Overview of UE 101: Algorithms and Programming

Transcription

1 Overview of UE 101: Algorithms and Programming Deepak D Souza Department of Computer Science and Automation Indian Institute of Science, Bangalore. Aug 2, 2017

2 Outline 1 What we study 2 Programs 3 Algorithms 4 Data Structures 5 Logistics for the Course

3 Programs as Recipes If a computer processor is like a kitchen robot, Then... A program is a recipe. 1. Keep a medium sized vessel and a cup. 2. Fill the cup with water. 3. Pour the cup into the vessel. 4. If the vessel is full go to step 5 Else go back to step 2 5. Put the vessel on the burner.... A problem is a dish (like a cake). Study of algorithms helps us to write efficient recipes for specific dishes.

4 What a computer looks like Stack Memory Stack Pointer Heap Memory Instruction Pointer AX Static Data EX Executable Code ALU Kernel Routines Central Processing Unit (CPU) Memory (RAM)

5 How a program runs on the CPU Stack Memory Stack Pointer Instruction Pointer AX EX ALU Heap Memory Static Data Executable Code Kernel Routines max: pushq %rbp movq %rsp, %rbp movl %edi, -20(%rbp) movl %esi, -24(%rbp) movl -20(%rbp), %eax cmpl -24(%rbp), %eax jg.l3 movl -24(%rbp), %eax movl %eax, -4(%rbp) jmp.l4.3: movl -20(%rbp), %eax movl %eax, -4(%rbp).L4: movl -4(%rbp), %eax popq %rbp ret #include <stdio.h> void main() { int a, b; scanf("%d%d", &a, &b); printf("%d\n", max(a,b)); } int max (int x, int y) { int max; if (x <= y) max = y; else max = x; return max; } Central Processing Unit (CPU) Memory (RAM)

6 Executing a program with pen-and-paper #include <stdio.h> void main() { int a, b; scanf("%d%d", &a, &b); printf("%d\n", max(a,b)); } int max (int x, int y) { int max; --> if (x <= y) max = y; else max = x; return max; } x: 10 y: 20 max: 0

7 Executing a program with pen-and-paper #include <stdio.h> void main() { int a, b; scanf("%d%d", &a, &b); printf("%d\n", max(a,b)); } int max (int x, int y) { int max; if (x <= y) max = y; else max = x; --> return max; } x: 10 y: 20 max: 20

8 Things we will study in programming Basic Data Types (char, int, float) Control-Flow (if-then-else, while, switch) Functions and Recursion Memory structures: Arrays, Heap-Allocated objects (lists, trees, graphs)

9 Programs and Algorithms Algorithms are for specific problems (like sort a list, find the shortest path from s to t ) Algorithms are specified in a more abstract language ( psuedocode ) than programs. Algorithms are expected to be correct (terminate on all inputs with the correct answer). Algorithms are implemented by programs.

10 Illustrative example: Max subsequence sum Given an array A of N integers, find the maximum value of A[k] i k j (over all possible 0 i j < N). Example: A: Max subsequence sum of A is:

11 Illustrative example: Max subsequence sum Given an array A of N integers, find the maximum value of A[k] i k j (over all possible 0 i j < N). Example: A: Max subsequence sum of A is: 20. Originates from pattern matching problem; Can also think of choosing a portion of a cake to maximize cherries over olives (1 olive = -1 cherry).

12 Naive algorithm bestsum = 0; for(i = 0 to N-1) for(j = 0 to N-1) { sum := sum A[i] to A[j]; if sum > bestsum bestsum = sum; } return bestsum; Runs time in O(N 3 ) (i.e. proportional to the cube of the number N of elements in the array).

13 A more efficient algorithm Divide given array A into two halves A L and A R. Find max subseq sum for A L and A R separately. Also find max subseq sum in A L ending at N/2 and max subseq sum in A R beginning at N/2. Use these to find max subseq sum of A. A: A L A R Runs in O(N log N) time. Follows a typical Divide-and-Conquer strategy. For large N, this algorithm may run in seconds compared to hours for the naive algorithm.

14 Illustrative Example 2: Computing Fibonacci numbers Fibonacci sequence: Given n, compute Fib(n). 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...

15 A naive algorithm Use recurrence: Fib(0) = 0 Fib(1) = 1 Fib(n+2) = Fib(n+1) + Fib(n) Runs in exponential time: 2 n.

16 A more efficient algorithm Keep track of previous two Fib numbers, and use it to compute current Fib number. Runs in linear time: O(n). Runs in seconds compared to light years for naive algorithm! Uses dynamic programming strategy.

17 Illustrative Example 3: Search Trees Data structures are useful for maintaining data and supporting quick queries on the data. Example: Google may want to store all taken ids, and quickly tell a new user whether her choice of id is available or not. Need to support both quick additions as well as membership queries. Naive algorithm: Store entries in an array. What is the running time of the queries add and is-member?

18 Binary Search Trees Can support add and is-member in O(log N) worst-case time. Add and search is proportional to the height of the tree. Uses idea of keeping the tree balanced, so that height is log N.

19 What we will study in Algo and Data Structures How to estimate the running time of an algorithm. Algorithms for sorting and searching. Algorithms on Graphs. Algorithm design techniques (Greedy, Divide-and-Conquer, Dynamic Programming). Efficient Data Structures (search trees, heaps, etc).

20 Why study programming and algorithms? Programmable processors are ubiquitous Pacemakers for controlling heart rhythm Medical infusion pumps Chemical process control Nuclear reactor Cell phones Programming skill needed in Writing apps Simulating physical/biological/chemical processes Pays to know how to program, how to estimate running time, and how to design an efficient algorithm to solve a problem.

21 Course details Meetings Classes: Mon, Wed 9:30am Tutorial: Thu 11:00am Lab Sessions: Mon-Thu 2-5pm. Attendence compulsary in all components. Course web site: Piazza discussion forum.

22 Course details: Evaluation Evaluation components: Midsem exam: (Weightage: 20%) Final exam (Weightage 40%) Assignments, Lab Exercises, Quizes (Weightage 40%). Misconduct Policy Assignments to be done on your own. No discussions, No copying solutions from the internet or other sources. If you refer to a source, you must mention it in your submission. Credit will be given for approach and your attempt to solve the problem. Misconduct Penalty: Any instance of copying in an assignment will fetch you a 0 in that assignment + one grade reduction.