C++前缀和算法：生成数组原理、源码及测试用例

emplate
class C1097Int
{
public:
C1097Int(long long llData = 0) :m_iData(llData% MOD)
{
}
C1097Int operator+(const C1097Int& o)const
{
return C1097Int(((long long)m_iData + o.m_iData) % MOD);
}
C1097Int& operator+=(const C1097Int& o)
{
m_iData = ((long long)m_iData + o.m_iData) % MOD;
return this;
}
C1097Int& operator-=(const C1097Int& o)
{
m_iData = (m_iData + MOD - o.m_iData) % MOD;
return this;
}
C1097Int operator-(const C1097Int& o)
{
return C1097Int((m_iData + MOD - o.m_iData) % MOD);
}
C1097Int operator(const C1097Int& o)const
{
return((long long)m_iData * o.m_iData) % MOD;
}
C1097Int& operator=(const C1097Int& o)
{
m_iData = ((long long)m_iData * o.m_iData) % MOD;
return *this;
}
bool operator<(const C1097Int& o)const
{
return m_iData < o.m_iData;
}
C1097Int pow(long long n)const
{
C1097Int iRet = 1, iCur = *this;
while (n)
{
if (n & 1)
{
iRet *= iCur;
}
iCur *= iCur;
n >>= 1;
}
return iRet;
}
C1097Int PowNegative1()const
{
return pow(MOD - 2);
}
int ToInt()const
{
return m_iData;
}
private:
int m_iData = 0;;
};
template
int operator+(int iData, const C1097Int& int1097)
{
int iRet = int1097.operator+(C1097Int(iData)).ToInt();
return iRet;
}
template
int& operator+=(int& iData, const C1097Int& int1097)
{
iData = int1097.operator+(C1097Int(iData)).ToInt();
return iData;
}
template
int operator*(int iData, const C1097Int& int1097)
{
int iRet = int1097.operator*(C1097Int<>(iData)).ToInt();
return iRet;
}
template
int& operator*=(int& iData, const C1097Int& int1097)
{
iData = int1097.operator*(C1097Int<>(iData)).ToInt();
return iData;
}
class Solution {
public:
int numOfArrays(int n, int m, int k) {
vector<vector<C1097Int<>>> pre(k + 1, vector<C1097Int<>>(m+1));//pre[k][j]表示res[0,i)的 最大值为j且search_cost 为k的数量
pre[0][0] = 1;
for (int i = 0; i < n; i++)
{
vector<vector<C1097Int<>>> dp(k + 1, vector<C1097Int<>>(m + 1));
for (int preMax = 0; preMax <= m; preMax++)
{
for (int preK = 0; preK <= k; preK++)
{
for (int cur = 1; cur <= m; cur++)
{
const int iNewK = (cur <= preMax) ? preK : preK + 1;
if (iNewK > k)
{
continue;
}
dp[iNewK][max(cur, preMax)] += pre[preK][preMax];
}
}
}
pre.swap(dp);
}
auto bi = std::accumulate(pre[k].begin(), pre[k].end(), C1097Int<>());
return bi.ToInt();
}
};

template
void Assert(const vector& v1, const vector& v2)
{
if (v1.size() != v2.size())
{
assert(false);
return;
}
for (int i = 0; i < v1.size(); i++)
{
assert(v1[i] == v2[i]);
}
}
template
void Assert(const T& t1, const T& t2)
{
assert(t1 == t2);
}
int main()
{
int res = Solution().numOfArrays(2,3,1);
Assert(6, res);
res = Solution().numOfArrays(20, 30, 5);
Assert(266034711, res);
res = Solution().numOfArrays(30, 20, 4);
Assert(835697098, res);
//CConsole::Out(res);
}

class Solution {
public:
int numOfArrays(int n, int m, int k) {
vector<vector<C1097Int<>>> pre(k + 1, vector<C1097Int<>>(m+1));//pre[k][j]表示res[0,i)的 最大值为j且search_cost 为k的数量
pre[0][0] = 1;
for (int i = 0; i < n; i++)
{
vector<vector<C1097Int<>>> dp(k + 1, vector<C1097Int<>>(m + 1));
for (int curK = 1; curK <= k; curK++)
{
C1097Int<> bi = 0;
for (int curMax = 1; curMax <= m; curMax++)
{
//preMax < curMax
bi += pre[curK-1][curMax - 1];
dp[curK][curMax] = bi;
//
dp[curK][curMax] += pre[curK][curMax] * (curMax);
}
}
pre.swap(dp);
}
auto bi = std::accumulate(pre[k].begin(), pre[k].end(), C1097Int<>());
return bi.ToInt();
}
};