差分&前缀和

前缀和;

一维的话，就没什么说的了，

我们来看一下二维：

好了，那我们可以来整题了；

 领地选择 - 洛谷

#include<bits/stdc++.h>
using namespace std;

const int N = 1010;
typedef long long LL; 
int n,m,c;

int a[N][N];

LL s[N][N];
int main()
{
	
	cin>>n>>m>>c;
	for(int i =1 ;i <= n;i ++)
		for(int j =1 ;j <=m ;j ++)
			cin>>a[i][j];
	
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
			s[i][j] = s[i-1][j] + s[i][j-1]- s[i-1][j-1] + a[i][j];
	
	LL res = -1e8;
	int x,y;
	for(int i =1 ;i <= n -c + 1 ;i ++)
		for(int j = 1 ;j <= m -c + 1 ;j ++)
		{
			int x1,y1,x2,y2;
			x1= i;
			y1 = j;
			x2 = i + c -1;
			y2 = j + c -1;
			
			LL mx = s[x2][y2]- s[x1-1][y2] - s[x2][y1-1] + s[x1-1][y1-1];
			if(mx > res)
			{
				res = mx;
				x = i,y = j;
			}
		}
	cout<<x<<" "<<y<<endl; 
	return 0;
}

差分;

我们在来整个差分的题吧;

海底高铁 - 洛谷

#include<bits/stdc++.h>
using namespace std;

const int N  = 100010;
typedef long long LL;


LL n,m;
queue<int> p;

LL a[N],b[N],c[N];

LL s[N];
LL res;
int main()
{
	scanf("%d%d",&n,&m);
	
	for(int i =1;i <= m;i ++)
	{
		int c;
		scanf("%d",&c);
		p.push(c);
	} 
	
	for(int i =1;i <= n - 1 ;i ++)	scanf("%d%d%d",&a[i],&b[i],&c[i]);
		
	int st,ed;
	st = p.front(),p.pop();
	while(!p.empty())
	{
		ed = p.front(), p.pop();
		
		if(st > ed)
		{
			s[ed] ++;
			s[st] --;	
		} 
		else 
		{
			s[st] ++;
			s[ed] --;
		}
		st = ed;
	}
	
	for(int i =1 ;i <= n - 1 ;i ++) s[i] += s[i - 1];
	
	
	for(int i =1 ;i <= n-1 ; i ++)
	{
		if(s[i] * a[i] > s[i]* b[i] + c[i]) res += s[i]* b[i] + c[i];
		else res += s[i] * a[i];
	}
	
	printf("%lld\n",res);
	return 0;
} 

 收工吧；