我要好offer之 排序算法大总结

1. 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;
}
}

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

// 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);
}

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)--;
}
}