搞了一天,代码还未AC过题,自己打的测试数据过了。。
算法:
1. 倍增算法求sa,rank数组,时间复杂度O(nlgn).
2. O(n)时间复杂度求height数组。。
3. RMQ,预处理,时间复杂度O(nlgn)
4.每次查询时间复杂度O(1)
代码:
#include<stdio.h> #include<stdlib.h> #include<string.h> #include<iostream> #include<vector> #include<string> #include<math.h> #include<map> #include<set> #include<algorithm> using namespace std; #define MAXN 10010int sa[MAXN], rank[MAXN], sum[MAXN], height[MAXN]; int wa[MAXN], wb[MAXN], wx[MAXN], wsum[MAXN]; char str[MAXN]; int dp[1010][20]; /* RMQ: dp[i][j] = max(dp[i][j-1], dp[i + 2 ^(j-1)][j-1]) dp[i][0] = A[i];求区间最值[i,j] int L =lg( j - i + 1 ) return max(dp[i][L], dp[j + 1 - 2 ^ L][L]); */ //预处理height数组 void pre(int n) {for( int i = 0; i <= n; i++)dp[i][0] = height[i];int L = (int) log2(n); for( int j = 1; j <= L; j++){for( int i = 1; i <= n + 1 - (1<<j); i++)dp[i][j] = min(dp[i][j-1], dp[i + (1<<(j-1))][j-1]);} }int get_min( int a, int b) {int L = (int) log2(b - a + 1 );return min(dp[a][L], dp[b + 1 - (1<<L)][L]); }//比较字符串是否相等 int cmp( int *r, int a, int b, int l) {return (r[a] == r[b] && r[a+l] == r[b+l]); }//倍增算法求sa数组 void get_sa(char *r, int *sa, int n, int m) //r为字符串, sa数组, n为字符串长度, m为字符串最大值 {int i, j,p, *x = wa, *y = wb, *t;for( i = 0; i < m; i++)sum[i] = 0;//对长度为1时后缀字符串排序 for( i = 0; i < n; i++)sum[ x[i] = r[i] ]++; //x相当于rank,但不是真正rank for( i = 1; i < m; i++) sum[i] += sum[i-1];for( i = n-1; i >= 0; i--)sa[--sum[x[i]]] = i; //对长度为2,4,...的后缀字符串排序for(j = 1, p = 1; p < n && j <= n; j *= 2){//首先对关键字y排序,排序后的结果保存在y数组中,即是这个后缀字符串的起始位置 for(p = 0,i = n - j; i < n; i++)y[p++] = i;for(i = 0; i < n; i++) if( sa[i] >= j ) y[p++] = sa[i] - j;//然后对关键字x排序,先要获取第1关键字xfor(i = 0; i < n; i++)wx[i] = x[y[i]]; for(i = 0; i < m; i++)wsum[i] = 0;for(i = 0; i < n; i++)wsum[ wx[i] ]++;for(i = 1; i < m; i++)wsum[i] += wsum[i-1];for(i = n - 1;i >= 0; i--)sa[--wsum[wx[i]]] = y[i];//更新xt = x, x = y, y = t;for( x[sa[0]] = 0,i = 1, p = 1; i < n; i++)x[ sa[i] ] = cmp(y, sa[i-1], sa[i], j) ? p - 1 : p++; } }//h[i] = height[rank[i]], h[i] >= h[i-1] - 1 void get_height(char *r, int n) {int i, j, k = 0;//sa[0] = len 就是我们补的那个0 for(i = 1; i <= n; i++)rank[sa[i]] = i;for(i = 0; i < n ; height[rank[i++]] = k ) for( k ? k-- : 0, j = sa[rank[i]-1]; r[i+k] == r[j+k]; k++); }int main( ) {int a, b, n, m;while( scanf("%s",str) != EOF ){int len = strlen(str);str[len] = '0';str[len+1] = 0;memset(wa,0,sizeof(wa));memset(wb,0,sizeof(wb));memset(sa,0,sizeof(sa));memset(height,0,sizeof(height));get_sa(str, sa, len + 1, 255);get_height( str, len );pre(len); /*for( int i = 0; i < len; i++){printf("%s %d %d\n",str+sa[i], rank[sa[i]], height[i]); }*/str[len] = 0;/*int h = -1;for( int i = 1; i < len; i++)h = max(h, height[i]);printf("可重叠最长重复子串为%d\n",h);*/ scanf("%d",&m);while( m-- ){scanf("%d%d",&a,&b);printf("%s %s\n", str+a, str+b);if( a == b ){printf("%d\n", strlen(str+a));continue;}int x1 = min(rank[a],rank[b]) + 1;int y1 = max(rank[a],rank[b]);printf("%d\n",get_min(x1,y1)); }} }