前端学算法之搜索算法

前面的话

　　本文将详细介绍搜索算法的实现

 

顺序搜索

　　顺序或线性搜索是最基本的搜索算法。它的机制是，将每一个数据结构中的元素和我们要找的元素做比较。顺序搜索是最低效的一种搜索算法

　　以下是其实现：

this.sequentialSearch = function(item){
  for (var i=0; i<array.length; i++){ //{1} 
    if (item === array[i])        //{2} 
    return i;    //{3}
    }
  }
  return -1; //{4}
};

　　顺序搜索迭代整个数组（行{1}），并将每个数组元素和搜索项作比较（行{2}）。如果搜索到了，算法将用返回值来标示搜索成功。返回值可以是该搜索项本身，或是true，又或是搜索项的索引（行{3}）。如果没有找到该项，则返回-1（行{4}），表示该索引不存在；也可以考虑返回false或者null

　　假定有数组[5, 4, 3, 2, 1]和待搜索值3，下图展示了顺序搜索的示意图：

 

二分搜索

　　二分搜索算法的原理和猜数字游戏类似，就是那个有人说“我正想着一个1到100的数字”的游戏。我们每回应一个数字，那个人就会说这个数字是高了、低了还是对了

　　这个算法要求被搜索的数据结构已排序。以下是该算法遵循的步骤。

　　1、选择数组的中间值

　　2、如果选中值是待搜索值，那么算法执行完毕（值找到了）

　　3、如果待搜索值比选中值要小，则返回步骤1并在选中值左边的子数组中寻找

　　4、如果待搜索值比选中值要大，则返回步骤1并在选种值右边的子数组中寻找

　　以下是其实现：

this.binarySearch = function(item){
    this.quickSort();
    var low = 0,
        high = array.length - 1,
        mid, element;
    while (low <= high){
        mid = Math.floor((low + high) / 2);
        element = array[mid];
        console.log('mid element is ' + element);
        if (element < item) {
            low = mid + 1;
            console.log('low is ' + low);
        } else if (element > item) {
            high = mid - 1;
            console.log('high is ' + high);
        } else {
            console.log('found it');
            return mid;
        }
    }
    return -1;
};
var partition = function(array, left, right) {
    var pivot = array[Math.floor((right + left) / 2)],
        i = left,
        j = right;
    console.log('pivot is ' + pivot + '; left is ' + left + '; right is ' + right);
    while (i <= j) {
        while (array[i] < pivot) {
            i++;
            console.log('i = ' + i);
        }
        while (array[j] > pivot) {
            j--;
            console.log('j = ' + j);
        }
        if (i <= j) {
            console.log('swap ' + array[i] + ' with ' + array[j]);
            swap(array, i, j);
            i++;
            j--;
        }
    }
    return i;
};
var quick = function(array, left, right){
    var index;
    if (array.length > 1) {
        index = partition(array, left, right);
        if (left < index - 1) {
            quick(array, left, index - 1);
        }
        if (index < right) {
            quick(array, index, right);
        }
    }
    return array;
};
this.quickSort = function(){
    quick(array,  0, array.length - 1);
};

　　开始前需要先将数组排序，可以选择任何一个排序算法。这里我们选择了快速排序。在数组排序之后，我们设置low（行{2}）和high（行{3}）指针（它们是边界）

　　当low比high小时（行{4}），我们计算得到中间项索引并取得中间项的值，此处如果low比high大，则意思是该待搜索值不存在并返回-1（行{12}）。接着，我们比较选中项的值和搜索值（行{7}）。如果小了，则选择数组低半边并重新开始。如果选中项的值比搜索值大了，则选择数组高半边并重新开始。若两者都是不是，则意味着选中项的值和搜索值相等，因此，直接返回该索引（行{11}）

　　给定下图所示数组，让我们试试看搜索2。这些是算法将会执行的步骤：

【完整代码】

　　下面是排序和搜索算法的完整代码

function ArrayList(){

    var array = [];

    this.insert = function(item){
        array.push(item);
    };

    var swap = function(array, index1, index2){
        var aux = array[index1];
        array[index1] = array[index2];
        array[index2] = aux;
        //ES2015 swap - Firefox only, for other browser, uncomment code above and coment line below
        //[array[index1], array[index2]] = [array[index2], array[index1]];
    };

    this.toString= function(){
        return array.join();
    };

    this.array= function(){
        return array;
    };

    this.bubbleSort = function(){
        var length = array.length;

        for (var i=0; i<length; i++){
            console.log('--- ');
            for (var j=0; j<length-1; j++ ){
                console.log('compare ' + array[j] + ' with ' + array[j+1]);
                if (array[j] > array[j+1]){
                    console.log('swap ' + array[j] + ' with ' + array[j+1]);
                    swap(array, j, j+1);
                }
            }
        }
    };

    this.modifiedBubbleSort = function(){
        var length = array.length;

        for (var i=0; i<length; i++){
            console.log('--- ');
            for (var j=0; j<length-1-i; j++ ){
                console.log('compare ' + array[j] + ' with ' + array[j+1]);
                if (array[j] > array[j+1]){
                    console.log('swap ' + array[j] + ' with ' + array[j+1]);
                    swap(j, j+1);
                }
            }
        }

    };

    this.selectionSort = function(){
        var length = array.length,
            indexMin;

        for (var i=0; i<length-1; i++){
            indexMin = i;
            console.log('index ' + array[i]);
            for (var j=i; j<length; j++){
                if(array[indexMin]>array[j]){
                    console.log('new index min ' + array[j]);
                    indexMin = j;
                }
            }
            if (i !== indexMin){
                console.log('swap ' + array[i] + ' with ' + array[indexMin]);
                swap(i, indexMin);
            }
        }
    };

    this.insertionSort = function(){
        var length = array.length,
            j, temp;
        for (var i=1; i<length; i++){
            j = i;
            temp = array[i];
            console.log('to be inserted ' + temp);
            while (j>0 && array[j-1] > temp){
                console.log('shift ' + array[j-1]);
                array[j] = array[j-1];
                j--;
            }
            console.log('insert ' + temp);
            array[j] = temp;
        }
    };

    var insertionSort_ = function(array){
        var length = array.length,
            j, temp;
        for (var i=1; i<length; i++){
            j = i;
            temp = array[i];
            while (j>0 && array[j-1] > temp){
                array[j] = array[j-1];
                j--;
            }
            array[j] = temp;
        }
    };

    this.mergeSort = function(){
        array = mergeSortRec(array);
    };

    var mergeSortRec = function(array){

        var length = array.length;

        if(length === 1) {
            console.log(array);
            return array;
        }

        var mid = Math.floor(length / 2),
            left = array.slice(0, mid),
            right = array.slice(mid, length);

        return merge(mergeSortRec(left), mergeSortRec(right));
    };

    var merge = function(left, right){
        var result = [],
            il = 0,
            ir = 0;

        while(il < left.length && ir < right.length) {

            if(left[il] < right[ir]) {
                result.push(left[il++]);
            } else{
                result.push(right[ir++]);
            }
        }

        while (il < left.length){
            result.push(left[il++]);
        }

        while (ir < right.length){
            result.push(right[ir++]);
        }

        console.log(result);

        return result;
    };

    this.quickSort = function(){
        quick(array,  0, array.length - 1);
    };

    var partition = function(array, left, right) {

        var pivot = array[Math.floor((right + left) / 2)],
            i = left,
            j = right;

        console.log('pivot is ' + pivot + '; left is ' + left + '; right is ' + right);

        while (i <= j) {
            while (array[i] < pivot) {
                i++;
                console.log('i = ' + i);
            }

            while (array[j] > pivot) {
                j--;
                console.log('j = ' + j);
            }

            if (i <= j) {
                console.log('swap ' + array[i] + ' with ' + array[j]);
                swap(array, i, j);
                i++;
                j--;
            }
        }

        return i;
    };

    var quick = function(array, left, right){

        var index;

        if (array.length > 1) {

            index = partition(array, left, right);

            if (left < index - 1) {
                quick(array, left, index - 1);
            }

            if (index < right) {
                quick(array, index, right);
            }
        }
        return array;
    };

    this.heapSort = function(){
        var heapSize = array.length;

        buildHeap(array);

        while (heapSize > 1) {
            heapSize--;
            console.log('swap (' + + array[0] + ',' + array[heapSize] + ')');
            swap(array, 0, heapSize);
            console.log('heapify ' + array.join());
            heapify(array, heapSize, 0);
        }
    };

    var buildHeap = function(array){
        console.log('building heap');
        var heapSize = array.length;
        for (var i = Math.floor(array.length / 2); i >= 0; i--) {
            heapify(array, heapSize, i);
        }
        console.log('heap created: ' + array.join());
    };

    var heapify = function(array, heapSize, i){
        var left = i * 2 + 1,
            right = i * 2 + 2,
            largest = i;

        if (left < heapSize && array[left] > array[largest]) {
            largest = left;
        }

        if (right < heapSize && array[right] > array[largest]) {
            largest = right;
        }

        console.log('Heapify Index = '+ i + ' and Heap Size = ' + heapSize);

        if (largest !== i) {
            console.log('swap index ' + i + ' with ' + largest + ' (' + + array[i] + ',' + array[largest] + ')');
            swap(array, i, largest);
            console.log('heapify ' + array.join());
            heapify(array, heapSize, largest);
        }
    };

    this.countingSort = function(){

        var i,
            maxValue = this.findMaxValue(),
            sortedIndex = 0,
            counts = new Array(maxValue + 1);

        for (i = 0; i < array.length; i++) {
            if (!counts[array[i]]) {
                counts[array[i]] = 0;
            }
            counts[array[i]]++;
        }

        console.log('Frequencies: ' + counts.join());

        for (i = 0; i < counts.length; i++) {
            while (counts[i] > 0) {
                array[sortedIndex++] = i;
                counts[i]--;
            }
        }
    };

    this.bucketSort = function(bucketSize){

        var i,
            minValue = this.findMinValue(),
            maxValue = this.findMaxValue(),
            BUCKET_SIZE = 5;

        console.log('minValue ' + minValue);
        console.log('maxValue ' + maxValue);

        bucketSize = bucketSize || BUCKET_SIZE;
        var bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;
        var buckets = new Array(bucketCount);
        console.log('bucketSize = ' + bucketCount);
        for (i = 0; i < buckets.length; i++) {
            buckets[i] = [];
        }

        for (i = 0; i < array.length; i++) {
            buckets[Math.floor((array[i] - minValue) / bucketSize)].push(array[i]);
            console.log('pushing item ' + array[i] + ' to bucket index ' + Math.floor((array[i] - minValue) / bucketSize));
        }

        array = [];
        for (i = 0; i < buckets.length; i++) {
            insertionSort_(buckets[i]);

            console.log('bucket sorted ' + i + ': ' + buckets[i].join());

            for (var j = 0; j < buckets[i].length; j++) {
                array.push(buckets[i][j]);
            }
        }
    };

    this.radixSort = function(radixBase){

        var i,
            minValue = this.findMinValue(),
            maxValue = this.findMaxValue(),
            radixBase = radixBase || 10;

        // Perform counting sort for each significant digit), starting at 1
        var significantDigit = 1;
        while (((maxValue - minValue) / significantDigit) >= 1) {
            console.log('radix sort for digit ' + significantDigit);
            array = countingSortForRadix(array, radixBase, significantDigit, minValue);
            console.log(array.join());
            significantDigit *= radixBase;
        }
    };

    var countingSortForRadix = function(array, radixBase, significantDigit, minValue){
        var i, countsIndex,
            counts = new Array(radixBase),
            aux = new Array(radixBase);

        for (i = 0; i < radixBase; i++) {
            counts[i] = 0;
        }

        for (i = 0; i < array.length; i++) {
            countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
            counts[countsIndex]++;
        }

        for (i = 1; i < radixBase; i++) {
            counts[i] += counts[i - 1];
        }

        for (i = array.length - 1; i >= 0; i--) {
            countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
            aux[--counts[countsIndex]] = array[i];
        }

        for (i = 0; i < array.length; i++) {
            array[i] = aux[i];
        }

        return array;
    };

    this.sequentialSearch = function(item){

        for (var i=0; i<array.length; i++){
            if (item === array[i]){
                return i;
            }
        }

        return -1;
    };

    this.findMaxValue = function(){
        var max = array[0];
        for (var i=1; i<array.length; i++){
            if (max < array[i]){
                max = array[i];
            }
        }

        return max;
    };

    this.findMinValue = function(){
        var min = array[0];
        for (var i=1; i<array.length; i++){
            if (min > array[i]){
                min = array[i];
            }
        }

        return min;
    };

    this.binarySearch = function(item){
        this.quickSort();

        var low = 0,
            high = array.length - 1,
            mid, element;

        while (low <= high){
            mid = Math.floor((low + high) / 2);
            element = array[mid];
            console.log('mid element is ' + element);
            if (element < item) {
                low = mid + 1;
                console.log('low is ' + low);
            } else if (element > item) {
                high = mid - 1;
                console.log('high is ' + high);
            } else {
                console.log('found it');
                return mid;
            }
        }
        return -1;
    };

}