[hdu3486]rmq+枚举优化

题意：给n个数，求最小的段数，使得每一段的最大值之和大于给定的k。每一段的长度相等，最后若干个丢掉。

思路：从小到大枚举段数，如果能o(1)时间求出每一段的和，那么总复杂度是O(n(1+1/2+1/3+...+1/n))=O(nlogn)的。但题目时限卡得比较紧，需加一点小优化，如果连续两个段数它们每一段的个数一样，那么这次只比上次需要多计算一个区间，用上一次的加上这个区间最大值得到当前分段的总和，这样能减少不少运算量。详见代码：

  1 #pragma comment(linker, "/STACK:10240000,10240000")

  2 

  3 #include <iostream>

  4 #include <cstdio>

  5 #include <algorithm>

  6 #include <cstdlib>

  7 #include <cstring>

  8 #include <map>

  9 #include <queue>

 10 #include <deque>

 11 #include <cmath>

 12 #include <vector>

 13 #include <ctime>

 14 #include <cctype>

 15 #include <set>

 16 #include <bitset>

 17 #include <functional>

 18 #include <numeric>

 19 #include <stdexcept>

 20 #include <utility>

 21 

 22 using namespace std;

 23 

 24 #define mem0(a) memset(a, 0, sizeof(a))

 25 #define lson l, m, rt << 1

 26 #define rson m + 1, r, rt << 1 | 1

 27 #define define_m int m = (l + r) >> 1

 28 #define rep_up0(a, b) for (int a = 0; a < (b); a++)

 29 #define rep_up1(a, b) for (int a = 1; a <= (b); a++)

 30 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--)

 31 #define rep_down1(a, b) for (int a = b; a > 0; a--)

 32 #define all(a) (a).begin(), (a).end()

 33 #define lowbit(x) ((x) & (-(x)))

 34 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {}

 35 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}

 36 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}

 37 #define pchr(a) putchar(a)

 38 #define pstr(a) printf("%s", a)

 39 #define sstr(a) scanf("%s", a);

 40 #define sint(a) ReadInt(a)

 41 #define sint2(a, b) ReadInt(a);ReadInt(b)

 42 #define sint3(a, b, c) ReadInt(a);ReadInt(b);ReadInt(c)

 43 #define pint(a) WriteInt(a)

 44 #define if_else(a, b, c) if (a) { b; } else { c; }

 45 #define if_than(a, b) if (a) { b; }

 46 #define test_print1(a) cout << "var1 = " << a << endl

 47 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl

 48 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = b" << ", var3 = " << c << endl

 49 

 50 typedef double db;

 51 typedef long long LL;

 52 typedef pair<int, int> pii;

 53 typedef multiset<int> msi;

 54 typedef set<int> si;

 55 typedef vector<int> vi;

 56 typedef map<int, int> mii;

 57 

 58 const int dx[8] = {0, 0, -1, 1};

 59 const int dy[8] = {-1, 1, 0, 0};

 60 const int maxn = 4e5 + 7;

 61 const int maxm = 1e3 + 7;

 62 const int maxv = 1e7 + 7;

 63 const int max_val = 1e6 + 7;

 64 const int MD = 22;

 65 const int INF = 1e9 + 7;

 66 const double pi = acos(-1.0);

 67 const double eps = 1e-10;

 68 

 69 template<class T>T gcd(T a, T b){return b==0?a:gcd(b,a%b);}

 70 template<class T>void ReadInt(T &x){char c=getchar();while(!isdigit(c))c=getchar();x=0;while(isdigit(c)){x=x*10+c-'0';c=getchar();}}

 71 template<class T>void WriteInt(T i) {int p=0;static int b[20];if(i == 0) b[p++] = 0;else while(i){b[p++]=i%10;i/=10;}for(int j=p-1;j>=0;j--)pchr('0'+b[j]);}

 72 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;}

 73 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;}

 74 template<class T>T condition(bool f, T a, T b){return f?a:b;}

 75 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];}

 76 int make_id(int x, int y, int n) { return x * n + y; }

 77 

 78 int f[maxn][20], t[maxn], a[maxn], sum[maxn];

 79 int n;

 80 void RMQ_Init() {

 81     rep_up0(i, n) f[i][0] = a[i];

 82     rep_up1(j, 18) {

 83         for (int i = 0; i + (1 << j) - 1 < n; i++) {

 84             f[i][j] = max(f[i][j - 1], f[i + (1 << (j - 1))][j - 1]);

 85         }

 86     }

 87 }

 88 int RMQ(int L, int R) {

 89     int p = t[R - L + 1];

 90     return max(f[L][p], f[R - (1 << p) + 1][p]);

 91 }

 92 LL getSum(int t, int x) {

 93     LL sum = 0;

 94     rep_up0(i, t) {

 95         sum += RMQ(i * x, i * x + x - 1);

 96     }

 97     return sum;

 98 }

 99 int main() {

100     //freopen("in.txt", "r", stdin);

101     //freopen("out.txt", "w", stdout);

102     int k;

103     rep_up1(i, 18) {

104         for (int j = (1 << (i - 1)) + 1; j <= (1 << i); j++) t[j] = i - 1;

105     }

106     while (cin >> n >> k, n >= 0 || k >= 0) {

107         rep_up0(i, n) {

108             sint(a[i]);

109             if (i) sum[i] = sum[i - 1] + a[i];

110             else sum[i] = a[i];

111         }

112         int ans = -1, last_sum = 0;

113         RMQ_Init();

114         for (int i = 1; i <= n; i++) {

115             int x = n / i;

116             LL sum = 0;

117             if (i > 1 && n / (i - 1) == x) sum = last_sum + RMQ(x * (i - 1), x * i - 1);

118             else sum = getSum(i, x);

119             if (sum > k) {

120                 ans = i;

121                 break;

122             }

123             last_sum = sum;

124         }

125         cout << ans << endl;

126     }

127     return 0;

128 }

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