排序

1. 插入排序

(1) 直接插入排序

void StraightInsertionSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    for (int i = 1; i < num.size(); ++i) {        int tmp = num.at(i);        int j = i - 1;        for (; j >= 0 && num.at(j) > tmp; --j) {            num.at(j + 1) = num.at(j);         }        num.at(j + 1) = tmp;    }}

(2) 折半插入排序

void BinaryInsertionSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    for (int i = 1; i < num.size(); ++i) {        int tmp = num.at(i);        int first = 0;   // 最终的first值即为插入位置        int last = i - 1;        while (first <= last) {            int mid = first + (last - first) / 2;            if (num.at(mid) < tmp) {                first = mid + 1;            } else if (num.at(mid) > tmp) {                last = mid - 1;            } else {                first = mid;                break;            }        }                for (int t = i - 1; t >= first; --t) {            num.at(t + 1) = num.at(t);        }        num.at(first) = tmp;    }}

 

2. 希尔排序

void ShellSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    for (int gap = num.size() / 2; gap > 0; gap /= 2) {        for (int i = gap; i < num.size(); ++i) {            for (int j = i - gap; j >= 0 && num.at(j) > num.at(j + gap); j -= gap) {                std::swap(num.at(j), num.at(j + gap));            }        }    }}

 

3. 冒泡排序

void BubbleSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    for (int i = 0; i < num.size(); ++i) {        for (int j = 0; j < num.size() - i - 1; ++j) {            if (num.at(j) > num.at(j + 1)) {                std::swap(num.at(j), num.at(j + 1));            }        }    }}

 

4. 快速排序

(1) 递归版

// 划分int Partition(std::vector<int>& num, int first, int last) {    assert(first >= 0 && first < num.size() && last >= 0 && last < num.size() && first <= last);    int mid = first + (last - first) / 2;    std::swap(num.at(first), num.at(mid));    int pos = first;    for (int i = first; i <= last; ++i) {        if (num.at(i) < num.at(first)) {            std::swap(num.at(++pos), num.at(i));        }    }    std::swap(num.at(first), num.at(pos));    return pos;}// 快速排序void quickSort(std::vector<int>& num, int first, int last) {    if (first < last) {        int pivotPos = Partition(num, first, last);        quickSort(num, first, pivotPos - 1);        quickSort(num, pivotPos + 1, last);    }}void QuickSort(std::vector<int>& num) {    quickSort(num, 0, num.size() - 1);}

 

(2) 非递归版

int Partition(std::vector<int>& num, int first, int last) {    assert(first >= 0 && first < num.size() && last >= 0 && last < num.size() && first <= last);    int mid = first + (last - first) / 2;    std::swap(num.at(first), num.at(mid));    int pos = first;    for (int i = first; i <= last; ++i) {        if (num.at(i) < num.at(first)) {            std::swap(num.at(++pos), num.at(i));        }    }    std::swap(num.at(first), num.at(pos));    return pos;}void QuickSort(std::vector<int>& num, int first, int last) {    if (first < last) {        std::stack<int> stk;        int pivotPos = Partition(num, first, last);        if (first < pivotPos - 1) {            stk.push(first);            stk.push(pivotPos - 1);        }        if (last > pivotPos + 1) {            stk.push(pivotPos + 1);            stk.push(last);        }        while (!stk.empty()) {            int right = stk.top();            stk.pop();            int left = stk.top();            stk.pop();            pivotPos = Partition(num, left, right);            if (left < pivotPos - 1) {                stk.push(left);                stk.push(pivotPos - 1);            }            if (right > pivotPos + 1) {                stk.push(pivotPos + 1);                stk.push(right);            }        }    }}

 

5. 简单选择排序

void SimpleSelectSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    for (int i = 0; i < num.size(); ++i) {        for (int j = i + 1; j < num.size(); ++j) {            if (num.at(j) < num.at(i)) {                std::swap(num.at(i), num.at(j));            }        }    }}

 

6. 堆排序

堆的有关操作

// 堆调整，注意结点编号kth从1开始void HeapAdjust(std::vector<int>& num, int kth, int vecSize) {    int left = 2 * kth;    int right = 2 * kth + 1;    int largest = INT_MIN;    if (left <= vecSize && num.at(left - 1) > num.at(kth - 1)) {        largest = left;    } else {        largest = kth;    }        if (right <= vecSize && num.at(right - 1) > num.at(largest - 1)) {        largest = right;    }    if (largest != kth) {        std::swap(num.at(kth - 1), num.at(largest - 1));        HeapAdjust(num, largest, vecSize);    }}// 建堆void BuildHeap(std::vector<int>& num) {    for (int i = num.size() / 2; i >= 0; --i) {        HeapAdjust(num, i + 1, num.size());    }}// 堆排序void HeapSort(std::vector<int>& num) {    BuildHeap(num);    int vecSize = num.size();    while (vecSize > 1) {        std::swap(num.at(0), num.at(vecSize - 1));        --vecSize;        HeapAdjust(num, 1, vecSize);    }}

 

7. 归并排序

void merge(std::vector<int>& num, int first, int mid, int last) {    std::vector<int> tmp(last - first + 1, 0);    int i = first;    int j = mid + 1;    int idx = 0;    while (i <= mid && j <= last) {        if (num.at(i) <= num.at(j)) {            tmp.at(idx++) = num.at(i++);        } else {            tmp.at(idx++) = num.at(j++);        }    }    while (i <= mid) {        tmp.at(idx++) = num.at(i++);    }    while (j <= last) {        tmp.at(idx++) = num.at(j++);    }    for (int i = first; i <= last; ++i) {        num.at(i) = tmp.at(i - first);    }}void MergeSort(std::vector<int>& num, int first, int last) {    if (first < last) {        int mid = first + (last -first) / 2;        MergeSort(num, first, mid);        MergeSort(num, mid + 1, last);        merge(num, first, mid, last);    }}

 

8. 计数排序

void CountSort(std::vector<int>& num) {    if (num.size() == 0 || num.size() == 1) return;    int minVal = *(std::min_element(num.begin(), num.end()));    int maxVal = *(std::max_element(num.begin(), num.end()));    int valRange = maxVal - minVal + 1;    std::vector<int> count(valRange, 0);    for (int i = 0; i < num.size(); ++i) {        count.at(num.at(i) - minVal)++;    }        for (int i = 1; i < count.size(); ++i) {        count.at(i) = count.at(i) + count.at(i - 1);    }        std::vector<int> tmp(num);        for (int i = tmp.size() - 1; i >= 0; --i) {        int lessNum = count.at(tmp.at(i) - minVal);        num.at(lessNum - 1) = tmp.at(i);        count.at(tmp.at(i) - minVal)--;    }}