[AcWing算法基础课] 一.基础算法

 Algorithms + Data Structures = Programs. ——Niklaus Wirth

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本章包括排序、二分、高精度、前缀和与差分、双指针算法、位运算、离散化、区间合并等内容

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目录

​​一.排序​​

​​快速排序​​

​​归并排序​​

​​模板​​

​​二.二分​​

​​三.高精度​​

​​四.前缀和与差分​​

​​五.双指针算法​​

​​六.离散化​​

​​七.区间合并​​

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一.排序

快速排序

​​AcWing 785. 快速排序​​

#include<iostream>
using namespace std;

const int N = 1e6 + 10;
int a[N];
void QuickSort(int a[],int l,int r)
{
    if(l>=r) return;
    
    int x=a[(l+r)>>1];
    int i=l-1,j=r+1;// 因为下面的是最开始就将i,j移动一位，再判断，所以要在边界的两端前一位开始
    while(i < j)
    {
        do i++; while(a[i] < x);
        do j--; while(a[j] > x);
        if(i < j)
            swap(a[i],a[j]);
    }
    
    QuickSort(a,l,j);
    QuickSort(a,j+1,r);
}
int main()
{
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i ++ )
        scanf("%d", &a[i]);
    
    QuickSort(a,0,n-1);
    for (int i = 0; i < n; i ++ )
        printf("%d ", a[i]);
    return 0;
}

归并排序

​​AcWing 787. 归并排序​​

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 1e5+10;
int a[N],tmp[N];

void Merge_sort(int a[],int l,int r)
{
    if(l >= r) return ;
    int mid = (l + r) >> 1;
    //先分后合
    Merge_sort(a, l, mid);
    Merge_sort(a, mid+1, r);
    int i = l,j = mid +1,k = 0;
    //归并
    while(i<=mid && j<=r)
    {
        if(a[i]<=a[j]) tmp[k++] = a[i++];
        else tmp[k++] = a[j++];
    }
    //续尾
    while(i <= mid) tmp[k++] = a[i++];
    while(j <= r) tmp[k++] = a[j++];
    for (i = l,j = 0; i <= r;)
        a[i++] = tmp[j++];
}
int main()
{
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i ++ ) scanf("%d",&a[i]);
    Merge_sort(a, 0, n-1);
    for (int i = 0; i < n; i ++ ) printf("%d ",a[i]);
    return 0;
}

模板

作者：yxc
链接：https://www.acwing.com/blog/content/277/
来源：AcWing

快速排序算法模板
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);
}


归并排序算法模板
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];
}

二.二分

 了解更多:

​​>>初识二分法​​

​​>>如何优雅的处理边界条件？一定要数据有序时才能使用二分法吗？​​

​​AcWing 789. 数的范围 ​​

输入样例：

6 3
1 2 2 3 3 4
3
4
5

输出样例：

3 4
5 5
-1 -1

#include <iostream>
using namespace std;

const int N = 1e5+10;

int n,m;

int a[N];
int main()
{
    cin>>n>>m;
    for(int i=0; i<n; i++) scanf("%d", &a[i]);
    int x;
    while (m -- )
    {
        cin >> x;
        int l = 0, r = n-1;
        while(l<r)
        {
            int mid = (l + r) >> 1;
            if(a[mid]>=x) r = mid;
            else l = mid + 1;
        } 
        if (a[l] != x) cout << "-1 -1" << endl;
        else{
            cout<<l<<' ';
            r = n-1;
            while(l<r)
            {
                int mid = (l + r + 1) >> 1;
                if(a[mid]>x) r = mid - 1;
                else l = mid;
            }
            cout<<r<<endl;
        }
    }

    return 0;
}

三.高精度

​​[练习] 高精度加减乘除_☆迷茫狗子的秘密基地☆​​

四.前缀和与差分

​​[练习](一二维 )前缀和 与 差分_☆迷茫狗子的秘密基地☆-​​

五.双指针算法

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 1e5+10;
int a[N],cnt[N];
int main()
{
    int n;
    int res=0;
    cin >> n;
    for (int i = 0; i < n; i ++ ) scanf("%d", &a[i]);
    for (int i = 0,j = 0; i < n; i ++ ){
        cnt[a[i]]++;
        while(cnt[a[i]]>1){
            cnt[a[j]]--;
            j ++;
        }
        res = max(res, i+1-j);
    }
    cout << res;
    return 0;
}

六.离散化

​​利用离散化求区间和_☆迷茫狗子的秘密基地☆​​

七.区间合并

输入样例：

3
1 2 3 2
2 5 2 3
1 4 3 4

输出样例：

8

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

typedef pair<int, int> PII;
vector<PII> area;

int main()
{
    int n;
    int l,r;
    cin >> n;
    for (int i = 0; i < n; i ++ )
    {
        cin >> l >> r;
        area.push_back({l,r});
    }
    sort(area.begin(), area.end());
    int cnt=0;
    int final=-2e9;
    for(auto t: area)
    {
        if(t.first>final){
            cnt++;
        }
        final=max(final,t.second);
    }
    cout << cnt;
    return 0;
}