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  • Weekly 10 小结

    A题

    模拟

     1 T = int(input())
     2 while T:
     3     T -= 1
     4     s = raw_input()
     5     n = len(s)
     6     res, pre = 0, 0
     7     for i in xrange(1, n):
     8         if (s[i] == s[pre]):
     9             res += 1
    10         else:
    11             pre = i
    12     print res

    B题

    模拟

     1 n, k = map(int, raw_input().split())
     2 s = raw_input()
     3 
     4 res = []
     5 ans = 0
     6 for i in xrange(n):
     7     if i >= k:
     8         ans ^= int(res[i-k])
     9     tmp = ans ^ int(s[i])
    10     res.append(tmp)
    11     ans ^= tmp
    12 print ''.join(map(str, res))

    C题

    题目大意:给出k种高度不同的积木,每种积木可以使用无数次,问使用这些积木拼成高度为N的塔的方法数对1e9 + 7的模是多少。

    另F(x)为拼接成高度为x的方法数,则F(x) = sigma(F(i)) (1 <= i <= k && high[i] <= x)

    可先处理出1~15的F函数的值,当N>15时,使用矩阵加速即可。

     1 #include <cmath>
     2 #include <cstdio>
     3 #include <vector>
     4 #include <cstring>
     5 #include <iostream>
     6 #include <algorithm>
     7 using namespace std;
     8 
     9 typedef long long LL;
    10 const int MOD = 1e9 + 7;
    11 #define rep(i, n) for (int i = (1); i <= (n); i++)
    12 LL N, K, A[20], f[20];
    13 struct Matrix {
    14     LL a[20][20];
    15     Matrix() {memset(a, 0, sizeof(a));}
    16     
    17     Matrix operator * (const Matrix &x) const {
    18         Matrix c;
    19         rep (i, 15) rep (k, 15) rep (j, 15) c.a[i][j] = (c.a[i][j] + x.a[k][j] * a[i][k]) % MOD;
    20         return c;
    21     }
    22 };
    23 
    24 Matrix pow_mod(Matrix a, LL b) {
    25     if (b < 0) return a;
    26     Matrix res; 
    27     rep (i, K) res.a[i][i] = 1;
    28     while (b > 0) {
    29         if (b & 1) res = res * a;
    30         a = a * a;
    31         b >>= 1;
    32     }
    33     return res;
    34 }
    35 
    36 
    37 int main() {
    38     ios::sync_with_stdio(false);
    39     cin >> N >> K;
    40     rep (i, K) cin >> A[i];
    41    
    42     sort(A + 1, A + K + 1);
    43     f[0] = 1;
    44     rep (i, 15) rep (j, K) if (i >= A[j]) f[i] = (f[i] + f[i - A[j]]) % MOD;
    45     rep (i, 15) cerr << f[i] << endl;
    46     if (N <= 15) {
    47         cout << f[N] * 2 % MOD << endl;
    48         return 0;
    49     }
    50     
    51     Matrix a; rep (i, 15) a.a[i][i-1] = 1;
    52     a.a[1][1] = 0; rep (i, K) a.a[1][A[i]] = 1;
    53     Matrix res = pow_mod(a, N - 15);
    54     LL ans = 0;
    55     rep (i, 15) ans = (ans + res.a[1][i] * f[16 - i]) % MOD;
    56     ans = (ans * 2) % MOD;
    57     cout << ans << endl;
    58     return 0;
    59 }

    D题

    题目大意:给出N个点,每个点有两个值V和P。要求从1开始走到N,在每个点选择有两种选择,要么将总得分加上V,要么还可以向前走P步。

    目标是使得走到N时的总得分最大。题目保证至少存在一种解。

    这题DP方程很明显,从后往前进行dp, dp[i] = min(dp[i], dp[j]), i < j <= i + P[i];

    所以对于每个点,要快速的求出dp[i]~dp[i + P[i]] 的最小值。

    直到做这个题我才知道原来BIT也可以用来求最值,原来0base和1base是这个含义。。(数组下标从0/1开始)

    原来BIT数组下标可以从0开始,貌似被称为0base邪教,如:for (int x = i; x >= 0; x -= ~x & x + 1) {}

    这里很巧妙的利用了~x = - x + 1,即~x = -(x + 1),还有运算符的优先级。摘自叉姐代码。

     1 #include <cmath>
     2 #include <cstdio>
     3 #include <vector>
     4 #include <iostream>
     5 #include <algorithm>
     6 using namespace std;
     7 
     8 #define rep(i, n) for (int i = (1); i <= (n); i++)
     9 typedef long long LL;
    10 const int MAX_N = 500050;
    11 const LL INF = (LL)1e18;
    12 int V[MAX_N], P[MAX_N]; 
    13 LL tree[MAX_N];
    14 int N;
    15 
    16 int main() {
    17     scanf("%d", &N);
    18     for (int i = 1; i <= N; i++) scanf("%d %d", V+i, P+i);
    19     
    20     fill(tree+1, tree+N+1, -INF); 
    21     LL ans = tree[N] = V[N], sum = 0;
    22     for (int i = N-1; i >= 1; i--) {
    23         ans = -INF;
    24         for (int x = min(i+P[i], N); x > 0; x -= x&-x) 
    25             ans = max(ans, tree[x]);
    26         if (ans > -INF) {
    27             for (int x = i; x <= N; x += x&-x) 
    28                 tree[x] = max(tree[x], ans - V[i]);
    29         }
    30         
    31         ans += sum;
    32         sum += V[i];
    33     }
    34     printf("%lld
    ", ans);
    35     
    36     return 0;
    37 }

    E题

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  • 原文地址:https://www.cnblogs.com/Stomach-ache/p/3977032.html
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