Codeforces Round #696 (Div. 2) 题解 (A-C)

菜死了,菜死了。
一定给出A-C,D看心情,我的心情从来没好过(其实就是太菜了难以理解→_→)。

A. Puzzle From the Future

题意

有两个数a和b(所有数位只有0和1),他们相加得到c,c去掉重复的相邻位得到d。现在a丢失了,求出a使得d最大。

题解

第一位数一定是1或2,后面的根据输入和上一位判断,保证最大且相邻位不重复即可。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define imax 0x3f3f3f3f
#define lmax 0x3f3f3f3f3f3f3f3f
int main(void)
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int _;
    cin>>_;
    while(_--){
        int n;
        char next,s;
        cin>>n;
        cin>>next;
        next++;
        cout<<1;
        for(int i=1;i<n;i++){
            cin>>s;
            if(next=='0'){
                if(s=='0') {
                    cout<<1;
                    next='1';
                    continue;
                }
                else{
                    cout<<1;
                    next='2';
                    continue;
                }
            }
            else if(next=='1'){
                if(s=='0') {
                    cout<<'0';
                    next='0';
                    continue;
                }
                else{
                    cout<<'1';
                    next='2';
                    continue;
                }
            }
            else{
                if(s=='0') {
                    cout<<1;
                    next='1';
                    continue;
                }
                else{
                    cout<<0;
                    next='1';
                    continue;
                }
            }
        }
        cout<<endl;
    }

    return 0;

}

B. Different Divisors

题意

给出一个数d,找出一个数a,使得a至少有4个因数,且每个因数之间的差大于等于d。

题解

我们可以推知,第一个一定是1,第二个因数至少是1+d,第三个至少是第一个因数+d,第四个为所求结果。
因为中间不能有其他因数,所以必须是质数,打一个质数表遍历就行了。
顺带一提,质数表打到20000会WA,我后来打到了40000。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define imax 0x3f3f3f3f
#define lmax 0x3f3f3f3f3f3f3f3f
int pri[4203]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8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3343,33347,33349,33353,33359,33377,33391,33403,33409,33413,33427,33457,33461,33469,33479,33487,33493,33503,33521,33529,33533,33547,33563,33569,33577,33581,33587,33589,33599,33601,33613,33617,33619,33623,33629,33637,33641,33647,33679,33703,33713,33721,33739,33749,33751,33757,33767,33769,33773,33791,33797,33809,33811,33827,33829,33851,33857,33863,33871,33889,33893,33911,33923,33931,33937,33941,33961,33967,33997,34019,34031,34033,34039,34057,34061,34123,34127,34129,34141,34147,34157,34159,34171,34183,34211,34213,34217,34231,34253,34259,34261,34267,34273,34283,34297,34301,34303,34313,34319,34327,34337,34351,34361,34367,34369,34381,34403,34421,34429,34439,34457,34469,34471,34483,34487,34499,34501,34511,34513,34519,34537,34543,34549,34583,34589,34591,34603,34607,34613,34631,34649,34651,34667,34673,34679,34687,34693,34703,34721,34729,34739,34747,34757,34759,34763,34781,34807,34819,34841,34843,34847,34849,34871,34877,34883,34897,34913,34919,34939,34949,34961,34963,34981,35023,35027,35051,35053,35059,35069,35081,35083,35089,35099,35107,35111,35117,35129,35141,35149,35153,35159,35171,35201,35221,35227,35251,35257,35267,35279,35281,35291,35311,35317,35323,35327,35339,35353,35363,35381,35393,35401,35407,35419,35423,35437,35447,35449,35461,35491,35507,35509,35521,35527,35531,35533,35537,35543,35569,35573,35591,35593,35597,35603,35617,35671,35677,35729,35731,35747,35753,35759,35771,35797,35801,35803,35809,35831,35837,35839,35851,35863,35869,35879,35897,35899,35911,35923,35933,35951,35963,35969,35977,35983,35993,35999,36007,36011,36013,36017,36037,36061,36067,36073,36083,36097,36107,36109,36131,36137,36151,36161,36187,36191,36209,36217,36229,36241,36251,36263,36269,36277,36293,36299,36307,36313,36319,36341,36343,36353,36373,36383,36389,36433,36451,36457,36467,36469,36473,36479,36493,36497,36523,36527,36529,36541,36551,36559,36563,36571,36583,36587,36599,36607,36629,36637,36643,36653,36671,36677,36683,36691,36697,36709,36713,36721,36739,36749,36761,36767,36779,36781,36787,36791,36793,36809,36821,36833,36847,36857,36871,36877,36887,36899,36901,36913,36919,36923,36929,36931,36943,36947,36973,36979,36997,37003,37013,37019,37021,37039,37049,37057,37061,37087,37097,37117,37123,37139,37159,37171,37181,37189,37199,37201,37217,37223,37243,37253,37273,37277,37307,37309,37313,37321,37337,37339,37357,37361,37363,37369,37379,37397,37409,37423,37441,37447,37463,37483,37489,37493,37501,37507,37511,37517,37529,37537,37547,37549,37561,37567,37571,37573,37579,37589,37591,37607,37619,37633,37643,37649,37657,37663,37691,37693,37699,37717,37747,37781,37783,37799,37811,37813,37831,37847,37853,37861,37871,37879,37889,37897,37907,37951,37957,37963,37967,37987,37991,37993,37997,38011,38039,38047,38053,38069,38083,38113,38119,38149,38153,38167,38177,38183,38189,38197,38201,38219,38231,38237,38239,38261,38273,38281,38287,38299,38303,38317,38321,38327,38329,38333,38351,38371,38377,38393,38431,38447,38449,38453,38459,38461,38501,38543,38557,38561,38567,38569,38593,38603,38609,38611,38629,38639,38651,38653,38669,38671,38677,38693,38699,38707,38711,38713,38723,38729,38737,38747,38749,38767,38783,38791,38803,38821,38833,38839,38851,38861,38867,38873,38891,38903,38917,38921,38923,38933,38953,38959,38971,38977,38993,39019,39023,39041,39043,39047,39079,39089,39097,39103,39107,39113,39119,39133,39139,39157,39161,39163,39181,39191,39199,39209,39217,39227,39229,39233,39239,39241,39251,39293,39301,39313,39317,39323,39341,39343,39359,39367,39371,39373,39383,39397,39409,39419,39439,39443,39451,39461,39499,39503,39509,39511,39521,39541,39551,39563,39569,39581,39607,39619,39623,39631,39659,39667,39671,39679,39703,39709,39719,39727,39733,39749,39761,39769,39779,39791,39799,39821,39827,39829,39839,39841,39847,39857,39863,39869,39877,39883,39887,39901,39929,39937,39953,39971,39979,39983,39989};
int main(void)
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int _;
    cin>>_;
    while(_--){
        int d;
        cin>>d;
        int num=1+d,d1=0,d2=0;;
        for(int j=0;j<4203;j++){
            if(d1==0&&pri[j]>=num){
                d1=pri[j];
            }
            //cout<<d2<<endl;
            if(d1!=0&&pri[j]>=d1+d){
                d2=pri[j];
                break;
            }
        }
        //cout<<d1<<" "<<d2<<endl;
        cout<<d1*d2<<endl;


    }

    return 0;

}

C. Array Destruction

题意

我们需要去掉一个长度为2n的数组a中的所有数。首先我们选择任意整数x,然后从a中选两个数b和c,使得b+c=x并去掉b和c,然后x=max(a,b),之后继续选择b和c……直到数组为空。

题解

我们假设b是大的数,c是较小的数。第一个b一定是数组中最大数,至于第一个c枚举即可。如果枚举所有的数还是不符合题意就no。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define imax 0x3f3f3f3f
#define lmax 0x3f3f3f3f3f3f3f3f
int main(void)
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int _;
    cin>>_;
    while(_--){
        int n,s;
        cin>>n;
        vector<int> num;
        map<int,int> m1;
        map<int,int> m2;
        for(int i=0;i<2*n;i++){
            cin>>s;
            num.push_back(s);
            m1[s]++;
        }
        sort(num.begin(),num.end());
        vector<pair<int,int>> re;
        int f=0;
        int k=2*n-1;
        int x=num[k];
        int j=0;
        int i=num[j];
        while(re.size()!=n){
            re.push_back({i,x});
            if(re.size()==n) break;
            m2[x]++;
            m2[i]++;
            m1[x]--;
            m1[i]--;
            k--;
            while(m1[num[k]]==0)k--;
            i=x-num[k];
            x=num[k];
            //for(auto it:m1) {
            //    for(int ii=0;ii<it.second;ii++) cout<<it.first<<" ";
            //}
            //cout<<endl;
            //for(auto it:m2) {
             //   for(int ii=0;ii<it.second;ii++) cout<<it.first<<" ";
            //}
            //cout<<endl;
            if(m1[i]==0||(i==x&&m1[i]<2)){
                //    cout<<"000000"<<endl;
                j++;
                i=num[j];
                re.clear();
                k=2*n-1;
                x=num[k];
                for(auto it:m2){
                    m1[it.first]+=it.second;
                }
                m2.clear();
            }
            if(j==2*n-1){
                f=1;
                break;
            }
        }
        if(f==1) cout<<"NO"<<endl;
        else{
            cout<<"YES"<<endl;
            cout<<re[0].first+re[0].second<<endl;
            for(int i=0;i<re.size();i++) cout<<re[i].first<<" "<<re[i].second<<endl;
        }
    }

    return 0;

}

题目来源于https://codeforces.com/contest/1474

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