21牛客多校第一场
A
从小到大搜索，对于一个未知状态 若不能一步到达必败态则该状态为新的必败态
搜索跑一下打表即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define ull unsigned long long
#define db double
#define MAXN 5010
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-(b))%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define mp(a,b) make_pair(a,b)
#define pb push_back
#define fi first
#define se second
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int x[5010]={2,5,9,11,14,17,19,24,26,28,29,31,37,42,44,45,47,49,50,55,57,64,67,72,74,77,81,82,83,85,89,90,94,95,97,103,105,106,108,112,115,120,122,125,131,132,133,135,138,139,141,142,143,148,149,151,152,154,158,163,168,170,171,172,176,179,184,185,188,189,192,194,201,205,207,208,210,212,213,214,217,220,221,223,226,231,234,238,243,244,245,248,250,252,255,258,261,263,270,273,276,283,285,288,291,293,295,296,300,303,311,312,319,324,329,331,334,336,337,338,342,343,345,348,349,352,354,355,356,357,361,364,366,369,374,377,381,382,384,388,393,395,397,399,400,402,404,405,407,410,413,417,419,420,421,423,425,427,429,430,431,434,437,439,440,442,443,448,451,452,453,458,459,460,463,466,469,472,473,476,477,481,491,492,498,499,503,504,507,508,513,514,515,516,523,534,535,539,540,543,547,548,551,555,562,563,564,567,572,576,579,582,583,585,592,593,594,595,598,599,605,606,607,609,612,616,617,619,622,626,628,630,634,637,641,643,644,655,656,657,663,668,669,675,676,678,679,680,682,685,687,689,695,699,700,704,706,708,710,713,714,718,721,725,728,730,732,734,739,742,743,746,747,750,751,754,756,757,759,763,765,770,774,782,784,790,791,793,794,796,797,802,803,807,808,813,814,815,816,820,824,830,833,835,838,839,841,844,847,848,851,852,853,859,861,862,863,864,868,873,874,875,881,882,885,888,890,895,898,901,902,906,908,909,914,915,922,923,926,927,931,933,939,940,942,943,950,952,954,959,960,962,963,966,967,971,972,973,975,978,980,981,984,988,993,994,998,999,1002,1004,1005,1006,1009,1012,1015,1016,1019,1022,1025,1027,1031,1034,1035,1042,1043,1045,1048,1050,1051,1057,1058,1060,1064,1067,1068,1069,1074,1075,1078,1084,1087,1088,1089,1092,1094,1096,1100,1104,1109,1112,1113,1115,1116,1124,1125,1127,1129,1133,1134,1136,1137,1139,1140,1142,1143,1144,1147,1148,1149,1152,1153,1155,1158,1159,1161,1163,1169,1171,1173,1174,1177,1178,1182,1183,1185,1188,1196,1197,1199,1200,1204,1210,1216,1217,1221,1223,1224,1229,1233,1235,1236,1237,1238,1239,1247,1250,1251,1253,1256,1257,1258,1260,1263,1264,1267,1271,1272,1276,1278,1281,1283,1287,1289,1290,1294,1299,1300,1301,1304,1305,1309,1310,1313,1316,1319,1320,1324,1325,1327,1333,1339,1340,1342,1343,1344,1350,1351,1352,1354,1356,1357,1360,1365,1368,1369,1370,1374,1375,1380,1383,1386,1392,1396,1399,1402,1407,1410,1412,1416,1418,1422,1424,1427,1430,1434,1436,1437,1440,1441,1442,1445,1448,1453,1460,1463,1467,1472,1474,1475,1479,1480,1483,1486,1487,1489,1490,1494,1495,1497,1501,1504,1505,1507,1508,1512,1513,1518,1520,1523,1524,1531,1545,1546,1549,1550,1551,1553,1554,1555,1557,1559,1565,1566,1568,1571,1573,1574,1579,1583,1584,1586,1587,1588,1589,1594,1596,1597,1601,1603,1604,1608,1609,1610,1614,1616,1621,1624,1628,1630,1632,1635,1638,1642,1645,1646,1647,1648,1650,1655,1657,1659,1663,1667,1668,1669,1670,1672,1673,1676,1681,1686,1689,1690,1691,1697,1698,1699,1700,1701,1704,1706,1712,1715,1716,1719,1723,1724,1726,1728,1732,1734,1735,1738,1740,1741,1743,1744,1745,1748,1749,1751,1753,1760,1761,1764,1771,1776,1779,1780,1781,1784,1789,1790,1792,1794,1797,1798,1801,1804,1805,1807,1808,1810,1814,1816,1817,1818,1827,1828,1830,1834,1835,1840,1841,1844,1849,1852,1856,1857,1858,1861,1862,1865,1868,1871,1873,1875,1876,1881,1886,1890,1891,1893,1894,1896,1897,1899,1900,1903,1908,1909,1911,1913,1916,1917,1921,1925,1926,1927,1931,1932,1933,1934,1937,1938,1940,1944,1951,1952,1955,1956,1958,1959,1961,1963,1968,1969,1974,1977,1980,1983,1985,1988,1989,1991,1996,1999,2006,2009,2013,2015,2016,2020,2021,2023,2025,2028,2035,2038,2039,2044,2045,2047,2048,2053,2055,2058,2061,2062,2064,2066,2069,2072,2074,2079,2082,2083,2084,2087,2090,2091,2092,2102,2109,2110,2111,2113,2114,2118,2119,2121,2122,2124,2125,2126,2128,2131,2139,2144,2147,2150,2151,2154,2155,2157,2158,2160,2165,2167,2170,2172,2173,2178,2179,2186,2187,2189,2197,2200,2207,2208,2211,2212,2214,2219,2221,2226,2227,2228,2232,2233,2236,2241,2242,2244,2248,2249,2251,2252,2253,2258,2259,2260,2263,2265,2267,2270,2273,2274,2275,2279,2280,2285,2290,2292,2295,2300,2301,2304,2305,2306,2308,2312,2314,2316,2320,2321,2324,2326,2328,2331,2334,2340,2343,2344,2349,2352,2353,2354,2360,2361,2364,2371,2372,2373,2374,2378,2379,2380,2383,2384,2387,2392,2397,2408,2409,2413,2417,2419,2423,2425,2429,2431,2433,2434,2441,2442,2443,2446,2448,2451,2452,2457,2461,2465,2467,2472,2475,2477,2478,2479,2481,2482,2484,2487,2488,2489,2497,2498,2499,2501,2504,2507,2508,2518,2519,2520,2521,2527,2529,2532,2533,2535,2537,2540,2541,2542,2543,2544,2553,2554,2555,2559,2560,2561,2563,2566,2569,2574,2578,2579,2580,2581,2582,2584,2585,2586,2587,2590,2594,2595,2599,2602,2606,2609,2615,2618,2619,2620,2621,2625,2626,2629,2630,2636,2637,2638,2644,2649,2650,2651,2652,2654,2656,2659,2663,2664,2667,2677,2678,2679,2680,2693,2694,2696,2698,2699,2706,2711,2712,2714,2715,2717,2718,2722,2723,2725,2726,2728,2731,2732,2735,2736,2737,2740,2741,2742,2745,2753,2756,2757,2763,2765,2767,2770,2771,2775,2777,2782,2784,2787,2791,2794,2795,2797,2800,2801,2802,2808,2812,2813,2818,2820,2823,2825,2828,2829,2838,2839,2842,2845,2848,2849,2852,2853,2855,2858,2859,2860,2861,2866,2867,2871,2872,2875,2876,2878,2886,2889,2893,2895,2897,2898,2901,2904,2907,2909,2912,2914,2923,2924,2929,2930,2933,2934,2936,2940,2941,2945,2948,2950,2952,2959,2962,2963,2964,2966,2967,2968,2976,2977,2978,2983,2988,2989,2990,2991,2995,2996,2999,3000,3003,3009,3010,3011,3014,3017,3019,3023,3028,3029,3030,3034,3035,3041,3043,3045,3050,3051,3053,3055,3059,3060,3063,3066,3069,3072,3074,3076,3080,3081,3086,3087,3091,3092,3093,3094,3096,3105,3108,3112,3115,3123,3127,3132,3133,3136,3137,3140,3143,3147,3150,3152,3153,3158,3162,3165,3167,3168,3171,3174,3175,3181,3184,3187,3189,3192,3195,3199,3204,3209,3211,3212,3215,3216,3220,3221,3223,3224,3227,3228,3231,3234,3237,3239,3243,3249,3256,3257,3260,3264,3265,3268,3271,3272,3275,3277,3278,3280,3283,3285,3291,3293,3296,3301,3306,3308,3309,3310,3316,3320,3322,3329,3331,3337,3347,3348,3349,3354,3357,3361,3364,3366,3370,3371,3383,3387,3389,3390,3398,3399,3400,3402,3404,3407,3411,3415,3417,3421,3427,3428,3429,3430,3432,3435,3436,3438,3440,3443,3446,3447,3448,3452,3453,3457,3458,3462,3469,3473,3474,3477,3482,3483,3485,3486,3490,3491,3492,3494,3497,3505,3514,3515,3517,3521,3524,3527,3528,3531,3532,3540,3542,3551,3555,3557,3562,3567,3568,3574,3576,3577,3580,3582,3583,3588,3591,3594,3595,3596,3603,3607,3609,3612,3613,3616,3617,3623,3625,3631,3633,3634,3637,3642,3645,3654,3655,3661,3662,3663,3669,3675,3680,3686,3692,3717,3726,3742,3750,3753};
int y[5010]={3,7,12,15,20,22,33,32,35,58,40,38,53,52,75,60,65,70,62,68,79,87,86,92,99,101,174,118,110,113,123,116,129,127,126,136,199,146,145,166,246,161,160,164,309,182,177,198,180,156,239,190,186,203,195,340,197,232,218,229,215,286,228,224,350,298,253,236,268,259,241,256,266,281,274,264,271,322,317,278,289,327,280,315,301,332,307,372,391,325,313,306,321,305,339,565,346,359,375,521,358,370,362,379,456,367,390,386,432,415,464,411,408,501,435,702,454,545,489,449,496,446,445,558,467,461,590,577,532,479,478,494,527,520,509,505,639,553,470,485,518,474,511,487,483,588,601,531,530,568,537,586,557,541,529,525,580,560,719,624,570,549,574,603,600,683,556,614,871,651,620,772,671,596,661,666,610,761,632,760,691,660,726,635,673,646,653,649,788,648,776,716,664,658,740,893,855,752,735,723,825,800,697,711,1202,771,693,737,744,766,780,986,768,748,877,811,805,722,1599,828,866,845,810,849,842,831,822,787,818,799,785,836,778,879,886,899,827,1046,918,876,870,989,929,985,857,912,904,896,1107,869,964,920,883,946,937,948,910,957,892,996,935,969,976,1358,1010,917,924,1167,1062,1036,1007,1065,1000,982,944,1020,1013,995,1854,991,1038,1150,1017,1032,1085,1082,1061,1090,956,1029,1023,1777,1072,1081,1079,1118,1117,1110,1040,1131,1070,1098,1053,1122,1201,1165,1322,1241,1225,1120,1190,1106,1076,1145,1206,1180,1130,1055,1156,1384,1212,1102,1194,1175,1164,1192,1186,1285,1227,2018,1211,1208,1261,1231,1245,1214,1394,1269,1363,1243,1274,1307,1405,1268,1381,1219,1265,1314,1254,1311,1297,1420,1295,1390,1279,1337,1302,1248,3859,1284,1547,1348,1317,1451,1378,1329,1812,1372,1336,1461,1400,1346,1366,1361,1465,1432,1419,1477,1376,1292,1633,1389,1371,1527,1334,1387,1458,2369,1331,1695,1414,1408,1446,1543,1521,1413,1514,1492,1428,1687,1499,1457,1397,1468,1455,1443,1425,1464,1481,1606,1539,1758,1484,1510,1449,1626,1516,1575,1509,1532,1502,1537,1438,1563,1470,1403,2604,1674,1581,1541,1536,1534,1569,1529,1525,1592,1561,1612,1619,1491,2077,1577,2623,1560,1665,1611,1906,1590,1653,1636,1679,2455,1736,1625,1640,1929,1717,1617,1730,1678,1651,1643,1622,1580,1605,1820,1746,1721,2215,1799,1661,1708,1769,1713,1795,2004,1707,1694,1692,1682,1664,1882,1702,1684,1866,1845,1756,1710,1825,1765,1832,1774,2810,1767,1811,1754,2388,1787,1729,2140,1822,1785,1850,1802,1782,2840,2288,1842,1831,1888,1762,1838,1879,1884,1878,1859,2836,2036,1824,1919,1904,1863,1901,1978,1966,1914,1877,2042,1847,1772,1935,2040,2981,1837,1975,1953,1923,2051,1994,1869,2209,1949,2007,1947,2011,2230,1942,2205,1922,2031,1941,2134,2657,2026,2107,2030,1992,1964,1997,2098,1986,1970,2003,1981,2191,2088,2096,1972,3303,2059,2076,2390,2056,2421,2094,2070,2129,2033,2029,2116,3159,2067,2050,2105,2001,2256,2161,2103,2338,2180,2148,2137,2100,2080,2168,3385,2085,2195,2152,2142,2329,2281,2203,2198,2176,2184,2669,2194,2145,3560,2302,2229,2224,2954,2298,2276,2255,2239,2310,2182,2217,2193,2640,2366,2356,2174,2293,2202,2347,2271,3335,2437,2237,2222,4572,2297,2268,2261,2234,2132,2287,2246,2607,2439,2341,2368,2322,2335,2283,2376,3235,2495,2427,2490,2163,2362,2350,2318,3156,2453,2254,2345,2426,2317,2406,2538,2381,2557,2411,2385,2449,2402,2358,2393,2404,2910,2375,3252,2516,2332,2435,2420,2473,2365,3712,2400,2398,2957,2469,2415,2634,2459,2751,2523,2493,2485,2879,2720,2551,2444,3273,2613,2513,3991,2505,2395,2830,2502,2576,2773,2525,2462,2743,2572,2709,2511,2600,2515,2567,4079,2509,2564,2530,2592,2575,2708,2550,2549,2492,4030,2700,2665,2642,2597,2570,2548,2661,2789,2689,2675,2647,2632,2616,2931,2761,2953,2691,2611,2673,2986,2645,2738,2687,2546,2707,2780,2704,3078,2682,2556,2729,2684,2938,2702,2779,2671,3048,4593,2832,2627,3121,2785,2749,2668,4805,2747,2733,3037,2759,2806,2754,2902,2816,2809,2850,3254,3207,2856,2798,2956,2768,2746,2891,3138,2864,2758,2883,2804,4706,2788,2925,2921,2899,2834,2826,2778,3334,2882,3811,2881,3039,2869,2970,2862,4055,2814,2919,2792,2943,2873,3020,2843,2927,2917,3478,2846,2985,3244,2915,3067,3036,3908,2905,3024,2946,3261,3229,3015,2997,3064,2972,2960,3061,3007,2974,3119,3001,3148,3089,3026,3110,3099,2979,3433,2993,3046,3006,3338,3032,3004,3589,3097,3031,3172,3333,3057,3193,3084,3460,3163,3125,3130,3118,3425,3128,3218,3082,3117,3250,3012,3113,3202,3570,3396,3145,3763,3519,3197,3101,3423,3217,4038,3585,3289,3247,3177,3731,3213,3106,3201,3169,3314,3182,3810,3359,3190,3179,3103,3512,3258,4507,3393,3116,3341,3225,3327,3317,3302,3269,4240,3281,3232,3351,3552,3206,3413,3246,3299,3864,3598,3287,3500,3345,3286,3498,3297,3294,4154,3495,3325,3384,3941,3358,3355,3441,3381,3374,3350,3471,3368,3412,3379,3534,3323,3838,3693,3544,3488,3405,3924,3395,3391,3592,3538,3241,3510,3502,3422,3699,3536,3467,3459,3454,3377,3684,3475,3343,3312,3722,3409,3372,3466,3558,3518,3464,4125,3628,3605,3601,3525,3739,3418,3578,3508,3667,3480,3463,3621,4089,3671,3547,3449,3367,3584,3569,4619,3506,3772,3748,3720,3658,3529,4018,3614,3565,3844,3638,3640,3977,3619,4162,3665,3643,3549,4815,3600,4479,3635,3814,3852,3727,3759,3689,3651,3832,3676,3647,3898,3917,3719,3673,4052,3698,3825,3974,3709,3705,4012,3681,3890,4608,3656,3862,3714,3957,3762,3733,3704,3769,3848,3787,3743,3854,3771,3756,4075,3724,3999,3793,4745,3888,3932,3886,4550,3824,3777,3955,3882,3781,3776,3809,3737,4390,4186,3907,3767,4044,3900,3880,4011,3835,4782,3801,3995,4336,3935,3822,3916,3971,4197,4109,3927,3872,4192,4135,3923,3841,3798,4152,3948,3944,4027,4138,4199,4160,3921,4082,3896,3795,4151,3982,3966,3998,4779,4231,4121,4081,4074,3965,4363,4060,4302,4237,4017,3952,4443,4010,4037,4103,4176,4141,3914,4107,4070,4111,4051,4128,4249,4016,4097,3961,4700,4049,4330,3877,4278,4150,4057,3821,4263,4033,4140,4100,4447,4234,4219,4120,4223,4324,4449,4503,4222,4119,4173,4429,4184,4195,4146,4262,4210,4209,4026,4253,4169,4243,4272,4182,4563,4361,4543,4683,4271,4300,4395,4068,4291,4296,4247,4348,4307,4338,4261,4172,4314,4277,4343,4319,4992,4506,4495,4446,4425,4373,4375,4305,4528,4454,4471,4345,4610,4581,4290,4547,4549,4310,4356,4539,4270,4165,4526,4341,4493,4473,4546,4678,4453,4452,4442,4384,4466,4288,4511,4416,4298,4317,4663,4635,4523,4744,4519,4383,4522,4525,4650,4552,4438,4399,4914,4622,4532,4468,4372,4559,4434,4489,4579,4810,4725,4631,4897,4691,4605,4478,4398,4690,4601,4487,4712,4571,4675,4670,4599,4567,4437,4803,4595,4945,4578,4892,4856,4708,4660,4628,4733,4621,4882,4717,4674,4809,4681,4847,4836,4742,4751,4657,4763,4876,4761,4969,4722,4789,4181,4773,4850,4832,4705,4941,4644,4786,4921,4740,4768,4979,4778,4967,4928,4818,4772,4586,4839,4428,4801,4889,4652,4939,4871,4821,4765,4935,4926,4807,4845,4977,4814,4959,4907,4972,4878,4771,4865,4888,4956,4775,4948,4903,4932,5000,4732,4953};
int ans[5010][5010],tot=1359;
int main()
{
rep(i,0,tot-1) ans[x[i]][y[i]]=1,ans[y[i]][x[i]]=1;
int a,b;rep(T,1,read())
{
a=read(),b=read();
puts(ans[a][b]?"Bob":"Alice");
}
}
B
简单数学题，延长补全三角形后使用相似即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 100100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
const db eps=1e-10;
db h,r,a,b,l;
int main()
{
scanf("%lf%lf%lf%lf",&r,&a,&b,&h);
if(r*2<=b-eps) return puts("Drop"),0;
l=sqrt(h*h+(b-a)*(b-a)/4);
puts("Stuck");printf("%.8lf\n",(2*l*r-h*b)/(a-b));
}
C
线段树合并+点分治 咕
D
签到题，暴力\(check\)即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 100100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,m,ans;char s[2020][2020];
int main()
{
n=read(),m=read();rep(i,1,n) scanf("%s",s[i]+1);
rep(i,1,n) rep(j,1,n) if(s[i][j]=='0')
{
int t=j;while(s[i][t]=='0'&&t<=n) t++;
t--;
if(t-j+1>=m) ans+=(t-j+1)-m+1;
j=t;
}
printf("%d\n",ans);
}
E
大模拟 咕
F
显然每一位只能取\(1\)或\(2\)，则三位数及以上一定存在整除\(3\)的字串
\(check\)所有二位数是否满足条件即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 100100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline ll read()
{
ll x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
ll l,r,sum[110];ll ans;
int cheq(int x)
{
if(x<10) return x%3==0;
int a=x%10,b=x/10;
a%=3,b%=3;
if(a==1&&b==1) return 0;
if(a==2&&b==2) return 0;
return 1;
}
int main()
{
rep(i,1,99)
{
sum[i]=sum[i-1];
if(cheq(i)) sum[i]++;
}
rep(T,1,read())
{
l=read()-1,r=read(),ans=0;
ans+=(r>=100?r-99+sum[99]:sum[r]);
ans-=(l>=100?l-99+sum[99]:sum[l]);
printf("%lld\n",ans);
}
}
G
考虑这样一个转换，对所有数前面安排一个正负号，需要保证每一对数的符号分别为一正一负
对于\(n=2\) 答案由\(k\)奇偶性决定 单独讨论
对\(n\ge2\) 的情况，有：
交换\(k\)次和交换至多\(k\)次等价，因为总可以找到正负号相同的\(a_i,a_j\) 交换后不改变答案
考虑一对\((a_i,b_i) (a_j,b_j)\) 若交换后对答案产生贡献则说明这两个区间不相交即
产生贡献\(2[min(a_ i,b_i)-max(a_j,b_j)]\)
找到\(min\)值最大的\(k\)个与\(max\)值最小的\(k\)个作差即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 500100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,k,a[MAXN],b[MAXN];ll ans;
int main()
{
n=read(),k=read();rep(i,1,n) a[i]=read();rep(i,1,n) b[i]=read();
if(n==2)
{
if(k&1) ans=abs(a[1]-b[2])+abs(a[2]-b[1]);
else ans=abs(a[1]-b[1])+abs(a[2]-b[2]);
printf("%lld\n",ans);return 0;
}
rep(i,1,n) {if(a[i]>b[i]) swap(a[i],b[i]);ans+=b[i]-a[i];}
sort(a+1,a+n+1);sort(b+1,b+n+1);
rep(i,1,k) if(a[n-i+1]>b[i]) ans+=2LL*(a[n-i+1]-b[i]);else break;
printf("%lld\n",ans);
}
H
要求最小\(M\)使得\(\exists\ a_i,a_j\ \ \ a_i-a_j\neq 0(mod\ M)\)
即找最小\(M\)使得\(M\)的所有倍数均不为数列中两数的差
令\(F_x\)表示每一个数\(x\)在数列中的出现次数
考虑对于差\(x\)的出现次数，\(cnt_x=\sum\limits_{t=0}^{Lim-x}F_t\cdot F_{t+x}\) 其中\(Lim\)表示元素最大值
不妨令\(G\)为\(F\)的倒序，则\(cnt_x=\sum\limits_{t=0}^{Lim-x}F_t\cdot G_{Lim-t-x}\) 是一个很好的卷积形式，\(NTT\)即可
处理出\(cnt\)后暴力枚举倍数判断
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 1001001
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,a[MAXN<<1],b[MAXN<<1],fac[MAXN],ifac[MAXN];
int rev[MAXN<<1],lim,lg,pw[30],ipw[30],ans;
int q_pow(int bas,int t,int res=1)
{
for(;t;t>>=1,bas=mul(bas,bas)) if(t&1) res=mul(res,bas);return res;
}
#define inv(x) q_pow(x,MOD-2)
void ntt(int *a,int n,int f)
{
rep(i,0,n-1) if(i<rev[i]) swap(a[i],a[rev[i]]);
for(int i=1,t=1;i<n;i<<=1,++t)
{
int wn= f>0?pw[t]:ipw[t];for(int j=0;j<n;j+=i<<1)
{
int w=1,x,y;for(int k=0;k<i;++k,w=mul(w,wn))
x=a[j+k],y=mul(a[j+k+i],w),a[j+k]=pls(x,y),a[j+k+i]=mns(x,y);
}
}
if(f>0) return ;int nv=inv(n);rep(i,0,n-1) a[i]=mul(a[i],nv);
}
int main()
{
n=read();rep(i,1,n) a[read()]++;n=500000;rep(i,0,n) b[i]=a[n-i];
fac[0]=ifac[0]=1;rep(i,1,n) fac[i]=mul(fac[i-1],i),ifac[i]=inv(fac[i]);
for(lim=1,lg=1;lim<=(n+1<<1);lim<<=1,lg++)
pw[lg]=q_pow(3,(MOD-1)/(1<<lg)),ipw[lg]=inv(pw[lg]);
rep(i,1,lim-1) rev[i]=(rev[i>>1]>>1)|((i&1)<<lg-2);
ntt(a,lim,1);ntt(b,lim,1);rep(i,0,lim-1) a[i]=mul(a[i],b[i]);ntt(a,lim,-1);
rep(i,0,n) b[i]=a[n-i];int flg;
rep(i,1,n+1)
{
flg=0;
for(int j=i;j<=n;j+=i) if(b[j]) {flg=1;break;}
if(!flg) return printf("%d\n",i),0;
}
}
I
设\(f[i][j][0/1]\)表示第一个人选到\(i\)，第二个人选到\(j\)，下一轮该谁选，这一状态的剩余轮数期望
则最终答案为\(\frac{1}{n}\sum\limits_{i=1}^{n}f[0][i][0]\)
考虑朴素的转移方程：\(f[i][j][0]=1+\frac{1}{cnt[i][j][0]}\sum f[k][j][1]\) 其中\(k>i\)且\(a_k>a_j,a_k>a_i\)而\(cnt\)为这样状态的数量
由于\(a_j>a_i\)，因此在倒序\(dp\)的时候决定\(sum\)和\(cnt\)的仅有\(a_k\)与\(a_j\)的大小关系
不妨设\(i\)为倒序\(dp\)时的外层变量，则可以令\(s_j,c_j\)表示满足$a_k>a_j \(的\)f[k] [j][1]$的和与数量
而\(dp\)到\(i\)时的\(sum\)与\(cnt[i][j][0]\)恰为\(s_j,c_j\) 可以\(O(1)\)转移和更新答案
对于\(f[i][j][1]\)同理，但由于\(j\)为内层变量，只需要开两个变量记录并转移即可
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 100100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,inv[5050],p[5050],ans,g[5050],cnt[5050],sum[5050],dp[5050][5050][2];
int main()
{
n=read();rep(i,1,n) g[i]=read();int s,tot;
inv[1]=1;rep(i,2,n) inv[i]=mul(MOD-MOD/i,inv[MOD%i]);
dwn(i,n,0)
{
dwn(j,n,0) if(g[j]>g[i]) dp[i][j][0]=mul(sum[j],inv[cnt[j]])+1;
s=tot=0;
dwn(j,n,0)
if(g[i]>g[j]) dp[i][j][1]=mul(s,inv[tot])+1;
else if(i^j) s=pls(s,dp[i][j][0]),tot++;
dwn(j,n,0) if(g[i]>g[j]) sum[j]=pls(sum[j],dp[i][j][1]),cnt[j]++;
}
rep(i,1,n) ans=pls(ans,dp[0][i][0]);
printf("%d\n",mul(ans,inv[n]));
}
J
考虑用线段树维护区间的信息 只需要维护每个区间最晚的合法进入区间时间与最早的合法离开区间时间
在合并时，若左侧区间离开时间晚于右侧区间的进入时间则合并后区间不合法
对合法的情况，大区间离开时间即为右区间离开时间与左区间离开时间+右区间耗时 取\(max\)即可
事实上，只要右区间内出现等待，则从左侧更新的值就不会优于原本右侧的值 因此这个转移是正确的
进入时间的计算同理
查询\([l,r]\)的时候 在线段树上求区间\([l,r-1]\)的最早离开时间，判断是否能进入\(r\)车站
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 1001001
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n;
struct node{ll l,r,sum;}tr[MAXN<<2],g[MAXN];
node operator + (node a,node b)
{
if(a.r>b.l) return {-1,inf,0};node res;
res.l=min(a.l,b.l-a.sum);res.r=max(a.r+b.sum,b.r);
res.sum=a.sum+b.sum;
return res;
}
inline void upd(node *x,node w){*x=w,(*x).r+=w.sum;}
void build(int k,int l,int r)
{
if(l==r) {upd(&tr[k],g[l]);return ;}int mid=l+r>>1;
build(k<<1,l,mid);build(k<<1|1,mid+1,r);tr[k]=tr[k<<1]+tr[k<<1|1];
}
void mdf(int k,int l,int r,int x)
{
if(l==r) {upd(&tr[k],g[x]);return ;}int mid=l+r>>1;
x<=mid?mdf(k<<1,l,mid,x):mdf(k<<1|1,mid+1,r,x);tr[k]=tr[k<<1]+tr[k<<1|1];
}
node query(int k,int l,int r,int a,int b)
{
if(a<=l&&r<=b) return tr[k];int mid=l+r>>1;
if(a<=mid&&b>mid) return query(k<<1,l,mid,a,b)+query(k<<1|1,mid+1,r,a,b);
else if(a<=mid) return query(k<<1,l,mid,a,b);
else if(b>mid) return query(k<<1|1,mid+1,r,a,b);
}
int main()
{
int a,b,c;node t;rep(T,1,read())
{
n=read();rep(i,1,n) g[i].r=read();rep(i,1,n) g[i].l=read();
rep(i,1,n-1) g[i].sum=read();
build(1,1,n);
rep(Q,1,read())
{
c=read();
if(!c)
{
a=read(),b=read();
if(a==b) puts("Yes");
else {t=query(1,1,n,a,b-1);puts(t.r<=g[b].l?"Yes":"No");}
}
else if(c&1) {a=read(),b=read();g[a].sum=b;mdf(1,1,n,a);}
else {a=read(),g[a].r=read(),g[a].l=read();mdf(1,1,n,a);}
}
}
}
K
奇怪的题，可以按照这样一种贪心思路通过
按照位置的差从小到大插入，如果存在与\(i\)的差为\(d\)的数就把这个数放在\(i\)的位置
这样从小到大插完为止
#include<bits/stdc++.h>
#define inf 2139062143
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define MAXN 100100
#define MOD 998244353
#define Fill(a,x) memset(a,x,sizeof(a))
#define rep(i,s,t) for(int i=(s),i##end=(t);i<=i##end;++i)
#define dwn(i,s,t) for(int i=(s),i##end=(t);i>=i##end;--i)
#define ren for(int i=fst[x];i;i=nxt[i])
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,cnt[1010],ans[1010];
int main()
{
rep(T,1,read())
{
n=read();rep(i,0,n-1) cnt[i]=0,ans[i]=-1;
rep(i,1,n) cnt[read()]++;
rep(i,0,n-1)
{
rep(j,i,n-1)
if(ans[j]==-1&&cnt[j-i]) ans[j]=j-i,cnt[j-i]--;
rep(j,0,n-1-i)
if(ans[j]==-1&&cnt[j+i]) ans[j]=j+i,cnt[j+i]--;
}
rep(i,0,n-1) printf("%d%c",ans[i],i==n-1?'\n':' ');
}
}
