2018-2019 ACM-ICPC Nordic Collegiate Programming Contest (NCPC 2018) - 4.28
赛后补了几道
赛中我就写了两个...
A - Altruistic AmphibiansGym - 101933A
看了眼榜没几个人做。就没看。
最后发现就是一个DP(但是我觉得复杂度有点迷)
题意:$n$只青蛙有参数$l,w,h$分别表示弹跳力,体重,身高,在一口深为$d$的井里
一只青蛙不能承受比他重的重量,问最多有多少只能出去(达到高度严格大于d)
重的肯定比轻的晚出去,那么轻的肯定由重的来转移,所以先排序,从重到轻的排
$dp_{i}$表示体重为i最高能叠多高 瞎jb转移一下就好了
#include <cstdio> #include <algorithm> #include <cstring> #define ll long long using namespace std;inline int read() {int x = 0, f = 1; char ch = getchar();while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); }while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); }return x * f; }const int N = 1e5 + 10; const int M = 1e8 + 10; struct P {int l, w, h;bool operator < (const P &rhs) const {return w > rhs.w;} } p[N]; int dp[M], n, d, ans;int main() {n = read(), d = read();for (int i = 1; i <= n; i++) p[i].l = read(), p[i].w = read(), p[i].h = read();ans = 0;sort(p + 1, p + n + 1);for (int i = 1; i <= n; i++) {if (dp[p[i].w] + p[i].l > d) ans++;for (int j = p[i].w + 1; j < min(p[i].w * 2, M); j++) {dp[j - p[i].w] = max(dp[j-p[i].w], dp[j] + p[i].h);} }printf("%d\n", ans);return 0; }
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B - Baby Bites Gym - 101933B
#include <cstdio> #include <cstring> using namespace std;const int N = 1010; int a[N]; int n; char s[N];int main() {scanf("%d", &n);bool ans = true;for (int i = 1; i <= n; i++) {scanf("%s", s);int len = strlen(s);if (s[0] == 'm') a[i] = i;else {int x = 0;for (int j = 0; j < len; j++) x = x * 10 + s[j] - '0';a[i] = x;if (x != i) {ans = false;}}}puts(ans?"makes sense":"something is fishy");return 0; }
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C - Code Cleanups Gym - 101933C
阅读理解题啊。自己瞎糊了一发。读不下去。就丢给队友了。
不管了。
E - Explosion Exploit Gym - 101933E
题意:分别有$n,m$个士兵,每个士兵有一个血量,有d个攻击,等概率分给每一个士兵。
问敌方士兵全死(m)的概率是多少
队友过的。学习了新知识,概率记忆化+状压
用一个long long来表示状态
unordered_map来存状态对应的概率 再回溯搜索即可 tql
#include <bits/stdc++.h> #define ll long long using namespace std;inline int read() {int x = 0, f = 1; char ch = getchar();while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); }while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); }return x * f; }unordered_map<ll, double> mp; int a[2][10];ll getsta() {ll ret = 0;for (int i = 1; i <= 6; i++) ret = ret * 10 + 1LL * a[1][i];for (int i = 1; i <= 6; i++) ret = ret * 10 + 1LL * a[0][i];return ret; }double dfs(ll sta, int d) {if (mp.count(sta)) return mp[sta];if (sta < 1000000) return 1;if (d == 0) return 0;int sum = 0;for (int i = 0; i < 2; i++) for (int j = 1; j <= 6; j++)sum += a[i][j];double ret = 0;for (int i = 0; i < 2; i++) {for (int j = 1; j <= 6; j++) {if (!a[i][j]) continue;a[i][j]--;a[i][j-1]++;ll s = getsta();double res = dfs(s, d - 1);a[i][j]++;a[i][j-1]--;mp[s] = res;ret += a[i][j] * 1.0 / sum * res;}}return ret; }int main() {int n = read(), m = read(), d = read();for (int i = 1, x; i <= n; i++) x = read(), a[0][x]++;for (int i = 1, x; i <= m; i++) x = read(), a[1][x]++;double res = dfs(getsta(), d);printf("%.8f\n", res);return 0; }
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H - House Lawn Gym - 101933H
题意:有m台机器,每台机器有名字,价格p,每分钟能工作多少c,充一次电能工作多久t,充电需要多久r
有l面积的地待作,问平均每周能工作一次的机器中价格最小的那个,相同的按输入顺序输出
队友把10080说成10800能忍?
平均一下直接就把充电需要的时间给平均进来 得到每分钟工作多少的p'
再用$l/p'$和10080比就得出答案了
可能难就难在输入部分吧。
#include <bits/stdc++.h> using namespace std;struct Node {string name;int p , c, t, r;double cc; }b[105]; bool vis[105];int main() {ios::sync_with_stdio(false);int m;int l;cin >> l >> m;string a;getline(cin,a);for(int i=1;i<=m;i++){getline(cin,a);int sta = 0;b[i].name = "";b[i].p = b[i].c = b[i].r = b[i].t = 0;for(int j=0;j<a.length();j++){if(a[j]==','){sta++;continue;}if(sta == 0){b[i].name+=a[j];}if(sta == 1){b[i].p*=10;b[i].p+=a[j]-'0'; }if(sta == 2){b[i].c*=10;b[i].c+=a[j]-'0'; }if(sta == 3){b[i].t*=10;b[i].t+=a[j]-'0'; }if(sta == 4){b[i].r*=10;b[i].r+=a[j]-'0'; }}}int ans = 1e9;for (int i = 1; i <= m; i++) {b[i].cc = (b[i].c * b[i].t) * 1.0 / (b[i].t + b[i].r);if (l / b[i].cc <= 10080) {ans = min(ans, b[i].p);vis[i] = 1;}}if (ans == (int)1e9) puts("no such mower");else {for (int i = 1; i <= m; i++) {if (vis[i] && ans == b[i].p) {cout << b[i].name << '\n';}} }return 0; }
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J - Jumbled String Gym - 101933J
题意: 0 1串 给你00出现的次数a 01出现的次数b 10出现的次数c 11出现的次数d
问能否构造出01串
WA了好几发 一度崩溃
首先由a d能推出0和1的个数 必定是一个C(n, 2) 把a和d乘二开根 和加一相乘是否等于2a和2d来判断
第二部分
用两个数组表示
$a_{i}$表示第i个0后面出现了几个1
$b_{i}$表示第i个0前面出现了几个1
必定有$a_{i} + b_{i} = cnt_{1}$ $a_{i}\geq a_{i+1}$ $b_{i}\leq b_{i+1}$
$\sum ^{cnt_{0}}_{i=1}a_{i} = b$ $\sum ^{cnt_{0}}_{i=1}b_{i} = c$
所以$b + c = cnt_{0}\times cnt_{1}$才有解
随便举几个例子发现贪心的构造均能满足答案
如样例 3 4 2 1
得到$cnt_{0} = 3$ $cnt_{1} = 2$
$a_{i}$ : 2 2 0
$b_{i}$ : 0 0 2
得到 00110 也符合
所以直接构造就完了
不过要注意
0 0 0 0直接输出0或1就可以了
a为0或d为0的情况 如果$b + c = 0$ 那么对应的0的个数或1的个数为0 否则才为1
然后瞎jb输出就完了
#include <cstdio> #include <algorithm> #include <cmath> using namespace std;inline int read() {int x = 0, f = 1; char ch = getchar();while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar();}while (ch >= '0' && ch <= '9') { x = x * 10 + ch - 48; ch = getchar(); }return x * f; }int main() {int a = read(), b = read(), c = read(), d = read();int sqra = sqrt(2 * a), sqrd = sqrt(2 * d);bool ans = true;if ((a + b + c + d) == 0) {puts("0");return 0;}if (sqra * (sqra + 1) != a * 2 || sqrd * (sqrd + 1) != d * 2) {ans = false;} else {int cnt0 = sqra, cnt1 = sqrd;cnt0++, cnt1++;if (cnt1 == 1 && (b + c) == 0) cnt1 = 0;if (cnt0 == 1 && (b + c) == 0) cnt0 = 0;//printf("%d %d\n", cnt0, cnt1);if (b + c != cnt0 * cnt1) {ans = false;} else {if (cnt1 == 0) {while (cnt0--) putchar('0');return 0;}if (cnt0 == 0) {while (cnt1--) putchar('1');return 0;}int k = b / cnt1;for (int i = cnt0; i > cnt0 - k; i--) putchar('0');cnt0 -= k;k = b - k * cnt1;if (k) {k = cnt1 - k;for (int i = cnt1; i > cnt1 - k; i--) putchar('1');cnt1 -= k;putchar('0'), cnt0--;} while (cnt1--) putchar('1');while (cnt0--) putchar('0');return 0;}}if (!ans) puts("impossible");return 0; }
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K - King's Colors Gym - 101933K
题意:一棵树n个节点,k种颜色,问有多少种方案用上k个颜色并且相邻两节点颜色不同
我以为要用树形dp做,赛后看题解才明白是个容斥。
用k种的情况是$k\times \left( k-1\right) ^{n-1}$然后其中包含了只用了k-1种 只用了k-2种...的情况
容斥一下就好了
#include <bits/stdc++.h> #define ll long long using namespace std;inline ll read() {ll x = 0, f = 1; char ch = getchar();while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); }while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); }return x * f; }const ll mod = 1e9 + 7; const int N = 2550; ll C[N][N]; void init() {for (int i = 0; i < N; i++) C[i][0] = 1, C[i][1] = i;for (int i = 1; i < N; i++)for (int j = 2; j <= i; j++)C[i][j] = (C[i-1][j-1] + C[i-1][j]) % mod; }ll qm(ll a, ll b) {ll res = 1;while (b) {if (b & 1) res = res * a % mod;a = a * a % mod;b >>= 1;}return res; }int main() {init();ll n = read(), k = read();for (int i = 1; i < n; i++) read();ll ans = 0, flag = 1;for (int i = k; i >= 1; i--) {ll temp = flag * i * qm((ll)i - 1, n - 1) % mod * C[k][i];ans = (ans + temp + mod) % mod;flag = -flag;} printf("%lld\n", ans);return 0; }
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转载于:https://www.cnblogs.com/Mrzdtz220/p/10788014.html
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