【三月专题】Dp专练

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单调队列优化Dp

P1440 求m区间内的最小值

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
//#include <windows.h>
#define ll long long
#define rg register
#define ull unsigned long long 

using namespace std;

int n,m;
int k,tot,head=1,tail=0;
int a[2000009],q[2000009];

inline int read()
{
    int x=0,f=1;
    char ch;
    while (ch < '0' || ch > '9')  {if (ch=='-')f = -1;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x*10+ch-'0';ch = getchar();}
    return f*x;
}

int main()
{
	n=read(),m=read();
    for(rg int i=1;i<=n;i++)
        a[i]=read();
    for(rg int i=1;i<=n;i++)
    {
        printf("%d
",a[q[head]]);
        while(i-q[head]+1>m&&head<=tail)    
            head++;
        while(a[i]<a[q[tail]]&&head<=tail)
            tail--;
        q[++tail]=i;
    }
	//system("pause");
	return 0;
}

　　

P1886 滑动窗口

代码：

#include<bits/stdc++.h>
using namespace std;
#define re register int
#define ll long long
#define maxn 1000009
#define maxm
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+(ll)(ch-'0');ch=getchar();}
    return x*f;
}
int q[maxn],a[maxn];
int n,m,k,ans,tot,head,tail; 

void Ask_MIN()
{
    head=1,tail=0;
    for(int i=1;i<=n;i++)
    {
        while(head<=tail&&i-q[head]+1>m)
            head++;
        while(head<=tail&&a[q[tail]]>=a[i])
            tail--;
        q[++tail]=i;
        if(i>=m)
            printf("%d ",a[q[head]]);    
    }
}

void Ask_MAX()
{
    head=1,tail=0;
    for(int i=1;i<=n;i++)
    {
        while(head<=tail&&i-q[head]+1>m)
            head++;
        while(head<=tail&&a[q[tail]]<=a[i])
            tail--;
        q[++tail]=i;
        if(i>=m)
            printf("%d ",a[q[head]]);
    }
}
int main()
{
    n=read(),m=read();
    for(int i=1;i<=n;i++)
        a[i]=read();
    Ask_MIN();
    Ask_MAX();
    return 0;
}

 

P2629 好消息，坏消息

代码：

#include<bits/stdc++.h>
using namespace std;
#define re register int
#define ll long long
#define maxn 1000009
#define maxm
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+(ll)(ch-'0');ch=getchar();}
    return x*f;
}
int sum[maxn<<1],q[maxn<<1],a[maxn<<1];
int n,m,k,ans,tot,head,tail; 
int main()
{
    n=read();
    for(int i=1;i<=n;i++)
        a[i]=read(),a[i+n]=a[i];
    for(int i=1;i<=2*n;i++)
        sum[i]=sum[i-1]+a[i];
    head=1,tail=0;
    for(int i=1;i<=n*2-1;i++)
    {
        while(head<=tail&&i-q[head]+1>n)
            head++;
        while(head<=tail&&sum[i]<=sum[q[tail]])
            tail--;
        q[++tail]=i;
        if(i>=n&&sum[q[head]]-sum[i-n]>=0)
            ans++;
    }    
    printf("%d
",ans);
    return 0;
}

 

P1714 切蛋糕

代码：

#include<bits/stdc++.h>
using namespace std;
#define re register int
#define ll long long
#define maxn 500009
#define maxm
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+(ll)(ch-'0');ch=getchar();}
    return x*f;
}
int sum[maxn],q[maxn];
int n,m,k,ans,tot,mx,head,tail; 
int main()
{
    n=read(),m=read();
    for(int i=1;i<=n;i++)
    {
        int x=read();
        sum[i]=sum[i-1]+x;
    }
    head=1,tail=0;
    for(int i=1;i<=n;i++)
    {
        while(head<=tail&&i-q[head]>m)
            head++;    
        ans=max(ans,sum[i]-sum[q[head]]);
        while(head<=tail&&sum[q[tail]]>=sum[i])
            tail--;
        q[++tail]=i;    
    }
    printf("%d
",ans);
}