在Dota游戲中有一種匹配玩法,任意5人以下玩家組隊,加入匹配系統,由系統組合出5人 vs 5人的組合進行游戲,比如2人+3人 vs 1人+4人。抽象出這個問題,就變成兩邊各有m個玩家,最多允許n個人組隊(n <= m),計算所有的組合方式。思路是,先考慮單邊陣營的組合,比如5人,可以1+4,2+3,1+1+1+1+1...,用遞歸的方式可以計算出所有的單邊陣營組合。將單邊陣營的組合兩兩配對,就獲取到雙邊陣營的組合。假設單邊組合有n個,那么雙邊組合就會有c(n, 2)個。但是這里面會有重復的組合,還得把重復的組合去掉。
<pre>
void TestLadderRule()
{
define OUTPUT_INFO printf("input max camp amount and max team amount(e.g. 5 5): ");
OUTPUT_INFO;
int nCampMbr = 0;
int nMaxTeamMbr = 0;
while (scanf_s("%d %d", &nCampMbr, &nMaxTeamMbr) == 2)
{
LadderRule(nCampMbr, nMaxTeamMbr);
OUTPUT_INFO;
}
}
// 參數:陣營人數,最多允許組隊人數
void LadderRule( int nCampMbr, int nMaxTeamMbr )
{
if (nCampMbr < 1)
return;
if (nMaxTeamMbr < 0 || nMaxTeamMbr > nCampMbr)
return;
// 單陣營規則
vector< vector<int> > campRules;
// 匹配規則
vector<string> matchRules;
// 已經使用過的匹配規則
set<string> usedRules;
// 用于生成單陣營規則
int *rule = new int[nCampMbr+1];
memset(rule, 0, sizeof(int)*(nCampMbr+1));
// 找出單邊陣營的所有規則
int nTeamMbr = 1;
int nSum = 0;
bool bUpAmount = false;
while (true)
{
if (!nTeamMbr)
break;
if (nTeamMbr < nMaxTeamMbr)
{
if (bUpAmount)
{
++rule[nTeamMbr];
nSum += nTeamMbr;
bUpAmount = false;
}
if (nSum > nCampMbr)
{
nSum -= rule[nTeamMbr] * nTeamMbr;
rule[nTeamMbr] = 0;
--nTeamMbr;
bUpAmount = true;
}
else
{
++nTeamMbr;
}
}
else
{
if ((nCampMbr - nSum) % nMaxTeamMbr == 0)
{
rule[nMaxTeamMbr] = (nCampMbr - nSum) / nMaxTeamMbr;
vector<int> tempRule;
for (int i = 1; i <= nCampMbr; ++i)
tempRule.push_back(rule[i]);
campRules.push_back(tempRule);
}
rule[nMaxTeamMbr] = 0;
--nTeamMbr;
bUpAmount = true;
}
}
// 將單邊陣營的規則兩兩組合,形成匹配規則
for (size_t i = 0; i < campRules.size(); ++i)
{
for (size_t j = i; j < campRules.size(); ++j)
{
// 總的規則
char chRule[1025] = { 0 };
char *chPos = chRule;
int nLength = 1024;
for (int k = 0; k < nCampMbr; ++k)
{
sprintf_s(chPos, nLength, "%2d ", campRules[i][k] + campRules[j][k]);
chPos += 3;
nLength -= 3;
}
// 剔除重復的匹配規則
if (usedRules.count(chRule))
continue;
usedRules.insert(chRule);
sprintf_s(chPos, nLength, "| ");
chPos += 2;
nLength -= 2;
// 左邊陣營規則
for (int k = 0; k < nCampMbr; ++k)
{
sprintf_s(chPos, nLength, "%2d ", campRules[i][k]);
chPos += 3;
nLength -= 3;
}
sprintf_s(chPos, nLength, "| ");
chPos += 2;
nLength -= 2;
// 右邊陣營規則
for (int k = 0; k < nCampMbr; ++k)
{
sprintf_s(chPos, nLength, "%2d ", campRules[j][k]);
chPos += 3;
nLength -= 3;
}
matchRules.push_back(chRule);
}
}
sort(matchRules.begin(), matchRules.end());
printf("match rules' amount: %d\n", matchRules.size());
for (auto it = matchRules.begin(); it != matchRules.end(); ++it)
{
printf("%s\n", it->c_str());
}
delete[] rule;
}
</pre>