var sum = function(x, y) { return x + y;};

var square = function(x) { return x * x;};

var data = [1,1,3,5,5];

//計算平均值，reduce是ECMA5的方法

//var mean = data.reduce(sum)/data.length;

//利用自定義的reduce，判斷是否是ECMA5或ECMA3

//var mean = reduce(data, sum)/data.length;

//取出元素計算過的值

//var deviations = data.map(function(x) { return x - mean;});

//利用自定義的map，判斷是否是ECMA5或ECMA3

//var deviations = map(data, function(x) { return x - mean;});

//計算標準差，map是ECMA5的方法

//var stddev = Math.sqrt(deviations.map(square).reduce(sum)/(data.length-1));

//利用自定義的，判斷是否是ECMA5或ECMA3

//var stddev = Math.sqrt(reduce(map(deviations, square), sum)/(data.length-1));

//alert(stddev);

//高階Function

//var even = function(x){

// return x % 2 === 0;

//};

//var odd = not(even);

//alert([1,1,3,5,5].every(odd));

//partial function 實做1

var f = function(x, y, z) { return x * (y - z); };

partialLeft(f, 2)(3, 4);

partialRight(f, 2)(3, 4);

partial(f, undefined, 2)(3, 4);

//partial function 實做2

var increment = partialLeft(sum, 1);

var cubberoot = partialRight(Math.pow, 1/3);

alert(increment(3) + "_" + cubberoot(4));

String.prototype.first = partial(String.prototype.charAt, 0);

String.prototype.last = partial(String.prototype.substr, -1, 1);

var str1 = "abcd";

alert(str1.first() + "_" + str1.last());

//partial function 實做3

var not2 = partialLeft(compose, function(x) { return !x; });

var even = function(x) { return x % 2 ===0;};

var odd = not(even);

var isNumber = not(isNaN);

//利用partial function 在實做一次前面的平均值及標準差計算

var product = function(x, y) { return x * y; };

var neg = partial(product, -1);

var square2 = partial(Math.pow, undefined, 2);

var sqrt = partial(Math.pow, undefined, 0.5);

var reciprocal = partial(Math.pow, undefined, -1);

var mean2 = product(reduce(data, sum), reciprocal(data.length));

var stddev2 = sqrt(product(reduce(map(data,

compose(square,

partial(sum, neg(mean)))),

sum),

reciprocal(sum(data.length, -1))));

//memoize function 實做

var gcdmemo = memoize(gcd);

gcdmemo(85, 187);

var factorial = memoize(function(n){

return (n <= 1) ? 1 : n * factorial(n - 1);

});

factorial(5);

return function() {

var result = f.apply(this, arguments);

return !result;

};

var args = arguments;

return function(){

var a = array(args, 1);

a = a.concat(array(arguments));

return f.apply(this, a);

};

var args = arguments;

return function(){

var a = array(arguments);

a = a.concat(array(args, 1));

return f.apply(this, a);

};

var args = arguments;

return function(){

var a = array(args, 1);

var i = 0, j = 0;

for (; i < a.length; i++){

if (a[i] === undefined) a[i] = arguments[j++];

}

a = a.concat(array(arguments, j));

return f.apply(this, a);

};

var cache = {};

return function(){

var key = arguments.length + Array.prototype.join.call(arguments, ",");

if (key in cache) return cache[key];

else return cache[key] = f.apply(this, arguments);

};

var t;

if (a < b) t = b, b = a, a = t;

while(b !== 0) t = b, b = a % b, a = t;

return a;