習題解答
1: 請寫一個程式計算 10! ，也就是 10*9*8*....*1 。
第一版：沒用函數
f = 1;
i = 1;
while (i<=10) {
f = f * i;
i = i + 1;
}
console.log('f=', f);
第二版：有用函數
function factorial(n) {
f = 1;
i = 1;
while (i<=n) {
f = f * i;
i = i + 1;
}
return f;
}
console.log('factorial(10)=', factorial(10));
console.log('factorial(5)=', factorial(5));
console.log('factorial(3)=', factorial(3));
console.log('factorial(100)=', factorial(100));
寫一個程式把矩陣轉置。
檔案： matrix.js
function print(a)
{
var s = "";
for (var i=0; i<a.length; i++)
{
for (var j=0; j<a[i].length; j++)
{
s = s+a[i][j]+'\t';
}
s = s + '\n';
}
console.log(s);
}
function transpose(a)
{
var at=[];
for (var j=0; j<a[0].length; j++)
{
at[j] = [];
for (var i=0; i<a.length; i++)
{
at[j][i] = a[i][j];
}
}
return at;
}
var m = [[1,2,3], [3,12,1]];
console.log("====== m =========");
print(m);
console.log("====== mt =========");
print(transpose(m)); // => [[1,3], [2,2], [3,1]]
function add(a,b)
{
var c = [];
for (var i=0; i<a.length; i++)
{
c[i] = [];
for (var j=0; j<a[i].length; j++)
{
c[i][j] = a[i][j]+b[i][j];
}
}
return c;
}
function sub(a,b)
{
var c = [];
for (var i=0; i<a.length; i++)
{
c[i] = [];
for (var j=0; j<a[i].length; j++)
{
c[i][j] = a[i][j]-b[i][j];
}
}
return c;
}
var a = [[1,2,3], [1,1,1]], b=[[2,2,2],[3,1,1]];
console.log("==========a+b==========")
print(add(a,b));
console.log("==========a-b==========")
print(sub(a,b));
function mul(a,b) // a:m*n, b:n*k, c:m*k
{
var c = [];
for (var i=0; i<a.length; i++)
{
c[i] = [];
for (var k=0; k<b[0].length; k++)
{
c[i][k] = 0;
for (var j=0; j<a[i].length; j++)
{
c[i][k] = c[i][k]+a[i][j]*b[j][k];
}
}
}
return c;
}
var ma = [[1,2],
[1,1]],
mb = [[2,2],
[1,1]];
console.log("=========== c=ma*mb =============");
print(mul(ma,mb));
function neg(a)
{
var c=[];
for (var i=0; i<a.length; i++)
{
c[i] = [];
for (var j=0; j<a[i].length; j++)
{
c[i][j] = -a[i][j];
}
}
return c;
}
console.log("============ neg(a) ==========");
print(neg(a));
function isMagic(a)
{
var a0sum =0;
for (var j=0;j<a[0].length; j++)
{
a0sum = a0sum + a[0][j];
}
for (var i=0; i<a.length; i++)
{
var rsum = 0;
for (var j=0; j<a[i].length; j++)
rsum = rsum +a[i][j];
if (a0sum !== rsum)
return false;
}
for (var j=0; j<a[0].length; j++)
{
var csum = 0;
for (var i=0; i<a.length; i++)
csum = csum +a[i][j];
if (a0sum !== csum)
return false;
}
return true;
}
var magic = [[1,2,3], [2,3,1], [3,1,2]];
console.log('isMagic(magic)=', isMagic(magic));
var magic2 = [[1,2,3], [2,3,1], [3,2,1]];
console.log('isMagic(magic2)=', isMagic(magic2));
執行結果：
NQU-192-168-60-101:js1 csienqu$ node matrix.js
====== m =========
1 2 3
3 12 1
====== mt =========
1 3
2 12
3 1
回呼函數實作
2 請寫一個函數可以根據過濾函數f只留下符合的內容？ * 範例：filter(odd, [1,3,5,4,8,9])= [1,3,5,9] ，其中 odd 為判斷是否為奇數的函數。
檔案： filter.js
function filter(f, a) {
var fa = [];
for (var i=0; i < a.length; i++) {
if (f(a[i]))
fa.push(a[i]);
}
return fa;
}
function odd(n) {
return n%2===1;
}
var b = filter(odd, [2,3,4,5,6,7,8,9]);
console.log('b=', b);
執行結果：
$ node filter.js
b= [ 3, 5, 7, 9 ]
4 請用遞迴計算 sum(n) = 1+2+…+n ？ * 範例：sum(10) = 55
檔案： sumRecursive.js
function sum(n) {
if (n===0) {
return 0;
} else {
// console.log(n);
var fn = sum(n-1)+n;
// console.log('n=%d fn=%d', n, fn);
return fn;
}
}
console.log('sum(10)=', sum(10));
執行結果
$ node sumRecursive
sum(10)= 55