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二维前缀和

s[i][j] = s[i-1][j] + s[i][j-1] - s[i-1][j-1] + a[i][j];

二维区间和 (x1,y1) - (x2,y2)

sum = s[x2][y2] - s[x1-1][y2] - s[x2][y1-1] + s[x1-1][y1-1];

二维差分

d[i][j]= a[i][j] -a[i-1][j] - a[i][j-1] + a[i-1][j-1];

二维差分操作

d[x1][y1] += c;
d[x1][y2+1] -= c;
d[x2+1][y1] -= c;
d[x2+1][y2+1] += c;

差分还原

a[i][j] = a[i-1][j] + a[i][j-1] - a[i-1][j-1] + d[i][j];