算法模板

基础算法

快速排序

函数模板

void quick_sort(int q[], int l, int r)
{
    if (l >= r) return;

    int i = l - 1, j = r + 1, x = q[l + r >> 1];
    while (i < j)
    {
        do i ++ ; while (q[i] < x);
        do j -- ; while (q[j] > x);
        if (i < j) swap(q[i], q[j]);
    }
    quick_sort(q, l, j), quick_sort(q, j + 1, r);
}

完整程序

# include <iostream>

using namespace std;

const int N = 1e6 + 10;

int n;
int q[N];

void quick_sort(int q[], int l, int r)
{
	if (l >= r) return;
	
	int x = q[l], i = l - 1, j = r + 1;  // i 从 l-1 开始,保证 do i++ 后,i 第一个访问的是 l
	while(i < j){
		do i++; while (q[i] < x);
		do j--; while (q[j] > x);
		if (i < j) swap(q[i], q[j]); 
	}
	
	quick_sort(q, l, j);
	quick_sort(q, j + 1, r);
}

int main()
{
	scanf("%d", &n);
	for (int i = 0; i < n; i++) scanf("%d", &q[i]);
	
	quick_sort(q, 0, n - 1);  // 0 和 n-1 是左右边界的索引
	for (int i = 0; i < n; i++) printf("%d ", q[i]);

	return 0;
}

归并排序

函数模板

void merge_sort(int q[], int l, int r)
{
    if (l >= r) return;

    int mid = l + r >> 1;  // (l + r) / 2
    merge_sort(q, l, mid);
    merge_sort(q, mid + 1, r);

    int k = 0, i = l, j = mid + 1;
    while (i <= mid && j <= r)
        if (q[i] <= q[j]) tmp[k ++ ] = q[i ++ ];
        else tmp[k ++ ] = q[j ++ ];

    while (i <= mid) tmp[k ++ ] = q[i ++ ];
    while (j <= r) tmp[k ++ ] = q[j ++ ];

    for (i = l, j = 0; i <= r; i ++, j ++ ) q[i] = tmp[j];
}

完整程序

#include <iostream>
using namespace std;

const int N = 1000010;

int n;
int q[N], tmp[N];

void merge_sort(int q[], int l, int r)
{
	if (l >= r) return;
	
	int mid = (l + r) >> 1;
	
	merge_sort(q, l, mid), merge_sort(q, mid + 1, r);
	
	int k = 0, i = l, j = mid + 1;
	while (i <= mid && j <=r){
		if (q[i] <= q[j]) tmp[k++] = q[i++];
		else tmp[k++] = q[j++];
	}
	while (i <= mid) tmp[k++] = q[i++];
	while (j <= r) tmp[k++] = q[j++];
	
	for (i = l, j = 0; i <= r; i++, j++) q[i] = tmp[j];
} 

int main()
{
	scanf("%d", &n);
	for (int i = 0; i < n; i++) scanf("%d", &q[i]);
	
	merge_sort(q, 0, n-1);
	
	for (int i = 0; i < n; i++) printf("%d ", q[i]);
	
	return 0;
}

整数二分

函数模板

bool check(int x) {/* ... */}  // 检查x是否满足某种性质

// 区间[l, r]被划分成[l, mid]和[mid + 1, r]时使用:
int bsearch_1(int l, int r)
{
    while (l < r)
    {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;  // check()判断mid是否满足性质
        else l = mid + 1;
    }
    return l;
}
// 区间[l, r]被划分成[l, mid - 1]和[mid, r]时使用:
int bsearch_2(int l, int r)
{
    while (l < r)
    {
        int mid = l + r + 1 >> 1;  // 是否加1取决于是 l = mid 还是r = mid,和其他因素无关
        if (check(mid)) l = mid;
        else r = mid - 1;
    }
    return l;
}

完整程序

#include <iostream>

using namespace std;

const int N = 100010;

int n, m;
int q[N];

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 0; i < n; i ++ ) scanf("%d", &q[i]);

    while (m -- )
    {
        int x;
        scanf("%d", &x);

        int l = 0, r = n - 1;
        while (l < r)
        {
            int mid = l + r >> 1;
            if (q[mid] >= x) r = mid;
            else l = mid + 1;
        }

        if (q[l] != x) cout << "-1 -1" << endl;
        else
        {
            cout << l << ' ';

            int l = 0, r = n - 1;
            while (l < r)
            {
                int mid = l + r + 1 >> 1;
                if (q[mid] <= x) l = mid;
                else r = mid - 1;
            }

            cout << l << endl;
        }
    }

    return 0;
}

浮点数二分

函数模板

bool check(double x) {/* ... */}  // 检查x是否满足某种性质

double bsearch_3(double l, double r)
{
    const double eps = 1e-6;  // eps 表示精度,取决于题目对精度的要求
    while (r - l > eps)
    {
        double mid = (l + r) / 2;
        if (check(mid)) r = mid;
        else l = mid;
    }
    return l;
}

完整程序

#include <iostream>

using namespace std;

int main()
{
    double x;
    cin >> x;

    double l = -100, r = 100;
    while (r - l > 1e-8)
    {
        double mid = (l + r) / 2;
        if (mid * mid * mid >= x) r = mid;
        else l = mid;
    }

    printf("%.6lf\n", l);
    return 0;
}

xx

函数模板

完整程序