Chapter 8~12.

Signed-off-by: Cyitao <[email protected]>

ch10 概率/蚂蚁习题/Ants.cpp

@@ -0,0 +1,20 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+#define Mod 1000000007
+class Ants {
+public:
+	vector<int> collision(int n) 
+	{
+		int down=pow(2.0,n),up=down-2;
+		int temp=gcd(up,down);
+		vector<int> res;
+		res.push_back(up/temp);
+		res.push_back(down/temp);
+		return res;
+	}
+	int gcd(int x,int y)
+	{
+		return (!y)?x:gcd(y,x%y);
+	}
+};

ch10 概率/足球比赛练习题/Championship.cpp

@@ -0,0 +1,31 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+#define Mod 1000000007
+class Championship {
+public:
+	vector<int> calc(int k) 
+	{
+		vector<int> res;
+		int up=1,down=1,i=2*k-1;
+		while(i>0)
+		{
+			down*=i;
+			i=i-2;
+		}
+		i=k+1;
+		while(i>2)
+		{
+			up*=i;
+			i--;
+		}
+		int Com=gcd(down-up,down);
+		res.push_back((down-up)/Com);
+		res.push_back(down/Com);
+		return res;
+	}
+	int gcd(int x, int y)
+	{
+		return (!y)?x:gcd(y,x%y);
+	}
+};

ch10 概率/随机01练习题/Random01.cpp

@@ -0,0 +1,23 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+class RandomP {
+public:
+	static int f();
+};
+
+class Random01 {
+public:
+	// ÓÃRandomP::f()ʵÏֵȸÅÂʵÄ01·µ»Ø
+	int random01() 
+	{
+		int a,b;
+		while(1)
+		{
+			a=RandomP::f();
+			b=RandomP::f();
+			if(a!=b)
+				return (a>b)?0:1;
+		}
+	}
+};

ch10 概率/随机函数练习题/Random7.cpp

@@ -0,0 +1,25 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+// 以下内容请不要修改
+class Random5 {
+public:
+	static int randomNumber();
+};
+
+class Random7 {
+public:
+	int rand5() {
+		return Random5::randomNumber();
+	}
+	// 以上内容请不要修改
+
+
+	int randomNumber() 
+	{
+		int a=5*(rand5()-1)+rand5()-1;
+		while(a>20)
+			a=5*(rand5()-1)+rand5()-1;
+		return a%7+1;
+	}  
+};

ch10 概率/随机区间函数练习题/RandomSeg.cpp

@@ -0,0 +1,20 @@
+#include<iostream>
+using namespace std;
+class RandomSeg {
+public:
+	// 等概率返回[0,1)
+	double f() {
+		return rand() * 1.0 / RAND_MAX;
+	}
+	// 通过调用f()来实现
+	double random(int k, double x) 
+	{
+		double res=-1;
+		for(int i=0;i<k;i++)
+		{
+			double b=f();
+			res=(res>b)?res:b;
+		}
+		return res;
+	}
+};

ch10 概率/随机数组打印练习题/RandomPrint.cpp

@@ -0,0 +1,17 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+class RandomPrint {
+public:
+	vector<int> print(vector<int> arr, int N, int M) 
+	{
+		vector<int> res;
+		for(int i=0;i<M;i++)
+		{
+			int pos=rand()%(N-i);
+			res.push_back(arr[pos]);
+			swap(arr[pos],arr[N-i-1]);
+		}
+		return res;
+	}
+};

ch12 动态规划/01背包练习题/Backpack.cpp

@@ -0,0 +1,36 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+class Backpack {
+public:
+	int maxValue(vector<int> w, vector<int> v, int n, int cap) 
+	{
+		int **dp=new int*[n+1];
+		for(int i=0;i<n+1;i++)
+			dp[i]=new int[cap+1];
+		for(int i=0;i<n+1;i++)
+			dp[i][0]=0;
+		for(int i=0;i<cap+1;i++)
+			dp[0][i]=0;
+		for(int i=1;i<n+1;i++)
+			for(int j=1;j<cap+1;j++)
+			{
+				int temp=dp[i-1][j];
+				if(j-w[i-1]>=0)
+					temp=max(temp,dp[i-1][j-w[i-1]]+v[i-1]);
+				dp[i][j]=temp;
+			}
+			return dp[n][cap];
+	}
+};
+
+int main()
+{
+	int a[8]={42,25,30,35,42,21,26,28};
+	int b[8]={261,247,419,133,391,456,374,591};
+	vector<int> arr(a,a+8);
+	vector<int> brr(b,b+8);
+	Backpack B;
+	cout<<B.maxValue(arr,brr,8,297);
+	return 0;
+}

ch12 动态规划/LCS练习题/LCS.cpp

@@ -0,0 +1,41 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+class LCS {
+public:
+	int findLCS(string A, int n, string B, int m) 
+	{
+		int **dp=new int*[n];
+		for(int i=0;i<n;i++)
+			dp[i]=new int[m];
+		for(int i=0,temp=0;i<n;i++)
+		{
+			if(B[0]==A[i])
+				temp=1;
+			dp[i][0]=temp;
+		}
+		for(int i=0,temp=0;i<m;i++)
+		{
+			if(A[0]==B[i])
+				temp=1;
+			dp[0][i]=temp;
+		}
+		for(int i=1;i<n;i++)
+			for(int j=1;j<m;j++)
+			{
+				int m=max(dp[i-1][j],dp[i][j-1]);
+				if(A[i]==B[j])
+					m=max(dp[i-1][j-1]+1,m);
+				dp[i][j]=m;
+			}
+			return dp[n-1][m-1];
+	}
+};
+
+int main()
+{
+	string A="1A2C3D4B56",B="B1D23CA45B6A";
+	LCS f;
+	cout<<f.findLCS(A,10,B,12);
+	return 0;
+}

ch12 动态规划/LIS练习题/LongestIncreasingSubsequence.cpp

@@ -0,0 +1,26 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+class LongestIncreasingSubsequence {
+public:
+	int getLIS(vector<int> A, int n) 
+	{
+		int *dp=new int[n],res=0;
+		dp[0]=1;
+		for(int i=1;i<A.size();i++)
+		{
+			int max=0,j=0;
+			while(j<i)
+			{
+				if(A[j]<A[i]&&dp[j]>max)
+					max=dp[j];
+				j++;
+			}
+			dp[i]=max+1;
+		}
+		for(int i=0;i<A.size();i++)
+			if(res<dp[i])
+				res=dp[i];
+		return res;
+	}
+};

ch12 动态规划/台阶问题练习题/GoUpstairs.cpp

@@ -0,0 +1,16 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+#define Mod 1000000007
+class GoUpstairs {
+public:
+	int countWays(int n) 
+	{
+		int *dp=new int[n];
+		dp[0]=1;
+		dp[1]=2;
+		for(int i=2;i<n;i++)
+			dp[i]=(dp[i-1]+dp[i-2])%Mod;
+		return dp[n-1];
+	}
+};

ch12 动态规划/找零钱练习题/Exchange.cpp

@@ -0,0 +1,113 @@
+#include<iostream>
+#include<vector>
+using namespace std;
+//动态规划
+class Exchange {
+public:
+	int countWays(vector<int> penny, int n, int aim) 
+	{
+		if(n==0||aim<0)
+			return 0;
+		int **map=new int*[n];
+		for(int i=0;i<n;i++)
+			map[i]=new int[aim+1];
+		for(int i=0;i<n;i++)
+			for(int j=0;j<aim+1;j++)
+				map[i][j]=-1;
+		for(int i=0;i<n;i++)
+			map[i][0]=1;
+		for(int i=0;i<aim+1;i++)
+			if(i%penny[0]==0)
+				map[0][i]=1;
+			else 
+				map[0][i]=0;
+		for(int i=1;i<n;i++)
+			for(int j=1;j<aim+1;j++)
+				if((j-penny[i])>=0)
+					map[i][j]=map[i][j-penny[i]]+map[i-1][j];
+				else
+					map[i][j]=map[i-1][j];
+		return map[n-1][aim];
+	}
+
+};
+
+
+/*记忆搜索
+class Exchange {
+public:
+	int countWays(vector<int> penny, int n, int aim) 
+	{
+		if(n==0||aim<0)
+			return 0;
+		int **map=new int*[n];
+		for(int i=0;i<n;i++)
+			map[i]=new int[aim+1];
+		for(int i=0;i<n;i++)
+			for(int j=0;j<aim+1;j++)
+				map[i][j]=-1;
+		return process(penny,0,aim,map);
+
+	}
+	int process(vector<int> arr,int index,int aim,int **map)
+	{
+		int res;
+		if(arr.size()-1==index)
+		{
+			if(map[index][aim]==-1)
+				map[index][aim]=(aim%arr[index])?0:1;
+			return map[index][aim];
+		}
+		else
+		{
+			res=0;
+			int k=aim/arr[index];
+			for(int i=0;i<=k;i++)
+			{
+				if(map[index+1][aim-i*arr[index]]==-1)
+					map[index+1][aim-i*arr[index]]=process(arr,index+1,aim-i*arr[index],map);
+				res+=map[index+1][aim-i*arr[index]];
+			}
+		}
+		return res;
+	}
+};*/
+
+/*暴力搜索
+class Exchange {
+public:
+	int countWays(vector<int> penny, int n, int aim) 
+	{
+		if(n==0||aim<0)
+			return 0;
+		return process(penny,0,aim);
+
+	}
+	int process(vector<int> arr,int index,int aim)
+	{
+		int res;
+		if(arr.size()-1==index)
+		{
+			res=(aim%arr[index])?0:1;
+			return res;
+		}
+		else
+		{
+			res=0;
+			int k=aim/arr[index];
+			for(int i=0;i<=k;i++)
+				res+=process(arr,index+1,aim-i*arr[index]);
+		}
+		return res;
+	}
+};*/
+
+int main()
+{
+	int a[3]={1,2,3};
+	vector<int> arr(a,a+3);
+	Exchange e;
+	cout<<e.countWays(arr,3,3);
+
+	return 0;
+}