cf 393017C 石头剪刀布 Metacamp2022-onlineA-dev
五维的DP
g[i][D][r][s][p]
i: 到了第i个位置
D: 最后有D个点放在后面
r,s,p: 已经选择了r,s,p个石头,剪刀,布放到后面
四维的DP
f[i][D][r][s][p]
i: 到了第i个位置
D: 目前有D个点放在后面
r,s,p: 已经选择了r,s,p个石头,剪刀,布放到后面
其中D=r+s+p，从而减去一维
注意，放到后面的r,s,p，它们可以有不同的顺序，并不是按照数字编号的顺序往后放。
初始化，DP的时候，实际上不需要10^2^4，因为R+S+P=N，总执行数R*S*P*N最多是100*33*33*34。
注意边界初始化
别人题解
我的代码、数据 和 暴力造数据、获得结果
1 #include <bits/stdc++.h> 2 using namespace std; 3 #define LL long long 4 #define ULL unsigned long long 5 6 const LL mod_1=1e9+7; 7 const LL mod_2=998244353; 8 9 const double eps_1=1e-5; 10 const double eps_2=1e-10; 11 12 const int maxn=1e2+10; 13 14 int f[maxn][maxn][maxn][maxn],qa[maxn],qb[maxn],prea[3][maxn],preb[3][maxn], n; 15 char str[maxn]; 16 17 int cal(int x, int y) 18 { 19 if ((x+1)%3==y) 20 return 1; 21 return 0; 22 } 23 24 int getv(array<int,3> arr) 25 { 26 int u=arr[0]+arr[1]+arr[2], value=0, i,ii; 27 28 for (i=0;i<3;i++) 29 { 30 ii=(i+1)%3; 31 value += min(arr[i], preb[ii][n]-preb[ii][n-u]); 32 } 33 34 return value; 35 } 36 37 int main() 38 { 39 int i,j,r,s,p,u,result=0,cur_v; 40 41 scanf("%d",&n); 42 43 scanf("%s",str+1); 44 for (i=1;i<=n;i++) 45 { 46 if (str[i]=='r') 47 qa[i]=0; 48 else if (str[i]=='s') 49 qa[i]=1; 50 else 51 qa[i]=2; 52 } 53 54 scanf("%s",str+1); 55 for (i=1;i<=n;i++) 56 { 57 if (str[i]=='r') 58 qb[i]=0; 59 else if (str[i]=='s') 60 qb[i]=1; 61 else 62 qb[i]=2; 63 } 64 65 for (j=0;j<2;j++) 66 prea[j][0]=0; 67 for (i=1;i<=n;i++) 68 { 69 for (j=0;j<3;j++) 70 prea[j][i]=prea[j][i-1]; 71 prea[ qa[i] ][i]++; 72 } 73 74 for (j=0;j<2;j++) 75 preb[j][0]=0; 76 for (i=1;i<=n;i++) 77 { 78 for (j=0;j<3;j++) 79 preb[j][i]=preb[j][i-1]; 80 preb[ qb[i] ][i]++; 81 } 82 83 84 /* 85 for (i=1;i<=n;i++) 86 for (r=0;r<=prea[0][i];r++) 87 for (s=0;s<=prea[1][i];s++) 88 for (p=0;p<=prea[2][i];p++) 89 f[i][r][s][p]=-210; 90 */ 91 ///try prea[0][n]+5 -> couldn't 92 for (i=0;i<=n;i++) 93 for (r=0;r<=prea[0][n];r++) 94 for (s=0;s<=prea[1][n];s++) 95 for (p=0;p<=prea[2][n];p++) 96 f[i][r][s][p]=-1000; 97 f[0][0][0][0]=0; 98 ///max: 100*33*33*34=3,702,600 99 ///内存也可以这样减少 100 101 for (i=1;i<=n;i++) 102 for (r=0;r<=prea[0][i];r++) 103 for (s=0;s<=prea[1][i];s++) 104 for (p=0;p<=prea[2][i];p++) 105 { 106 u=r+s+p; 107 cur_v = getv({r,s,p}); 108 109 if (r<=prea[0][i-1] && s<=prea[1][i-1] && p<=prea[2][i-1]) 110 f[i][r][s][p] = f[i-1][r][s][p] + cal(qa[i],qb[i-u]); 111 112 if (r>0 && qa[i]==0) 113 f[i][r][s][p] = max(f[i][r][s][p], 114 f[i-1][r-1][s][p] + cur_v - 1 - getv({r-1,s,p}) ); 115 116 if (s>0 && qa[i]==1) 117 f[i][r][s][p] = max(f[i][r][s][p], 118 f[i-1][r][s-1][p] + cur_v - 1 - getv({r,s-1,p}) ); 119 120 if (p>0 && qa[i]==2) 121 f[i][r][s][p] = max(f[i][r][s][p], 122 f[i-1][r][s][p-1] + cur_v - 1 - getv({r,s,p-1}) ); 123 } 124 125 for (r=0;r<=prea[0][n];r++) 126 for (s=0;s<=prea[1][n];s++) 127 for (p=0;p<=prea[2][n];p++) 128 result = max(result, f[n][r][s][p]); 129 130 printf("%d\n",result); 131 132 return 0; 133 } 134 /* 135 136 6 137 pssrss 138 rrsppr 139 140 ------ 141 3 142 wrong 4 143 144 145 146 6 147 ssrpps 148 rpssps 149 150 ------ 151 2 152 wrong 3 153 154 155 156 157 158 ====== 159 160 2 161 rs 162 ps 163 164 f[1][0][0][0]=0 165 f[1][1][0][0]=0 166 167 ====== 168 169 5 170 rrrrr 171 sssss 172 173 ===== 174 175 5 176 sssss 177 rrrrr 178 179 ===== 180 181 182 10 183 rspprsprps 184 spprssrppr 185 186 187 ~~~~~~~~~ 188 189 rsppr"sp"rps 190 spprssrppr 191 192 193 194 rspprrps"sp" 195 spprssrppr 196 197 198 f[5][0][0][0]=4 199 f[6][0][1][0]=3 200 f[7][0][1][1]=4 201 f[8][0][1][1]=5 202 f[9][0][1][1]=6 203 204 205 f[9][0][1][1]=6 206 i==9 && r==0 && s==1 && p==1 207 208 209 210 ====== 211 212 213 10 214 rspprsprps 215 spprssrppr 216 217 10 218 sprrsprsrp 219 prrsppsrrs 220 221 10 222 prssprspsr 223 rssprrpssp 224 225 ====== 226 227 1 228 r 229 s 230 231 1 232 r 233 p 234 235 ====== 236 237 10 rrrrrrrrrr 238 20 rrrrrrrrrrrrrrrrrrrr 239 40 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 240 80 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 241 100 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 242 243 pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp 244 245 246 100 247 pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp 248 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 249 250 251 100 252 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 253 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr 254 255 256 ====== 257 258 259 6 260 sppsss 261 rpsrrs 262 263 ------ 264 1 265 wrong 2 266 267 268 269 6 270 pssrss 271 rrsppr 272 273 ------ 274 3 275 wrong 4 276 277 278 279 6 280 ssrpps 281 rpssps 282 283 ------ 284 2 285 wrong 3 286 287 288 289 290 6 291 rpppsp 292 rppsrs 293 294 ------ 295 2 296 wrong 3 297 298 299 300 10 301 prpprrpsps 302 ssrppprrsp 303 304 ------ 305 4 306 wrong 6 307 308 309 310 311 10 312 sppsrrppsr 313 spsrsrsprr 314 315 ------ 316 4 317 wrong 5 318 319 320 321 322 */
1 #include <bits/stdc++.h> 2 using namespace std; 3 #define LL long long 4 #define ULL unsigned long long 5 6 const LL mod_1=1e9+7; 7 const LL mod_2=998244353; 8 9 const double eps_1=1e-5; 10 const double eps_2=1e-10; 11 12 const int maxn=2e4+10; 13 14 int n=6,result=0; 15 int a[maxn],b[maxn]; 16 char ch[3]={'r','s','p'}; 17 18 bool vis[maxn]; 19 int last[maxn],a_new[maxn]; 20 21 char str[maxn]; 22 bool use_test1=0,test11=1,test12=1; 23 24 void build_data() 25 { 26 int i; 27 for (i=1;i<=n;i++) 28 { 29 a[i]=rand()%3; 30 b[i]=rand()%3; 31 } 32 33 printf("%d\n",n); 34 for (i=1;i<=n;i++) 35 printf("%c", ch[ a[i] ]); 36 printf("\n"); 37 for (i=1;i<=n;i++) 38 printf("%c", ch[ b[i] ]); 39 printf("\n"); 40 } 41 42 int cal_a_new_b(int step) 43 { 44 int i,r=0; 45 for (i=1;i<=n;i++) 46 if ((a_new[i]+1)%3==b[i]) 47 r++; 48 return r-step; 49 } 50 51 int cal(int step) 52 { 53 int i,j=0; 54 if (use_test1) 55 { 56 if (step==2 && test11 && test12) 57 printf("ok\n"); 58 } 59 60 61 for (i=1;i<=n;i++) 62 if (!vis[i]) 63 a_new[++j] = a[i]; 64 for (i=0;i<step;i++) 65 a_new[n-step+1+i] = a[ last[i] ]; 66 67 return cal_a_new_b(step); 68 } 69 70 void dfs(int step) 71 { 72 int i; 73 result = max(result, cal(step)); 74 75 for (i=1;i<=n;i++) 76 if (!vis[i]) 77 { 78 if (use_test1) 79 { 80 if (step==0) 81 { 82 if (i==5) 83 test11=1; 84 else 85 test11=0; 86 } 87 if (step==1) 88 { 89 if (i==6) 90 test12=1; 91 else 92 test12=0; 93 } 94 } 95 96 vis[i]=1; 97 last[step]=i; 98 99 dfs(step+1); 100 101 vis[i]=0; 102 } 103 } 104 105 void get_result() 106 { 107 memset(vis,0,sizeof(vis)); 108 result = 0; 109 dfs(0); 110 printf("%d\n",result); 111 } 112 113 int main() 114 { 115 srand(time(NULL)); 116 117 int i; 118 int mode=2; 119 int T=10; 120 121 if (mode==1) 122 { 123 while (T--) 124 { 125 build_data(); 126 127 printf("\n------\n"); 128 129 get_result(); 130 131 printf("\n\n======\n\n"); 132 133 } 134 } 135 else if (mode==2) 136 { 137 scanf("%d",&n); 138 139 scanf("%s",str+1); 140 for (i=1;i<=n;i++) 141 { 142 if (str[i]=='r') 143 a[i]=0; 144 else if (str[i]=='s') 145 a[i]=1; 146 else 147 a[i]=2; 148 } 149 150 scanf("%s",str+1); 151 for (i=1;i<=n;i++) 152 { 153 if (str[i]=='r') 154 b[i]=0; 155 else if (str[i]=='s') 156 b[i]=1; 157 else 158 b[i]=2; 159 } 160 161 get_result(); 162 } 163 164 return 0; 165 } 166 /* 167 3 168 rrr 169 sss 170 171 ====== 172 173 174 175 176 177 10 178 sppsrrppsr 179 spsrsrsprr 180 181 ------ 182 4 183 184 185 ====== 186 187 10 188 rssrrpspss 189 ssrrprpppr 190 191 ------ 192 6 193 194 195 ====== 196 197 10 198 rssspsspps 199 psprrrrrrs 200 201 ------ 202 5 203 204 205 ====== 206 207 10 208 rpsrssrrrp 209 srsrrppsrs 210 211 ------ 212 5 213 214 215 ====== 216 217 10 218 prpprrpsps 219 ssrppprrsp 220 221 ------ 222 4 223 224 225 ====== 226 227 10 228 rspsssssrp 229 rsrsspsrrr 230 231 ------ 232 3 233 234 235 ====== 236 237 10 238 spsspssrrs 239 pspsprsrrs 240 241 ------ 242 4 243 244 245 ====== 246 247 10 248 prpprpsrps 249 rpspsrpsrp 250 251 ------ 252 7 253 254 255 ====== 256 257 10 258 sssprrspps 259 rprssssspr 260 261 ------ 262 4 263 264 265 ====== 266 267 10 268 rrsprsrspp 269 prrsrssrrr 270 271 ------ 272 4 273 274 275 ====== 276 277 278 279 280 281 282 283 6 284 sspspp 285 prssss 286 287 ------ 288 1 289 290 291 ====== 292 293 6 294 srssrp 295 srpssr 296 297 ------ 298 3 299 300 301 ====== 302 303 6 304 rpppsp 305 rppsrs 306 307 ------ 308 2 309 310 311 ====== 312 313 6 314 rpppsp 315 rprrpr 316 317 ------ 318 4 319 320 321 ====== 322 323 6 324 ssrpps 325 rpssps 326 327 ------ 328 2 329 330 331 ====== 332 333 6 334 pssrss 335 rrsppr 336 337 ------ 338 3 339 340 341 ====== 342 343 6 344 prrsps 345 sspssp 346 347 ------ 348 2 349 350 351 ====== 352 353 6 354 ppppsr 355 sprsrp 356 357 ------ 358 2 359 360 361 ====== 362 363 6 364 sppsss 365 rpsrrs 366 367 ------ 368 1 369 370 371 ====== 372 373 6 374 pprspr 375 psrrss 376 377 ------ 378 2 379 380 381 ====== 382 383 384 385 386 387 388 389 390 */
