thanks prof. Abhiram Ranade for his vedio on Longest Common Subsequence ‘s back track search view in lecture 19, nice explanation indeed.

// back track, recursive, 390 ms, O(m*n) memory

#include <cstdio>

#include <vector>

#include <string>

#include <iostream>

#include <algorithm>

#define MAXSIZE 1001

using std::string;

char *p1, *p2;

int M, N;

int table[MAXSIZE][MAXSIZE];

int solveLCSlength(int i, int j) {

    if(table[i][j]>=0) return table[i][j];

    int k;

    for(k=j;k<N && p2[k]!=p1[i];++k) {}

    if(k!=N) table[i][j]=std::max(solveLCSlength(i+1,j),1+solveLCSlength(i+1,k+1));

    else table[i][j]=solveLCSlength(i+1,j);

    return table[i][j];

}

int LCSlength(string &s1, string &s2) {

    p1=&s1[0], p2=&s2[0], M=s1.size(), N=s2.size();

    for(int i=0;i<M;++i) {

    for(int j=0;j<N;++j) { table[i][j]=-1; }

        table[i][N]=0;

    }

    for(int j=0;j<=N;++j) { table[M][j]=0; }

    return solveLCSlength(0,0);

}

int main() {

    string s1, s2;

    while(std::cin >> s1 >> s2) {

        printf("%d\n",LCSlength(s1,s2));

    }

    return 0;

}

// turn recursive backtrack version to iterative and reduce memory cost to O(m+n) , 312ms

#include <cstdio>

#include <cstring>

#include <algorithm>

#define MAXSIZE 1001

int LCSlength(char *s1, char *s2) {

    static int table[MAXSIZE<<1];

    int len1,len2, i,j,k, *prev,*curr;

    len1=strlen(s1), len2=strlen(s2);

    prev=&table[0], curr=&table[len2+1];

    for(i=0;i<=len2;++i) prev[i]=0;

    curr[len2]=0;

    for(i=len1-1;i>=0;--i) {

            char tmp=s1[i];

        for(j=len2-1;j>=0;--j) {

            for(k=j;k<len2 && tmp!=s2[k];++k) {}

            curr[j]=prev[j];

            if(k!=len2 && curr[j]==prev[k+1]) ++curr[j];

        }

        std::swap(prev,curr);

    }

    return prev[0];

}

int main() {

    char s1[MAXSIZE], s2[MAXSIZE];

    while(scanf("%s%s",s1,s2)==2) {

        printf("%d\n",LCSlength(s1,s2));

    }

    return 0;

}

// incremental, 31ms, O(m+n) memory

#include <cstdio>

#include <algorithm>

#define MAXSIZE 1001

int main() {

    char s1[MAXSIZE], s2[MAXSIZE];

    int table[MAXSIZE<<1], *prev, *curr;

    int len1,len2, i,j;

    while(scanf("%s%s",s1,s2)==2) {

        len1=strlen(s1), len2=strlen(s2);

        prev=table, curr=&table[len2+1];

        for(i=0;i<=len2+1;++i) prev[i]=0;

        for(i=1;i<=len1;++i) {

            for(j=1;j<=len2;++j) {

                if(s1[i-1]==s2[j-1]) curr[j]=1+prev[j-1];

                else curr[j]=prev[j]>curr[j-1]?prev[j]:curr[j-1];

            }

            std::swap(curr,prev);

        }

        printf("%d\n",prev[len2]);

    }

    return 0;

}

版权声明：本文为博主原创文章，未经博主允许不得转载。// p.s. If in any way improment can be achieved, better performance or whatever, it will be well-appreciated to let me know, thanks in advance.