October 2002 10.001 Introduction to Computer MethodsArrays and Pointers. Lecture Plan. • Intro into arrays.definition and syntaxdeclaration & initializationmajor advantagesmultidimensional arraysexamples• Intro into pointers.address and indirection operatorsdefinition of pointerspointers and arrays – comparisonpointer arithmeticOctober 2002 10.001 Introduction to Computer MethodsArrays and PointersArray is a group of elements that share a common name, and that are different from one another by their positions within the array. C syntax: x[1]=3.14;x[2]=5.2;x[3]=6347;Declaration: int x[5];type name sizeSets aside memory for the arrayArray indexOctober 2002 10.001 Introduction to Computer MethodsArrays and PointersInitialization: int grade[]={100,99,85}; int grade[3]={100,99,85};int grade[100]={1,3,5,7};– grade[4]-grade[99] will be zeros.grade[36] = 87;Multidimensionality:Scalar variable aVector variable (1D) a0, a1, a2,...Matrix variable (2D) a00, a01,a02,...a10,a11,a12,...a20,a21,a22,......October 2002 10.001 Introduction to Computer MethodsArrays and PointersDeclaration: int L=100, M=100, N=100;float a[L][M][N];Initialization: alpha[2][2]={1,2,3,4};alpha[2][2]={{1,2},{3,3}};alpha[0][1]=3;alpha[1][1]=2;NB: Array size is fixed at declaration.#define L 100#define M 100#define N 100...int a[L][M][N]October 2002 10.001 Introduction to Computer MethodsArrays and PointersNB: If x[5] is accessed, no error will result!Utility: simplify programming of repetitive operationsimprove clarityimprove modularityimprove flexibilityNB: In C numbers of array elements start form zero:x[0], x[1], x[2], x[3], x[4]. There is no x[5].October 2002 10.001 Introduction to Computer MethodsArrays and PointersExample: a program to compute the class average of the midterm.Scalar form:int main(void){float average;int sum=0,grade1,grade2,..;scanf(“%d”,&grade1);scanf(“%d”,&grade2);...sum += grade1;sum += grade2;...average = sum/95.0;}Vector (array) form:int main(void){float average;int i,n,sum=0,grade[100];scanf(“%d”,&n);for(i=0;i<n,&n;i++){scanf(“%d”,&grade[i]);sum += grade[i];} ...average = (float)sum/n;}October 2002 10.001 Introduction to Computer MethodsArrays and PointersExample: Integration using Composite Trapezoid Rule[]∑∑=−=−++=+=NiNiiiixfbfafhxfxfhI1111)(2)()()()(2Continuous function f(x), x belongs to [a,b] a set of discrete values f(xi), xibelong to [a,b].∫=badxxfI )(October 2002 10.001 Introduction to Computer MethodsArrays and PointersGiven a function y=f(x) to integrate form x=a to x=b:int main(void) {...h=(b-a)/n;integral =0.5*(func(a)+func(b));for(i=1;i<n;i++)integral += func(a+i*h);integral *=h;...return(0);}October 2002 10.001 Introduction to Computer MethodsArrays and PointersGiven discrete data yi= f(xi) integrate form x=a to x=b:int main(void) {...for (i=0; i<=n; i++)scanf(“%f”,&y[i]); /*reading f(xi)*/integral =0.5*(y[0]+y[n]);for(i=1; i<n; i++){scanf(“%f”,&y); /*summing f(x[i])*/integral += y;}scanf(“%f”, &a)scanf(“%f”, &b)integral *= (b-a)/n;...return(0);}October 2002 10.001 Introduction to Computer MethodsArrays and PointersCalculating the average. Version 1. /*No arrays.*/#include <stdio.h>int main(void){float ave;int sum=0;int data1, data2, data3;scanf(“%d”, &data1);scanf(“%d”, &data2);scanf(“%d”, &data3);sum == data1;sum += data2;sum += data3;ave = sum/3.0;...}• inefficient coding• only works for a fixed number of data pointsOctober 2002 10.001 Introduction to Computer MethodsArrays and PointersCalculating the average. Version 2. /* no arrays, scalar “for” loop */#include <stdio.h>int main(void){float ave;int i, n, datai, sum=0;scanf(“%d”, &n);for (i=0;i<n;i++){scanf(“%d”, &datai);sum += datai;}ave = (float) sum/n;... }October 2002 10.001 Introduction to Computer MethodsArrays and PointersCalculating the average. Version 3. /* with arrays */#include <stdio.h>#include <math.h>#define NMAX 100int main(void){float ave;int i, n, data[NMAX], sum=0;scanf(“%d”, &n);if(n>NMAX) printf(“number of pts > NMAX);for (i=0; i<n; i++)scanf(“%d”, &data[i]);sum += data[i];}ave = float(sum)/n;... }• array size is fixed at declaration• use #define to have some flexibilityOctober 2002 10.001 Introduction to Computer MethodsArrays, Summing up•The name identifies the location in memory, big enough to store the whole array.• a[k] refers to the k-th element of the array, the indexing starting from 0.• The memory allocation happens when the array is declared: use # to set the dimensions.• Advantages: clear and compact coding, better modularity, take advantage of loops for repetitive operations.October 2002 10.001 Introduction to Computer MethodsArrays and PointersIntro into pointers.& - address operator, unary, right to left precedencev – variable &v – location (address) of v in the memoryThe special type of variable to operate with the address is needed: POINTER pv = &v;Identifier vpvMemory address 1776 1997Value51776October 2002 10.001 Introduction to Computer MethodsArrays and PointersDeclaration: int *p; p – pointer to integer variable.Value range: zero or NULL address and a set of positive integers.Assignment: p=0; p=NULL; p=&i; p=(int *)1776;address of icast as “pointer to int”Indirection (dereferencing) operator * - “inverse” to &.Gives the value of the variable pointed to by the pointer.p = &i; i = *p; We can access any variable, if know the variable’s address!&i = p; illegal, addresses are allocated by declarations.p = &3; p = &(i+j); illegal: constants and expressions do not have addresses.October 2002 10.001 Introduction to Computer MethodsArrays and PointersRelationship between arrays and pointers:• Array name is a pointer constant, it’s value is the address of the first element of the array.• Pointers can be subscribeda[i] = *(a + i) a – address of a[0](base address or the array)a[i] = *(p + i) points to i-th element of the arrayNB: a is a constant pointer, a=p, ++a, &aare illegal.October 2002 10.001 Introduction to Computer MethodsArrays and PointersPointer arithmetic is equivalent to array indexing:p = a + 1 p = &a[1]p = a + m p = &a[m]Summing the array using pointers:for (p = a; p < &a[N]; ++p)sum += *p;orfor (i = 0; i < N; ++i)sum += *(a + i);October 2002 10.001 Introduction to Computer MethodsArrays and PointersPointer arithmetic:p + 1 ++p p + i p += iHowever, pointers and numbers are not quite the