dp 溯源问题
三国杀有个武将叫做张梁，技能描述如下
大概描述是将方和其中一张手牌组成36点，那么这不就裸的01背包吗
可是问题是能判断出有没有还完全不行，还得学会溯源
其实溯源问题很简单，我们只需要看当前这次dp的更新有没有影响就可以了。
如果没有影响那么就是可有可无的存在，那么就是没有。
如果有影响那么就要挑出来，然后去除他，然后继续往下看。
for (int i = cnt1; i >= 1; i--)
{
if (dp[i][tot] == dp[i - 1][tot])judge[i] = false;
else
{
tot -= save[i];
judge[i] = true;
}
源码
#include<bits/stdc++.h>
using namespace std;
string Fang = "";
string now = "";
int save[1000];
int hand[1000];
int cnt1 = 0, cnt2 = 0;
int dp[40][1000];
bool judge[1000];
queue<char>ans;
bool sw = true;
bool Find(int num)
{
memset(dp, 0, sizeof(dp));
memset(judge, false, sizeof(judge));
num = 36 - num;
for (int i = 1; i <= cnt1; i++)
for (int j = num; j >= 0; j--)
if (j >= save[i])
dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - save[i]] + save[i]);
else
dp[i][j] = dp[i - 1][j];
if (dp[cnt1][num] != num)return false;
int tot = num;
for (int i = cnt1; i >= 1; i--)
{
if (dp[i][tot] == dp[i - 1][tot])judge[i] = false;
else
{
tot -= save[i];
judge[i] = true;
}
}
return true;
}
void OUT()
{
sw = false;
for (int i = 1; i <= cnt1; i++)
if (judge[i])
{
if (save[i] > 10) {
if (save[i] == 11)ans.push('J');
else if (save[i] == 12)ans.push('Q');
else if (save[i] == 13)ans.push('K');
}
else if (save[i] == 10)ans.push('*');
else ans.push(char(save[i] + '0'));
}
if (ans.front() == '*')
cout << 10;
else cout << ans.front();
ans.pop();
while (!ans.empty())
{
if (ans.front() == '*')
cout << " " << 10;
else cout << " " << ans.front();
ans.pop();
}
cout << endl;
}
int main()
{
Fang = "2k8";
now = "8kq45";
for (int i = 0; Fang[i]; i++)
{
if (Fang[i] == '1' && Fang[i + 1] == '0')save[++cnt1] = 10, i++;
else if (Fang[i] >= '0' && Fang[i] <= '9')save[++cnt1] = Fang[i] - '0';
else if (Fang[i] == 'A' || Fang[i] == 'a')save[++cnt1] = 1;
else if (Fang[i] == 'j' || Fang[i] == 'J')save[++cnt1] = 11;
else if (Fang[i] == 'q' || Fang[i] == 'Q')save[++cnt1] = 12;
else if (Fang[i] == 'k' || Fang[i] == 'K')save[++cnt1] = 13;
}
for (int i = 0; now[i]; i++)
{
if (now[i] == '1' && now[i + 1] == '0')hand[++cnt2] = 10, i++;
else if (now[i] >= '0' && now[i] <= '9')hand[++cnt2] = now[i] - '0';
else if (now[i] == 'A' || now[i] == 'a')hand[++cnt2] = 1;
else if (now[i] == 'j' || now[i] == 'J')hand[++cnt2] = 11;
else if (now[i] == 'q' || now[i] == 'Q')hand[++cnt2] = 12;
else if (now[i] == 'k' || now[i] == 'K')hand[++cnt2] = 13;
}
for (int i = 1; i <= cnt2; i++)
{
bool res = Find(hand[i]);
if (res)
{
cout << "手牌选择:";
if (hand[i] > 10) {
if (hand[i] == 11)putchar('J');
else if (hand[i] == 12)putchar('Q');
else if (hand[i] == 13)putchar('K');
}
else cout << hand[i];
cout << endl;
cout << "方的选择:";
OUT();
cout << endl;
}
}
}