lightoj1044--Palindrome Partitioning(记忆化搜索)
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Description
A palindrome partition is the partitioning of a string such that each separate substring is a palindrome.
For example, the string "ABACABA" could be partitioned in several different ways, such as {"A","B","A","C","A","B","A"}, {"A","BACAB","A"}, {"ABA","C","ABA"}, or {"ABACABA"}, among others.
You are given a string s. Return the minimum possible number of substrings in a palindrome partition of s.
Input
Input starts with an integer T (≤ 40), denoting the number of test cases.
Each case begins with a non-empty string s of uppercase letters with length no more than 1000.
Output
For each case of input you have to print the case number and the desired result.
Sample Input
3
AAAA
ABCDEFGH
QWERTYTREWQWERT
Sample Output
Case 1: 1
Case 2: 8
Case 3: 5
题意:给你一个字符串,让你找出回文串的最少个数
思路:这是一道动态规划,将一条字符串切割成两条(或者不切割),判断两条子串符合条件的值的和的最小值
优化思路:先给字符串的回文子串打表ok[i][j],在切割的同时判断右半边是否是回文的,是则d[i]=min(d[i],1+d[i-j]),不是说明这种情况必定不是最优
递归代码:
#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <cmath>#include <stack>#include <map>using namespace std;typedef long long ll;string a;int d[1005][1005];int ok[1005][1005];int dp(int l,int r){ if(d[l][r]>=0)return d[l][r]; if(ok[l][r])return d[l][r]=1; int minn=1001; for(int i=l; i<r; i++) if(ok[l][i]) minn=min(minn,1+dp(i+1,r)); return d[l][r]=minn;}int main(){ int t,fir=1; cin>>t; while(t--) { cin>>a; memset(d,-1,sizeof(d)); memset(ok,0,sizeof(ok)); int n=a.length(); for(int i=0; i<n; i++)ok[i][i]=1; for(int i=0; i<n-1; i++)ok[i][i+1]=(a[i]==a[i+1]); for(int len=3; len<=n; len++) for(int i=0; i+len-1<n; i++) { int j=i+len-1; ok[i][j]=(a[i]==a[j])&&ok[i+1][j-1]; } printf("Case %d: %d\n",fir++,dp(0,n-1)); } return 0;}
非递归代码:
#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <cmath>#include <stack>#include <map>using namespace std;typedef long long ll;string a;int d[1005];int ok[1005][1005];int main(){ int t,fir=1; cin>>t; while(t--) { cin>>a; memset(ok,0,sizeof(ok)); int n=a.length(); for(int i=0; i<n; i++)ok[i][i]=1; for(int i=0; i<n-1; i++)ok[i][i+1]=(a[i]==a[i+1]); for(int len=3; len<=n; len++) for(int i=0; i+len-1<n; i++) { int j=i+len-1; ok[i][j]=(a[i]==a[j])&&ok[i+1][j-1]; } for(int i=0; i<n; i++) { d[i]=i+1; for(int j=0; j<=i; j++) if(ok[j][i]) { if(j==0) d[i]=1; else d[i]=min(d[i],1+d[j-1]); } } printf("Case %d: %d\n",fir++,d[n-1]); } return 0;}
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