[poj]2789:计算图像方差

如果按照公式直接计算，会超时

这里有2个技巧：1、利用积分图像 2、方差的公式变换 s^2=1/n[(x1^2+x2^2+...+xn^2)-nx']

代码如下，但是不知道为什么总是WA，实在是找不到问题所在

 

#include<stdio.h>
#include<string.h>
#include<vector>
#include<algorithm>
#include<math.h>

using namespace std;

double calVar(vector<vector<int> >& image,vector<vector<int> >& interalMap,vector<vector<int> >& squareInteralMap,int x,int y,int p,int N)
{
	int xbegin=max(1,x-p),xend=min(N,x+p);
	int ybegin=max(1,y-p),yend=min(N,y+p);
	int nums=(xend-xbegin+1)*(yend-ybegin+1);

	double avg=(interalMap[xend][yend]-interalMap[xbegin-1][yend]-interalMap[xend][ybegin-1]+interalMap[xbegin-1][ybegin-1])*1.0/nums;
	double squareavg=(squareInteralMap[xend][yend]-squareInteralMap[xbegin-1][yend]-squareInteralMap[xend][ybegin-1]+squareInteralMap[xbegin-1][ybegin-1])*1.0/nums;
	double var=0.0;

	var=squareavg-avg*avg;

	return var;
}

int main()
{
	int n;
	scanf("%d",&n);
	vector<vector<int> > image(n+1,vector<int>(n+1));
	vector<vector<int> > interalMap(n+1,vector<int>(n+1,0));
	vector<vector<int> > squareInteralMap(n+1,vector<int>(n+1,0));
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			scanf("%d",&image[i][j]);

	interalMap[1][1]=image[1][1];
	for(int i=2;i<=n;i++)
	{
		interalMap[1][i]=interalMap[1][i-1]+image[1][i];
		interalMap[i][1]=interalMap[i-1][1]+image[i][1];
	}
	for(int i=2;i<=n;i++)
		for(int j=2;j<=n;j++)
			interalMap[i][j]=interalMap[i-1][j]+interalMap[i][j-1]-interalMap[i-1][j-1]+image[i][j];

	squareInteralMap[1][1]=image[1][1]*image[1][1];
	for(int i=2;i<=n;i++)
	{
		squareInteralMap[1][i]=squareInteralMap[1][i-1]+image[1][i]*image[1][i];
		squareInteralMap[i][1]=squareInteralMap[i-1][1]+image[i][1]*image[i][1];
	}
	for(int i=2;i<=n;i++)
		for(int j=2;j<=n;j++)
			squareInteralMap[i][j]=squareInteralMap[i-1][j]+squareInteralMap[i][j-1]-squareInteralMap[i-1][j-1]+image[i][j]*image[i][j];
	
	int p;
	while(scanf("%d",&p)&&p)
	{
		double var=0.0;

		for(int i=1;i<=n;i++)
			for(int j=1;j<=n;j++)
				var+=calVar(image,interalMap,squareInteralMap,i,j,p,n);
		
		printf("%d\n",(int)floor(var));
	}
	return 0;
}