//LSD Radix Sort
var counter = [];
function radixSort(arr, maxDigit) {
    var mod = 10;
    var dev = 1;
    for (var i = 0; i < maxDigit; i++, dev *= 10, mod *= 10) {
        for(var j = 0; j < arr.length; j++) {
            var bucket = parseInt((arr[j] % mod) / dev);
            if(counter[bucket]==null) {
                counter[bucket] = [];
            }
            counter[bucket].push(arr[j]);
        }
        var pos = 0;
        for(var j = 0; j < counter.length; j++) {
            var value = null;
            if(counter[j]!=null) {
                while ((value = counter[j].shift()) != null) {
                      arr[pos++] = value;
                }
          }
        }
    }
    return arr;
}

function bucketSort(arr, bucketSize) {
    if (arr.length === 0) {
      return arr;
    }

    var i;
    var minValue = arr[0];
    var maxValue = arr[0];
    for (i = 1; i < arr.length; i++) {
      if (arr[i] < minValue) {
          minValue = arr[i];                // 输入数据的最小值
      } else if (arr[i] > maxValue) {
          maxValue = arr[i];                // 输入数据的最大值
      }
    }

    //桶的初始化
    var DEFAULT_BUCKET_SIZE = 5;            // 设置桶的默认数量为5
    bucketSize = bucketSize || DEFAULT_BUCKET_SIZE;
    var bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;   
    var buckets = new Array(bucketCount);
    for (i = 0; i < buckets.length; i++) {
        buckets[i] = [];
    }

    //利用映射函数将数据分配到各个桶中
    for (i = 0; i < arr.length; i++) {
        buckets[Math.floor((arr[i] - minValue) / bucketSize)].push(arr[i]);
    }

    arr.length = 0;
    for (i = 0; i < buckets.length; i++) {
        insertionSort(buckets[i]);                      // 对每个桶进行排序，这里使用了插入排序
        for (var j = 0; j < buckets[i].length; j++) {
            arr.push(buckets[i][j]);                      
        }
    }

    return arr;
}

function countingSort(arr, maxValue) {
    var bucket = new Array(maxValue+1),
        sortedIndex = 0;
        arrLen = arr.length,
        bucketLen = maxValue + 1;

    for (var i = 0; i < arrLen; i++) {
        if (!bucket[arr[i]]) {
            bucket[arr[i]] = 0;
        }
        bucket[arr[i]]++;
    }

    for (var j = 0; j < bucketLen; j++) {
        while(bucket[j] > 0) {
            arr[sortedIndex++] = j;
            bucket[j]--;
        }
    }

    return arr;
}

var len;    // 因为声明的多个函数都需要数据长度，所以把len设置成为全局变量

function buildMaxHeap(arr) {   // 建立大顶堆
    len = arr.length;
    for (var i = Math.floor(len/2); i >= 0; i--) {
        heapify(arr, i);
    }
}

function heapify(arr, i) {     // 堆调整
    var left = 2 * i + 1,
        right = 2 * i + 2,
        largest = i;

    if (left < len && arr[left] > arr[largest]) {
        largest = left;
    }

    if (right < len && arr[right] > arr[largest]) {
        largest = right;
    }

    if (largest != i) {
        swap(arr, i, largest);
        heapify(arr, largest);
    }
}

function swap(arr, i, j) {
    var temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

function heapSort(arr) {
    buildMaxHeap(arr);

    for (var i = arr.length-1; i > 0; i--) {
        swap(arr, 0, i);
        len--;
        heapify(arr, 0);
    }
    return arr;
}

function quickSort(arr, left, right) {
    var len = arr.length,
        partitionIndex,
        left = typeof left != 'number' ? 0 : left,
        right = typeof right != 'number' ? len - 1 : right;

    if (left < right) {
        partitionIndex = partition(arr, left, right);
        quickSort(arr, left, partitionIndex-1);
        quickSort(arr, partitionIndex+1, right);
    }
    return arr;
}

function partition(arr, left ,right) {     // 分区操作
    var pivot = left,                      // 设定基准值（pivot）
        index = pivot + 1;
    for (var i = index; i <= right; i++) {
        if (arr[i] < arr[pivot]) {
            swap(arr, i, index);
            index++;
        }        
    }
    swap(arr, pivot, index - 1);
    return index-1;
}

function swap(arr, i, j) {
    var temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}
function partition2(arr, low, high) {
  let pivot = arr[low];
  while (low < high) {
    while (low < high && arr[high] > pivot) {
      --high;
    }
    arr[low] = arr[high];
    while (low < high && arr[low] <= pivot) {
      ++low;
    }
    arr[high] = arr[low];
  }
  arr[low] = pivot;
  return low;
}

function quickSort2(arr, low, high) {
  if (low < high) {
    let pivot = partition2(arr, low, high);
    quickSort2(arr, low, pivot - 1);
    quickSort2(arr, pivot + 1, high);
  }
  return arr;
}

function mergeSort(arr) {  // 采用自上而下的递归方法
    var len = arr.length;
    if(len < 2) {
        return arr;
    }
    var middle = Math.floor(len / 2),
        left = arr.slice(0, middle),
        right = arr.slice(middle);
    return merge(mergeSort(left), mergeSort(right));
}

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

    while (left.length && right.length) {
        if (left[0] <= right[0]) {
            result.push(left.shift());
        } else {
            result.push(right.shift());
        }
    }

    while (left.length)
        result.push(left.shift());

    while (right.length)
        result.push(right.shift());

    return result;
}