JS模拟排序算法和搜索算法

Typescript版本的排序和搜索算法

排序算法

算法中用到的公共函数

const Compare = {
  LESS_THAN: -1,
  BIGGER_THAN: 1,
  EQUALS: 0
};

const DOES_NOT_EXIST = -1;

function lesserEquals(a, b, compareFn) {
  const comp = compareFn(a, b);
  return comp === Compare.LESS_THAN || comp === Compare.EQUALS;
}

function biggerEquals(a, b, compareFn) {
  const comp = compareFn(a, b);
  return comp === Compare.BIGGER_THAN || comp === Compare.EQUALS;
}

function defaultCompare(a, b) {
  if (a === b) {
    return Compare.EQUALS;
  }
  return a < b ? Compare.LESS_THAN : Compare.BIGGER_THAN;
}

function defaultEquals(a, b) {
  return a === b;
}

function defaultToString(item) {
  if (item === null) {
    return 'NULL';
  } else if (item === undefined) {
    return 'UNDEFINED';
  } else if (typeof item === 'string' || item instanceof String) {
    return `${item}`;
  }
  return item.toString();
}

function swap(array, a, b) {
  [array[a], array[b]] = [array[b], array[a]];
}
function reverseCompare(compareFn) {
  return (a, b) => compareFn(b, a);
}

function defaultDiff(a, b) {
  return Number(a) - Number(b);
}

冒泡排序

function bubbleSort(array, compareFn = defaultCompare) {
  const { length } = array;
  for (let i = 0; i < length; i++) {
    for (let j = 0; j < length - 1; j++) {
      if (compareFn(array[j], array[j + 1]) === Compare.BIGGER_THAN) {
        swap(array, j, j + 1);
      }
    }
  }
  return array;
}

改进的冒泡排序(减少中间比较)

function modifiedBubbleSort(array, compareFn = defaultCompare) {
  const { length } = array;
  for (let i = 0; i < length; i++) {
    for (let j = 0; j < length - 1 - i; j++) {
      if (compareFn(array[j], array[j + 1]) === Compare.BIGGER_THAN) {
        swap(array, j, j + 1);
      }
    }
  }
  return array;
}

选择排序

function selectionSort (array, compareFn = defaultCompare) {
  const { length } = array;
  let indexMin;
  for (let i = 0; i < length - 1; i++) {
    indexMin = i;
    for (let j = i; j < length; j++) {
      if (compareFn(array[indexMin], array[j]) === Compare.BIGGER_THAN) {
        indexMin = j;
      }
    }
    if (i !== indexMin) {
      swap(array, i, indexMin);
    }
  }
  return array;
};

插入排序

function insertionSort(array, compareFn = defaultCompare) {
  const { length } = array;
  let temp;
  for (let i = 1; i < length; i++) {
    let j = i;
    temp = array[i];
    while (j > 0 && compareFn(array[j - 1], temp) === Compare.BIGGER_THAN) {
      array[j] = array[j - 1];
      j--;
    }
    array[j] = temp;
  }
  return array;
};

归并排序

function merge(left, right, compareFn) {
  let i = 0;
  let j = 0;
  const result = [];
  while (i < left.length && j < right.length) {
    result.push(compareFn(left[i], right[j]) === Compare.LESS_THAN ? left[i++] : right[j++]);
  }
  return result.concat(i < left.length ? left.slice(i) : right.slice(j));
}
function mergeSort(array, compareFn = defaultCompare) {
  if (array.length > 1) {
    const { length } = array;
    const middle = Math.floor(length / 2);
    const left = mergeSort(array.slice(0, middle), compareFn);
    const right = mergeSort(array.slice(middle, length), compareFn);
    array = merge(left, right, compareFn);
  }
  return array;
}

快速排序

 // 划分过程
function partition(array, left, right, compareFn) {
  const pivot = array[Math.floor((right + left) / 2)];
  let i = left;
  let j = right;
  while (i <= j) {
    while (compareFn(array[i], pivot) === Compare.LESS_THAN) {
      i++;
    }
    while (compareFn(array[j], pivot) === Compare.BIGGER_THAN) {
      j--;
    }
    if (i <= j) {
      swap(array, i, j);
      i++;
      j--;
    }
  }
  return i;
}
function quick(array, left, right, compareFn) {
  let index;
  if (array.length > 1) {
    index = partition(array, left, right, compareFn);
    if (left < index - 1) {
      quick(array, left, index - 1, compareFn);
    }
    if (index < right) {
      quick(array, index, right, compareFn);
    }
  }
  return array;
}
function quickSort(array, compareFn = defaultCompare) {
  return quick(array, 0, array.length - 1, compareFn);
}

计数排序

function countingSort(array) {
  if (array.length < 2) {
    return array;
  }
  const maxValue = findMaxValue(array);
  let sortedIndex = 0;
  const counts = new Array(maxValue + 1);
  array.forEach(element => {
    if (!counts[element]) {
      counts[element] = 0;
    }
    counts[element]++;
  });
  counts.forEach((element, i) => {
    while (element > 0) {
      array[sortedIndex++] = i;
      element--;
    }
  });
  return array;
}

桶排序

// 引入前面的插入排序
import { insertionSort } from './insertion-sort';

function createBuckets(array, bucketSize) {
  let minValue = array[0];
  let maxValue = array[0];
  for (let i = 1; i < array.length; i++) {
    if (array[i] < minValue) {
      minValue = array[i];
    } else if (array[i] > maxValue) {
      maxValue = array[i];
    }
  }
  const bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;
  const buckets = [];
  for (let i = 0; i < bucketCount; i++) {
    buckets[i] = [];
  }
  for (let i = 0; i < array.length; i++) {
    buckets[Math.floor((array[i] - minValue) / bucketSize)].push(array[i]);
  }
  return buckets;
}
function sortBuckets(buckets) {
  const sortedArray = [];
  for (let i = 0; i < buckets.length; i++) {
    if (buckets[i] != null) {
      insertionSort(buckets[i]);
      sortedArray.push(...buckets[i]);
    }
  }
  return sortedArray;
}
function bucketSort(array, bucketSize = 5) {
  if (array.length < 2) {
    return array;
  }
  const buckets = createBuckets(array, bucketSize);
  return sortBuckets(buckets);
}

基数排序

function findMaxValue(array, compareFn = defaultCompare) {
  if (array && array.length > 0) {
    let max = array[0];
    for (let i = 1; i < array.length; i++) {
      if (compareFn(max, array[i]) === Compare.LESS_THAN) {
        max = array[i];
      }
    }
    return max;
  }
  return undefined;
}
function findMinValue(array, compareFn = defaultCompare) {
  if (array && array.length > 0) {
    let min = array[0];
    for (let i = 1; i < array.length; i++) {
      if (compareFn(min, array[i]) === Compare.BIGGER_THAN) {
        min = array[i];
      }
    }
    return min;
  }
  return undefined;
}

const getBucketIndex = (value, minValue, significantDigit, radixBase) =>
  Math.floor(((value - minValue) / significantDigit) % radixBase);

const countingSortForRadix = (array, radixBase, significantDigit, minValue) => {
  let bucketsIndex;
  const buckets = [];
  const aux = [];
  for (let i = 0; i < radixBase; i++) {
    buckets[i] = 0;
  }
  for (let i = 0; i < array.length; i++) {
    bucketsIndex = getBucketIndex(array[i], minValue, significantDigit, radixBase);
    buckets[bucketsIndex]++;
  }
  for (let i = 1; i < radixBase; i++) {
    buckets[i] += buckets[i - 1];
  }
  for (let i = array.length - 1; i >= 0; i--) {
    bucketsIndex = getBucketIndex(array[i], minValue, significantDigit, radixBase);
    aux[--buckets[bucketsIndex]] = array[i];
  }
  for (let i = 0; i < array.length; i++) {
    array[i] = aux[i];
  }
  return array;
};
function radixSort(array, radixBase = 10) {
  if (array.length < 2) {
    return array;
  }
  const minValue = findMinValue(array);
  const maxValue = findMaxValue(array);
  // Perform counting sort for each significant digit, starting at 1
  let significantDigit = 1;
  while ((maxValue - minValue) / significantDigit >= 1) {
    array = countingSortForRadix(array, radixBase, significantDigit, minValue);
    significantDigit *= radixBase;
  }
  return array;
}

堆排序

function heapify(array, index, heapSize, compareFn) {
  let largest = index;
  const left = (2 * index) + 1;
  const right = (2 * index) + 2;
  if (left < heapSize && compareFn(array[left], array[index]) > 0) {
    largest = left;
  }
  if (right < heapSize && compareFn(array[right], array[largest]) > 0) {
    largest = right;
  }
  if (largest !== index) {
    swap(array, index, largest);
    heapify(array, largest, heapSize, compareFn);
  }
}

function buildMaxHeap(array, compareFn) {
  for (let i = Math.floor(array.length / 2); i >= 0; i -= 1) {
    heapify(array, i, array.length, compareFn);
  }
  return array;
}

function heapSort(array, compareFn = defaultCompare) {
  let heapSize = array.length;
  buildMaxHeap(array, compareFn);
  while (heapSize > 1) {
    swap(array, 0, --heapSize);
    heapify(array, 0, heapSize, compareFn);
  }
  return array;
}

希尔排序

function shellSort(array, compareFn = defaultCompare) {
  let increment = array.length / 2;
  while (increment > 0) {
    for (let i = increment; i < array.length; i++) {
      let j = i;
      const temp = array[i];
      while (j >= increment && compareFn(array[j - increment], temp) === Compare.BIGGER_THAN) {
        array[j] = array[j - increment];
        j -= increment;
      }
      array[j] = temp;
    }
    if (increment === 2) {
      increment = 1;
    } else {
      increment = Math.floor((increment * 5) / 11);
    }
  }
  return array;
}

搜索算法

顺序搜索

function sequentialSearch(array, value, equalsFn = defaultEquals) {
  for (let i = 0; i < array.length; i++) {
    if (equalsFn(value, array[i])) {
      return i;
    }
  }
  return DOES_NOT_EXIST;
}

二分搜索

// 引入文章前面的快速排序方法
import { quickSort } from 'quicksort';

function binarySearch(array, value, compareFn = defaultCompare) {
  const sortedArray = quickSort(array);
  let low = 0;
  let high = sortedArray.length - 1;
  while (low <= high) {
    const mid = Math.floor((low + high) / 2);
    const element = sortedArray[mid];
    if (compareFn(element, value) === Compare.LESS_THAN) {
      low = mid + 1;
    } else if (compareFn(element, value) === Compare.BIGGER_THAN) {
      high = mid - 1;
    } else {
      return mid;
    }
  }
  return DOES_NOT_EXIST;
}

二分搜索——递归实现

// 引入文章前面的快速排序方法
import { quickSort } from 'quicksort';

function binarySearchRecursive(array, value, low, high, compareFn = defaultCompare) {
  if (low <= high) {
    const mid = Math.floor((low + high) / 2);
    const element = array[mid];
    if (compareFn(element, value) === Compare.LESS_THAN) {
      return binarySearchRecursive(array, value, mid + 1, high, compareFn);
    }
    if (compareFn(element, value) === Compare.BIGGER_THAN) {
      return binarySearchRecursive(array, value, low, mid - 1, compareFn);
    }
    return mid;
  }
  return DOES_NOT_EXIST;
}

function binarySearch(array, value, compareFn = defaultCompare) {
  const sortedArray = quickSort(array);
  const low = 0;
  const high = sortedArray.length - 1;
  return binarySearchRecursive(array, value, low, high, compareFn);
}

内插搜索

// 引入前面的工具函数和相关变量
import {
  biggerEquals,
  Compare,
  defaultCompare,
  defaultEquals,
  defaultDiff,
  DOES_NOT_EXIST,
  lesserEquals
} from '../../util';

function interpolationSearch(
  array,
  value,
  compareFn = defaultCompare,
  equalsFn = defaultEquals,
  diffFn = defaultDiff
) {
  const { length } = array;
  let low = 0;
  let high = length - 1;
  let position = -1;
  let delta = -1;
  while (
    low <= high &&
    biggerEquals(value, array[low], compareFn) &&
    lesserEquals(value, array[high], compareFn)
  ) {
    delta = diffFn(value, array[low]) / diffFn(array[high], array[low]);
    position = low + Math.floor((high - low) * delta);
    if (equalsFn(array[position], value)) {
      return position;
    }
    if (compareFn(array[position], value) === Compare.LESS_THAN) {
      low = position + 1;
    } else {
      high = position - 1;
    }
  }
  return DOES_NOT_EXIST;
}

随机算法Fisher—Yates(洗扑克牌)

function shuffle(array) {
    for(let i=array.length;i>0;i--) {
        const randomIndex = Math.floor(Math.random()*(i+1));
        swap(array, i, randomIndex);
    }
    return array;
}