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// 1-indiziert. Array t: [4*n][4*m]. Nur die _x-Varianten aufrufen.
// Laufzeit: build: O(n*m), update, sum: O(log(n)*log(m))
void build_y(int vx, int lx, int rx, int vy, int ly, int ry) {
if (ly == ry) {
if (lx == rx)vt[vx][vy] = a[lx][ly];
else t[vx][vy] = t[vx*2][vy] + t[vx*2+1][vy];
} else {
int my = (ly + ry) / 2;
build_y(vx, lx, rx, vy*2, ly, my);
build_y(vx, lx, rx, vy*2+1, my+1, ry);
t[vx][vy] = t[vx][vy*2] + t[vx][vy*2+1];
}}
void build_x(int vx = 1, int lx = 0, int rx = N-1) {
if (lx != rx) {
int mx = (lx + rx) / 2;
build_x(vx*2, lx, mx);
build_x(vx*2+1, mx+1, rx);
}
build_y(vx, lx, rx, 1, 0, m-1);
}
int sum_y(int vx, int vy, int tly, int try_, int ly, int ry) {
if (ly > ry) return 0;
if (ly == tly && try_ == ry) return t[vx][vy];
int tmy = (tly + try_) / 2;
return sum_y(vx, vy*2, tly, tmy, ly, min(ry,tmy))
+ sum_y(vx, vy*2+1, tmy+1, try_, max(ly,tmy+1), ry);
}
int sum_x(int vx=1, int tlx=0, int trx=n-1,int lx,int rx,int ly,int ry) {
if (lx > rx) return 0;
if (lx == tlx && trx == rx) return sum_y(vx, 1, 0, m-1, ly, ry);
int tmx = (tlx + trx) / 2;
return sum_x(vx*2, tlx, tmx, lx, min(rx,tmx), ly, ry)
+ sum_x(vx*2+1, tmx+1, trx, max(lx,tmx+1), rx, ly, ry);
}
void update_y(int vx, int lx, int rx, int vy, int ly, int ry,
int x, int y, int new_val) {
if (ly == ry) {
if (lx == rx) t[vx][vy] = new_val;
else t[vx][vy] = t[vx*2][vy] + t[vx*2+1][vy];
} else {
int my = (ly + ry) / 2;
if (y <= my) update_y(vx, lx, rx, vy*2, ly, my, x, y, new_val);
else update_y(vx, lx, rx, vy*2+1, my+1, ry, x, y, new_val);
t[vx][vy] = t[vx][vy*2] + t[vx][vy*2+1];
}}
void update_x(int vx=1, int lx=0, int rx=n-1, int x, int y, int new_val) {
if (lx != rx) {
int mx = (lx + rx) / 2;
if (x <= mx) update_x(vx*2, lx, mx, x, y, new_val);
else update_x(vx*2+1, mx+1, rx, x, y, new_val);
}
update_y(vx, lx, rx, 1, 0, m-1, x, y, new_val);
}
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