UVA 11992 - Fast Matrix Operations
给定一个r*c(r<=20,r*c<=1e6)的矩阵，其元素都是0，现在对其子矩阵进行操作。
1 x1 y1 x2 y2 val 表示将(x1,y1,x2,y2)（x1<=x2,y1<=y2）子矩阵中的所有元素add上val；
2 x1 y1 x2 y2 val 表示将(x1,y1,x2,y2)（x1<=x2,y1<=y2）子矩阵中的所有元素set为val；
3 x1 y1 x2 y2 val 表示输出(x1,y1,x2,y2)（x1<=x2,y1<=y2）子矩阵中的所有元素的sum，最大最小值max,min;
思路：线段树区间更新+lazy
每行维护一个线段树，然后，线段树维护四个值，max，min,sum，set，add。如果当前set，add都有值，那么先操作set再add,复杂度(n*log(n));
1 #include<stdio.h> 2 #include<algorithm> 3 #include<iostream> 4 #include<string.h> 5 #include<queue> 6 #include<stack> 7 #include<math.h> 8 using namespace std; 9 typedef long long LL; 10 typedef struct node 11 { 12 int addv; 13 int setv; 14 int maxx; 15 int minn; 16 int sum; 17 int l; 18 int r; 19 node() 20 { 21 addv = 0; 22 setv = 0; 23 maxx = 0; 24 sum = 0; 25 } 26 } tr; 27 tr tree[30][100005*8]; 28 tr flag[100005*8]; 29 void build(int l,int r,int k); 30 void update(int k,int id); 31 void add(int l,int r,int k,int nn,int mm,int id,int a); 32 void sett(int l,int r,int k,int nn,int mm,int id,int a); 33 int asksum(int l,int r,int k,int nn,int mm,int id); 34 int askminn(int l,int r,int k,int nn,int mm,int id); 35 int askmaxx(int l,int r,int k,int nn,int mm,int id); 36 int main(void) 37 { 38 int n,m,q; 39 while(scanf("%d %d %d",&n,&m,&q)!=EOF) 40 { memset(tree,0,sizeof(tree)); 41 memset(flag,0,sizeof(flag));build(1,m,0); 42 while(q--) 43 { 44 int val ; 45 scanf("%d",&val); 46 if(val == 1) 47 { 48 int x1,y1,x2,y2,v; 49 scanf("%d %d %d %d %d",&x1,&y1,&x2,&y2,&v); 50 int i,j; 51 for(i = x1;i <= x2;i++) 52 { 53 add(y1,y2,0,1,m,i,v); 54 } 55 } 56 else if(val == 2) 57 { 58 int x1,y1,x2,y2,v;int i,j; 59 scanf("%d %d %d %d %d",&x1,&y1,&x2,&y2,&v); 60 for(i = x1;i <= x2;i++) 61 { 62 sett(y1,y2,0,1,m,i,v); 63 } 64 } 65 else 66 { 67 int x1,y1,x2,y2;int i,j; 68 scanf("%d %d %d %d",&x1,&y1,&x2,&y2); 69 int su = 0;int ma = 0;int mi = 1e9; 70 for(i = x1;i <= x2;i++) 71 { 72 su += asksum(y1,y2,0,1,m,i); 73 ma = max(askmaxx(y1,y2,0,1,m,i),ma); 74 mi = min(mi,askminn(y1,y2,0,1,m,i)); 75 } 76 printf("%d %d %d ",su,mi,ma); 77 } 78 } 79 } 80 return 0; 81 } 82 void build(int l,int r,int k) 83 { 84 if(l == r) 85 { 86 flag[k].l = l; 87 flag[k].r = r; 88 return ; 89 } 90 else 91 { 92 flag[k].l = l; 93 flag[k].r = r; 94 build(l,(l+r)/2,2*k+1); 95 build((l+r)/2+1,r,2*k+2); 96 } 97 } 98 void update(int k,int id) 99 { 100 while(k>0) 101 { 102 k = (k-1)/2; 103 int x1 = 2*k+1; 104 int x2 = 2*k+2; 105 if(tree[id][x1].setv) 106 { //printf("1 "); 107 int xx1 = x1; 108 tree[id][2*xx1+1].setv = tree[id][x1].setv; 109 tree[id][2*xx1+2].setv = tree[id][x1].setv; 110 tree[id][2*xx1+1].addv = tree[id][x1].addv; 111 tree[id][2*xx1+2].addv = tree[id][x1].addv; 112 tree[id][x1].maxx = tree[id][x1].setv + tree[id][x1].addv; 113 tree[id][x1].minn = tree[id][x1].setv + tree[id][x1].addv; 114 tree[id][x1].sum = tree[id][x1].maxx*(flag[x1].r-flag[x1].l+1); 115 tree[id][x1].setv = 0; 116 tree[id][x1].addv = 0; 117 } 118 else if(tree[id][x1].addv) 119 { 120 int xx1 = x1; 121 tree[id][2*xx1+1].addv += tree[id][x1].addv; 122 tree[id][2*xx1+2].addv += tree[id][x1].addv; 123 tree[id][x1].maxx = tree[id][x1].maxx + tree[id][x1].addv; 124 tree[id][x1].minn = tree[id][x1].minn + tree[id][x1].addv; 125 tree[id][x1].sum += (flag[x1].r-flag[x1].l+1)*(tree[id][x1].addv); 126 tree[id][x1].setv = 0; 127 tree[id][x1].addv = 0; 128 } 129 if(tree[id][x2].setv) 130 { 131 int xx1 = x2; 132 tree[id][2*xx1+1].setv = tree[id][x2].setv; 133 tree[id][2*xx1+2].setv = tree[id][x2].setv; 134 tree[id][2*xx1+1].addv = tree[id][x2].addv; 135 tree[id][2*xx1+2].addv = tree[id][x2].addv; 136 tree[id][x2].maxx = tree[id][x2].setv + tree[id][x2].addv; 137 tree[id][x2].minn = tree[id][x2].setv + tree[id][x2].addv; 138 tree[id][x2].sum = tree[id][x2].maxx*(flag[x2].r-flag[x2].l+1); 139 tree[id][x2].setv = 0; 140 tree[id][x2].addv = 0; 141 } 142 else if(tree[id][x2].addv) 143 { //printf("%d ",1); 144 int xx1 = x2; 145 tree[id][2*xx1+1].addv += tree[id][x2].addv; 146 tree[id][2*xx1+2].addv += tree[id][x2].addv; 147 tree[id][x2].maxx = tree[id][x2].maxx + tree[id][x2].addv; 148 tree[id][x2].minn = tree[id][x2].minn + tree[id][x2].addv; 149 tree[id][x2].sum += (flag[x2].r-flag[x2].l+1)*(tree[id][x2].addv); 150 tree[id][x2].setv = 0; 151 tree[id][x2].addv = 0; 152 } 153 tree[id][k].maxx = max(tree[id][x1].maxx,tree[id][x2].maxx); 154 tree[id][k].minn = min(tree[id][x1].minn,tree[id][x2].minn); 155 tree[id][k].sum = tree[id][x1].sum+tree[id][x2].sum; 156 } 157 } 158 void add(int l,int r,int k,int nn,int mm,int id,int a) 159 { 160 if(l > mm||r < nn) 161 return ; 162 else if(l <= nn&&r >= mm) 163 { 164 tree[id][k].addv += a; 165 if(tree[id][k].setv ) 166 { 167 tree[id][2*k+1].setv = tree[id][k].setv; 168 tree[id][2*k+2].setv = tree[id][k].setv; 169 tree[id][2*k+1].addv = tree[id][k].addv; 170 tree[id][2*k+2].addv = tree[id][k].addv; 171 tree[id][k].sum = (tree[id][k].setv + tree[id][k].addv)*(mm-nn+1); 172 tree[id][k].maxx = tree[id][k].setv + tree[id][k].addv; 173 tree[id][k].minn = tree[id][k].setv + tree[id][k].addv; 174 tree[id][k].setv = 0; 175 tree[id][k].addv = 0; 176 // update(k,id); 177 } 178 else 179 { 180 tree[id][2*k+1].addv += tree[id][k].addv; 181 tree[id][2*k+2].addv += tree[id][k].addv; 182 //printf("%d ",tree[id][2*k+1].addv); 183 tree[id][k].sum += (mm-nn+1)*tree[id][k].addv; 184 tree[id][k].maxx += tree[id][k].addv; 185 tree[id][k].minn += tree[id][k].addv; 186 tree[id][k].addv = 0; 187 //printf("%d ",tree[id][k].sum); 188 } 189 update(k,id); 190 } 191 else 192 { 193 if(tree[id][k].setv) 194 { 195 tree[id][2*k+1].setv = tree[id][k].setv; 196 tree[id][2*k+2].setv = tree[id][k].setv; 197 tree[id][2*k+1].addv = tree[id][k].addv; 198 tree[id][2*k+2].addv = tree[id][k].addv; 199 tree[id][k].setv = 0; 200 tree[id][k].addv = 0; 201 } 202 else if(tree[id][k].addv) 203 { 204 tree[id][2*k+1].addv += tree[id][k].addv ; 205 tree[id][2*k+2].addv += tree[id][k].addv; 206 tree[id][k].addv = 0; 207 } 208 add(l,r,2*k+1,nn,(nn+mm)/2,id,a); 209 add(l,r,2*k+2,(nn+mm)/2+1,mm,id,a); 210 } 211 } 212 void sett(int l,int r,int k,int nn,int mm,int id,int a) 213 { 214 if(l > mm||r < nn) 215 return ; 216 else if(l <= nn&&r >= mm) 217 { 218 tree[id][k].setv = a; 219 if(tree[id][k].setv != 0) 220 { 221 tree[id][k].addv = 0; 222 tree[id][2*k+1].setv = tree[id][k].setv; 223 tree[id][2*k+2].setv = tree[id][k].setv; 224 tree[id][2*k+1].addv = tree[id][k].addv; 225 tree[id][2*k+2].addv = tree[id][k].addv; 226 tree[id][k].sum = (tree[id][k].setv + tree[id][k].addv)*(mm-nn+1); 227 tree[id][k].maxx = tree[id][k].setv + tree[id][k].addv; 228 tree[id][k].minn = tree[id][k].setv + tree[id][k].addv; 229 tree[id][k].setv = 0; 230 tree[id][k].addv = 0; 231 } 232 update(k,id); 233 } 234 else 235 { 236 if(tree[id][k].setv) 237 { 238 tree[id][2*k+1].setv = tree[id][k].setv; 239 tree[id][2*k+2].setv = tree[id][k].setv; 240 tree[id][2*k+1].addv = tree[id][k].addv; 241 tree[id][2*k+2].addv = tree[id][k].addv; 242 tree[id][k].setv = 0; 243 tree[id][k].addv = 0; 244 } 245 else if(tree[id][k].addv) 246 { 247 tree[id][2*k+1].addv += tree[id][k].addv ; 248 tree[id][2*k+2].addv += tree[id][k].addv; 249 tree[id][k].addv = 0; 250 } 251 sett(l,r,2*k+1,nn,(nn+mm)/2,id,a); 252 sett(l,r,2*k+2,(nn+mm)/2+1,mm,id,a); 253 } 254 } 255 int asksum(int l,int r,int k,int nn,int mm,int id) 256 { 257 if(l>mm||r<nn) 258 return 0; 259 else if(l <= nn&&r>=mm) 260 { //printf("%d %d ",id,k); 261 if(tree[id][k].setv ) 262 { 263 tree[id][2*k+1].setv = tree[id][k].setv; 264 tree[id][2*k+2].setv = tree[id][k].setv; 265 tree[id][2*k+1].addv = tree[id][k].addv; 266 tree[id][2*k+2].addv = tree[id][k].addv; 267 tree[id][k].sum = (tree[id][k].setv + tree[id][k].addv)*(mm-nn+1); 268 tree[id][k].maxx = tree[id][k].setv + tree[id][k].addv; 269 tree[id][k].minn = tree[id][k].setv + tree[id][k].addv; 270 tree[id][k].setv = 0; 271 tree[id][k].addv = 0; update(k,id); 272 } 273 else if(tree[id][k].addv) 274 { 275 tree[id][2*k+1].addv += tree[id][k].addv; 276 tree[id][2*k+2].addv += tree[id][k].addv; 277 tree[id][k].sum += (mm-nn+1)*tree[id][k].addv; 278 tree[id][k].maxx += tree[id][k].addv; 279 tree[id][k].minn += tree[id][k].addv; 280 tree[id][k].addv = 0; update(k,id); 281 } 282 return tree[id][k].sum; 283 } 284 else 285 { 286 if(tree[id][k].setv) 287 { 288 tree[id][2*k+1].setv = tree[id][k].setv; 289 tree[id][2*k+2].setv = tree[id][k].setv; 290 tree[id][2*k+1].addv = tree[id][k].addv; 291 tree[id][2*k+2].addv = tree[id][k].addv; 292 tree[id][k].setv = 0; 293 tree[id][k].addv = 0; 294 } 295 else if(tree[id][k].addv) 296 { 297 tree[id][2*k+1].addv += tree[id][k].addv ; 298 tree[id][2*k+2].addv += tree[id][k].addv; 299 tree[id][k].addv = 0; 300 } 301 int nx = asksum(l,r,2*k+1,nn,(nn+mm)/2,id); 302 int ny = asksum(l,r,2*k+2,(nn+mm)/2+1,mm,id); 303 return nx+ny; 304 } 305 306 } 307 int askminn(int l,int r,int k,int nn,int mm,int id) 308 { 309 if(l>mm||r<nn) 310 return 1e9; 311 else if(l <= nn&&r>=mm) 312 { 313 if(tree[id][k].setv != 0) 314 { 315 tree[id][2*k+1].setv = tree[id][k].setv; 316 tree[id][2*k+2].setv = tree[id][k].setv; 317 tree[id][2*k+1].addv = tree[id][k].addv; 318 tree[id][2*k+2].addv = tree[id][k].addv; 319 tree[id][k].sum = (tree[id][k].setv + tree[id][k].addv)*(mm-nn+1); 320 tree[id][k].maxx = tree[id][k].setv + tree[id][k].addv; 321 tree[id][k].minn = tree[id][k].setv + tree[id][k].addv; 322 tree[id][k].setv = 0; 323 tree[id][k].addv = 0; update(k,id); 324 } 325 else if(tree[id][k].addv) 326 { 327 tree[id][2*k+1].addv += tree[id][k].addv; 328 tree[id][2*k+2].addv += tree[id][k].addv; 329 tree[id][k].sum += (mm-nn+1)*tree[id][k].addv; 330 tree[id][k].maxx += tree[id][k].addv; 331 tree[id][k].minn += tree[id][k].addv; 332 tree[id][k].addv = 0; update(k,id); 333 } 334 // update(k,id); 335 return tree[id][k].minn; 336 } 337 else 338 { 339 if(tree[id][k].setv) 340 { 341 tree[id][2*k+1].setv = tree[id][k].setv; 342 tree[id][2*k+2].setv = tree[id][k].setv; 343 tree[id][2*k+1].addv = tree[id][k].addv; 344 tree[id][2*k+2].addv = tree[id][k].addv; 345 tree[id][k].setv = 0; 346 tree[id][k].addv = 0; 347 } 348 else if(tree[id][k].addv) 349 { 350 tree[id][2*k+1].addv += tree[id][k].addv ; 351 tree[id][2*k+2].addv += tree[id][k].addv; 352 tree[id][k].addv = 0; 353 } 354 int nx = askminn(l,r,2*k+1,nn,(nn+mm)/2,id); 355 int ny = askminn(l,r,2*k+2,(nn+mm)/2+1,mm,id); 356 return min(nx,ny); 357 } 358 } 359 int askmaxx(int l,int r,int k,int nn,int mm,int id) 360 { 361 if(l>mm||r<nn) 362 return 0; 363 else if(l <= nn&&r>=mm) 364 { 365 if(tree[id][k].setv != 0) 366 { 367 tree[id][2*k+1].setv = tree[id][k].setv; 368 tree[id][2*k+2].setv = tree[id][k].setv; 369 tree[id][2*k+1].addv = tree[id][k].addv; 370 tree[id][2*k+2].addv = tree[id][k].addv; 371 tree[id][k].sum = (tree[id][k].setv + tree[id][k].addv)*(mm-nn+1); 372 tree[id][k].maxx = tree[id][k].setv + tree[id][k].addv; 373 tree[id][k].minn = tree[id][k].setv + tree[id][k].addv; 374 tree[id][k].setv = 0; 375 tree[id][k].addv = 0; update(k,id); 376 } 377 else if(tree[id][k].addv) 378 { 379 tree[id][2*k+1].addv += tree[id][k].addv; 380 tree[id][2*k+2].addv += tree[id][k].addv; 381 tree[id][k].sum += (mm-nn+1)*tree[id][k].addv; 382 tree[id][k].maxx += tree[id][k].addv; 383 tree[id][k].minn += tree[id][k].addv; 384 tree[id][k].addv = 0; update(k,id); 385 } 386 //update(k,id); 387 return tree[id][k].maxx; 388 } 389 else 390 { 391 if(tree[id][k].setv) 392 { 393 tree[id][2*k+1].setv = tree[id][k].setv; 394 tree[id][2*k+2].setv = tree[id][k].setv; 395 tree[id][2*k+1].addv = tree[id][k].addv; 396 tree[id][2*k+2].addv = tree[id][k].addv; 397 tree[id][k].setv = 0; 398 tree[id][k].addv = 0; 399 } 400 else if(tree[id][k].addv) 401 { 402 tree[id][2*k+1].addv += tree[id][k].addv ; 403 tree[id][2*k+2].addv += tree[id][k].addv; 404 tree[id][k].addv = 0; 405 } 406 int nx = askmaxx(l,r,2*k+1,nn,(nn+mm)/2,id); 407 int ny = askmaxx(l,r,2*k+2,(nn+mm)/2+1,mm,id); 408 return max(nx,ny); 409 } 410 }