There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c[i, j] and b[i, j]. For the value of b[i, j], N denotes an up arrow, W denotes a left arrow, NW denotes an arrow to the upper-left. The value of b[4, 5] is

There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c[i, j] and b[i, j]. For the value of b[i, j], N denotes an up arrow, W denotes a left arrow, NW denotes an arrow to the upper-left. The value of c[5, 6] is

There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c[i, j] and b[i, j]. For the value of b[i, j], N denotes an up arrow, W denotes a left arrow, NW denotes an arrow to the upper-left. The value of b[4, 3] is

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. Write a brief justification to your answer to Q1-5.

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. Write a brief justification to your answer to Q1-1.

There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c[i, j] and b[i, j]. For the value of b[i, j], N denotes an up arrow, W denotes a left arrow, NW denotes an arrow to the upper-left. The LCS computed by the algorithm is

There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c[i, j] and b[i, j]. For the value of b[i, j], N denotes an up arrow, W denotes a left arrow, NW denotes an arrow to the upper-left. The value of c[5, 4] is

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. Write a brief justification to your answer to Q1-7.

List all primitive types. For the numeric primitive types, include their size in bits along with them.

You can declare a variable of type double and initialize it with a value of type int