problem1 link
设$f[i][j][k]$表示考虑了前$i$道题，剩下时间为$j$，剩下技能为$k$的最大得分．
从小到大计算二元组$(j,k)$的话，在存储上可以省略掉$i$这一维．
problem2 link
首先，不同的提交状态有８种．预计算每一种提交状态的每一个分值的种数，设为$g[mask][score]$．对于$g[mask][score]$的计算，可以枚举$mask$包含的一个题目，设为$i$,其分值为$p_{i}$，那么第$i$道题得分如果为$x$，那么其他$mask^{‘}=mask$^$2^{i}$题目得分为$score-x$，所以$g[mask][score]=\sum_{x=1}^{p_{i}}g[mask^{‘}][score-x]$
最后从前向后考虑每个人的得分．设$f[i][score]$表示前$i$个人的得分降序排列且第$i$个人得分为$score$的方案数．设第$i+1$个人的得分为$y$,由于第$i$个人的得分一定大于$y$，所以$f[i+1][y]=\sum_{x=y+1}^{MaxScore_{i}}f[i][x]$
由于计算数组$g$和$f$都是连续求和，可以通过预处理前缀和或者后缀和来加速记算
problem3 link
code for problem1
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
class SRMCodingPhase {
public:
int countScore(vector <int> points, vector <int> skills, int luck) {
vector<vector<int>> f(76, vector<int>(luck + 1, -1));
f[75][luck] = 0;
const int b[] = {2, 4, 8};
for (int i = 0; i < 3; ++ i) {
const int point = points[i];
const int skill = skills[i];
for (int j = 0; j <= 75; ++ j) {
for (int k = 0; k <= luck; ++ k) {
if (f[j][k] == -1) {
continue;
}
for (int t = 0; t <= k && t < skill; ++ t) {
const int last_point = point - b[i] * (skill - t);
if (last_point <= 0) {
continue;
}
if (skill - t > j) {
continue;
}
f[j - (skill - t)][k - t] = max(f[j - (skill - t)][k - t], last_point + f[j][k]);
}
}
}
}
int result = 0;
for (int j = 0; j <= 75; ++ j) {
for (int k = 0; k <= luck; ++ k) {
result = max(result, f[j][k]);
}
}
return result;
}
};
code for problem2
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
using namespace std;
#define mod 1000000007
#define MAX_SCORE 200000
int g[8][MAX_SCORE + 1];
int f[20][MAX_SCORE + 1];
class SRMIntermissionPhase {
public:
int countWays(vector<int> points, vector<string> description) {
Initialize(points);
const int mask0 = GetMask(description[0]);
for (int i = 0; i <= MAX_SCORE; ++ i) {
f[0][i] = GetRangeSum(mask0, i, i);
}
CalculateSuffixSum(0);
const int person_number = (int)description.size();
for (int i = 1; i < person_number; ++ i) {
const int mask = GetMask(description[i]);
for (int j = 0; j < MAX_SCORE; ++ j) {
f[i][j] = (long long)GetRangeSum(mask, j, j) * f[i - 1][j + 1] % mod;
}
CalculateSuffixSum(i);
}
return f[person_number - 1][0];
}
private:
void CalculateSuffixSum(int idx) {
for (int i = MAX_SCORE - 1; i >= 0; -- i) {
Add(f[idx][i], f[idx][i + 1]);
}
}
void CalculatePrefixSum(int idx) {
for (int i = 1; i <= MAX_SCORE; ++ i) {
Add(g[idx][i], g[idx][i - 1]);
}
}
int GetMask(const std::string& s) {
int mask = 0;
for (int i = 0; i < 3; ++ i) {
if (s[i] == ‘Y‘) {
mask |= 1 << i;
}
}
return mask;
}
void Initialize(const vector<int>& points) {
g[0][0] = 1;
CalculatePrefixSum(0);
for (int i = 1; i < 8; ++ i) {
int low_bit = 0;
for (int j = 0; j < 3; ++ j) {
if ((i & (1 << j)) != 0) {
low_bit = j;
break;
}
}
const int other = i ^ (1 << low_bit);
const int point = points[low_bit];
for (int k = 1; k <= MAX_SCORE; ++ k) {
g[i][k] = GetRangeSum(other, k - point, k - 1);
}
CalculatePrefixSum(i);
}
}
int GetRangeSum(int mask, int left, int right) {
if (left <= 0) {
return g[mask][right];
}
int result = g[mask][right] - g[mask][left - 1];
if (result < 0) {
result += mod;
}
return result;
}
void Add(int &x, int y) {
x += y;
if (x >= mod) {
x -= mod;
}
}
};
code for problem3
