weights , find a node partition such that , the total weight of edges crossing the cut, is maximized. Let us define be the neighbor of such that can be obtained from by moving one node from to , or one from to . We only choose a node which, when flipped, increases the cut value by at least . Then which of the following is true?
Among the following groups of concepts, which group is not totally relevant to a search engine?
A B+ tree of order 3 with 21 numbers has at most __ nodes of degree 2.
You are to maintain a collection of lists and to support the following operations.
(i) insert(item, list)
: insert item
into list
(cost = 1).
(ii) sum(list)
: sum the items in list
, and replace the list
with a list containing one item that is the sum (cost = length of list
).
We show that the amortized cost of an insert operation is O(1) and the amortized cost of a sum operation is O(1).
If we assume the potential function to be the number of elements in the list, which of the following is FALSE?
After deleting 10 from the red-black tree given in the figure, which one of the following statements must be FALSE?
Given the distance set D={1,1,2,2,2,2,3,3,3,4,5,5,6,6,8} in a Turnpike Reconstruction problem, first it can be sure that x1=0 and x6=8. Which of the following possible solutions will be checked next?
Delete the minimum number from the given leftist heap. Which one of the following statements is TRUE?
Given a 3-SAT formula with clauses, in which each clause has three variables, the MAX-3SAT problem is to find a truth assignment that satisfies as many clauses as possible. A simple randomized algorithm is to flip a coin, and to set each variable true with probability , independently for each variable. Which of the following statements is FALSE?
Insert { 9, 8, 7, 2, 3, 5, 6, 4} into an initially empty AVL tree. Which one of the following statements is FALSE?
Suppose Q is a problem in NP, but not necessarily NP-complete. Which of the following is FALSE?
Which of the following statement is true ?
When solving a problem with input size by divide and conquer, if at each step, the problem is divided into 9 sub-problems and each size of these sub-problems is , and they are conquered in . Which one of the following is the closest to the overall time complexity?
In dynamic programming, we derive a recurrence relation for the solution to one subproblem in terms of solutions to other subproblems. To turn this relation into a bottom up dynamic programming algorithm, we need an order to fill in the solution cells in a table, such that all needed subproblems are solved before solving a subproblem. Among the following relations, which one is impossible to be computed?
The function BinQueue_Merge
is to merge two binomial queues H1
and H2
, and return H1
as the resulting queue.
BinQueue BinQueue_Merge( BinQueue H1, BinQueue H2 )
{ BinTree T1, T2, Carry = NULL;
int i, j;
H1->CurrentSize += H2-> CurrentSize;
for ( i=0, j=1; j<= H1->CurrentSize; i++, j*=2 ) {
T1 = H1->TheTrees[i]; T2 = H2->TheTrees[i];
switch( 4*!!Carry + 2*!!T2 + !!T1 ) {
case 0:
case 1: break;
case 2: H1->TheTrees[i] = T2; H2->TheTrees[i] = NULL; break;
case 4: H1->TheTrees[i] = Carry; Carry = NULL; break;
case 3: Carry = CombineTrees( T1, T2 );
(3分); break;
case 5: Carry = CombineTrees( T1, Carry );
H1->TheTrees[i] = NULL; break;
case 6: (3分);
H2->TheTrees[i] = NULL; break;
case 7: H1->TheTrees[i] = Carry;
Carry = CombineTrees( T1, T2 );
H2->TheTrees[i] = NULL; break;
} /* end switch */
} /* end for-loop */
return H1;
}
The function Power
calculates the exponential function . But since the exponential function grows rapidly, you are supposed to return instead.
int Power(int N, int k);
Both N
and k
are integers, which are no more than 2147483647.
#include <stdio.h>
int Power(int, int);
const int MOD = 10007;
int main()
{
int N, k;
scanf("%d%d", &N, &k);
printf("%d\n", Power(N, k));
return 0;
}
/* Your function will be put here */
2 3
8
128 2
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