2015
05-23

# Image Recognition

Now there is an image recognition problem for you. Now you are given an image which is a N * N matrix and there are only 0s and 1s in the matrix. And we are interested in the squares in whose four edges there is no 0s. So it’s your task to find how many such squares in the image.

The first line of the input contains an integer T (1<=T<=10) which means the number of test cases.
For each test cases, the first line is one integer N (1<=N<=1000) which is the size of the image. Then there are N lines and each line has N integers each of which is either 0 or 1.

The first line of the input contains an integer T (1<=T<=10) which means the number of test cases.
For each test cases, the first line is one integer N (1<=N<=1000) which is the size of the image. Then there are N lines and each line has N integers each of which is either 0 or 1.

1
3
1 1 0
1 1 0
0 0 0

Case 1: 5

/*
* Author:  xioumu
* Created Time:  2012/8/4 10:44:31
* File Name: 1001.CPP
* solve: 1001.CPP
*/
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<string>
#include<map>
#include<set>
#include<iostream>
#include<vector>
using namespace std;
#define sz(v) ((int)(v).size())
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repf(i, a, b) for (int i = (a); i <= (b); ++i)
#define repd(i, a, b) for (int i = (a); i >= (b); --i)
typedef long long lint;
const int maxint = -1u>>1;
const double esp = 1e-8;
const int maxn = 1007;
int a[maxn][maxn], l[maxn][maxn], r[maxn][maxn], d[maxn][maxn], u[maxn][maxn];
int ans, n, m;
void  init(){
scanf("%d", &n);
memset(l, 0, sizeof(l));
memset(r, 0, sizeof(r));
memset(d, 0, sizeof(d));
memset(u, 0, sizeof(u));
repf (i, 1, n)
repf (j, 1, n){
scanf("%d", &a[i][j]);
if(a[i][j] == 0){
l[i][j] = u[i][j] = 0;
continue;
}
l[i][j] = l[i][j - 1] + a[i][j] ;
u[i][j] = u[i - 1][j] + a[i][j];
}
repd (i, n, 1)
repd (j, n, 1){
if(a[i][j] == 0){
r[i][j] = d[i][j] = 0;
continue;
}
r[i][j] = r[i][j + 1] + a[i][j];
d[i][j] = d[i + 1][j] + a[i][j];
}

//repf(i, 1, n){
//repf(j, 1, n)
//printf("%d ", r[i][j]);
//printf("\n");
//}
}
int f[10 * maxn];
void add(int *f, int i, int value){
for(; i < 2 * n; f[i] += value, i += (i & (-i)) );
}
int getsum(int *f, int i){
int s = 0;
for(; i > 0; s += f[i], i -= (i & (-i) ));
return s;
}
void gao2(int ox, int oy){
int k = 1, c[10 * maxn];
int x = ox, y = oy;
vector< pair<int, pair<int, int> > > b;
while(x <= n && y <= n){
c[k] = k - min(u[x][y], l[x][y]) + 1;
if(a[x][y] == 1){
if(k  - 1 != 0) b.push_back( make_pair(k - 1, make_pair(k, 1) ) );
b.push_back( make_pair(k + min(r[x][y], d[x][y]) - 1, make_pair(k, 2) ) );
//printf("(%d %d %d %d)\n", a[x][y], r[x][y], d[x][y], k + min(r[x][y], d[x][y]) - 1);
}
x++, y++;
k++;
}
sort(b.begin(), b.end());
x = ox, y = oy, k = 1;
int j = 0;
memset(f, 0, sizeof(f));
while(x <= n && y <= n){
if(a[x][y] == 1) add(f, c[k] , 1);
while(j < sz(b) && b[j].first <= k){
int op = 1;
if(b[j].second.second == 1) op = -1;
ans += op * getsum(f, b[j].second.first);
//printf("(%d,%d,%d)\n", b[j].first, b[j].second.first, getsum(f, b[j].second.first));
j++;
}
x++, y++, k++;
}
while(j < sz(b)){
ans += getsum(f, b[j].second.first);
j++;
}
//printf("%d %d %d\n", ox, oy, ans);
}
void gao() {
ans = 0;
repd (i, n, 1)
gao2(i, 1);
repf (i, 2, n)
gao2(1, i);
printf("%d\n", ans);
}
int main(){
int T;
scanf("%d", &T);
repf (i, 1, T){
init();
printf("Case %d: ", i);
gao();
}
return 0;
}