Suffix Rotation


Problem Statement :


Megan is playing a string game with the following rules:

It starts with a string, s.
During each turn, she performs the following move:

Choose an index in s. The chosen index must be strictly greater than any index chosen in a prior move.
Perform one or more circular rotations (in either direction) of the suffix starting at the chosen index.
For example, let's say s = abcdefjghi. During our move, we choose to do three right rotations of the suffix starting at index 6:
image
Note that this counts as one move.

The goal of the game is to convert s into the lexicographically smallest possible string in as few moves as possible. In other words, we want the characters to be in alphabetical order.
Megan plays this game g times, starting with a new string s each time. For each game, find the minimum number of moves necessary to convert s into the lexicographically smallest string and print that number on a new line.

Input Format

The first line contains an integer, g, denoting the number of games.
Each of the g subsequent lines contains a single string denoting the initial value of string s for a game.

Constraints
1 <= g <= 100
1 <= |s| <= 1000

s consists of lowercase English alphabetic letters only.
Output Format

For each game, print an integer on a new line denoting the minimum number of moves required to convert s into the lexicographically smallest string possible.


Solution :



title-img


                            Solution in C :

In C++ :





#include <bits/stdc++.h>
using namespace std;

#define N 1010
#define inf 1010

int t;
char s[N];
map <string, int> mp;

int solve(char *s) {
//	puts(s);
	int len = strlen(s);
	if (!len) return 0;
	if (mp.count(s)) return mp[s];
	char c = *min_element(s, s + len);
	if (s[0] == c) return mp[s] = solve(s + 1);
	int rlt = 0;
	char ss[N];
	int runs = 0;
	bool vis[N];
	for (int i = 0; i < len; i ++) if (s[i] != c) {
		ss[runs] = s[i];
		int prv = i ? i - 1 : len - 1;
		vis[runs++] = s[prv] == c;
		if (i < len - 1 && s[i+1] == c) rlt ++;
	}
	ss[runs] = 0;
	len = runs;
	c = *min_element(ss, ss + len);
	bool start_c = 0;
	for (int i = 0; i < len; i ++) {
		if (vis[i] && ss[i] == c) {
			start_c = 1; break;
		}
	}
	int mn = inf;
    char sss[N];
	for (int i = 0; i < len; i ++) if (vis[i]) {
		if (start_c && ss[i] != c) continue;
		for (int j = 0; j < len; j ++) sss[j] = ss[(j+i)%len];
		sss[len] = 0;
		mn = min(mn, solve(sss));
	}
	return mp[s] = rlt + mn;
}

int main() {
//	freopen("s.in", "r", stdin);
//	freopen("s.out", "w", stdout);
	scanf("%d", &t);
	while (t --) {
		scanf("%s", s);
		printf("%d\n", solve(s));
	}
	return 0;
}








In Java :





import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {
    static class SH {
        int id=0;
        int[] cnt;
        String cs;
        SH(String s,int[] ant) {
            cs=s;
            cnt=Arrays.copyOf(ant,26);
            prep();
        }
        void prep() {
            StringBuilder sb=new StringBuilder();
            while(id<cs.length()) {
                char mc=getMC();
                if(mc==cs.charAt(id)) {
                    ++id;
                    --cnt[mc-'a'];
                }
                else break;
            }
            /*
            for(int i=id;i<chs.length;++i) {
                if(i!=id&&chs[i]==chs[i-1]) {
                    --cnt[chs[i]-'a'];
                } else {
                    sb.append(chs[i]);
                }
            }
            cs=sb.toString();
            */
            cs=cs.substring(id);
            id=0;
        }
        public int mm(){
            if(hm.containsKey(cs)) return hm.get(cs);
            if(0==cs.length()) return 0;
            char mc=getMC();
            String[] stx=cs.split(""+mc);
            int res=0;
            cnt[mc-'a']=0;
            StringBuilder sb=new StringBuilder();
            for(String x:stx) {
                if(x.length()!=0) {
                    sb.append(x);
                    ++res;
                }
            }
            if(cs.charAt(cs.length()-1)!=mc) --res;
            mc=getMC();
            String ns="";
            int mt=sb.length();
            int j=0;
            HashSet<String> hs=new HashSet();
            for(String bx:stx) {
                if(j==res) break;
                if(bx.length()==0) continue;
                sb.delete(0,bx.length());
                sb.append(bx);
                String ts=sb.toString();
                int tmt=cMC(ts,mc);
                if(tmt<mt) {
                    ns=ts;
                    mt=tmt;
                    hs.clear();
                    hs.add(ts);
                } else if(tmt==mt) {
                    hs.add(ts);
                }
                ++j;
            }
            int rm=Integer.MAX_VALUE;
            for(String bx:hs) {
                int nm=new SH(bx,cnt).mm();
                if(nm<rm) rm=nm;
            }
            res+=rm;
            hm.put(cs,res);
            return res;
        }
        int cMC(String st,char x) {
            int res=0;
            String[] nxt=st.split(""+x);
            for(String tt:nxt) {
                if(tt.length()!=0) ++res;
            }
            if(st.charAt(st.length()-1)!=x) --res;
            if(st.charAt(0)==x) --res;
            return res;
            
        }
        char getMC() {
            for(char x='a';x<='z';++x) {
                if(cnt[x-'a']!=0) return x;
            }
            return '*';
        }
    }
    static HashMap<String,Integer> hm=new HashMap();
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int q = in.nextInt();
        for(int a0 = 0; a0 < q; a0++){
            String s = in.next();
            int[] cnt=new int[26];
            for(char x:s.toCharArray()) ++cnt[x-'a'];
            // your code goes here
            SH t=new SH(s,cnt);
            System.out.println(t.mm());
        }
    }
}








In C :





#include<stdio.h>
#include<string.h>
#include<stdbool.h>
#define FOR(a,b,c) for(int a=(b),_for=(c);a<_for;++a)
#define M 1000
#define Z 26
char c[M+5];
int n, P[M+5], A[M+5], B[M+5], C[Z+5], D[M+5], E[M+5];
int min(int a, int b)
{
    return a < b ? a : b;
}

int n;
int p[M+5];
char c[M+5];
int cnt[Z+5];
int dp[M+5];
int nju[M+5];
int nx[M+5];
int isti[M+5];

void solve(){
    scanf ("%s",c);
    n=strlen(c);
    FOR(i,0,n) p[i]=Z-1-(c[i]-'a');
    FOR(i,0,Z) cnt[i]=0;
    FOR(i,0,n) cnt[p[i]]++;
    FOR(i,0,n) dp[i]=0;
    FOR(i,0,n) nju[i]=0;
    FOR(i,0,n) nx[i]=0;
    FOR(i,0,n) isti[i]=0;
    FOR(cl,0,Z){
        if (!cnt[cl]) continue;
        FOR(i,0,n) dp[i]=nju[i];
        memset(nju,-1,n*sizeof(int));
        memset(isti,0,n*sizeof(int));
        int last=-1,prvi=-1,sum=0,b1=n,b2=n;
        FOR(i,0,n) if (p[i]<=cl){
            if (last>=0){
                nx[last]=i;
                if (p[last]!=p[i] && p[i]==cl) isti[i]=1,sum++;
            }
            else prvi=i;
            last=i;
        }
        nx[last]=prvi;
//        FOR(i,0,n) printf ("%d -> %d\n",i,nx[i]);
        if (p[last]!=p[prvi] && p[prvi]==cl) isti[prvi]=1,sum++;
        int pb1=-1;
        FOR(i,0,n) if (p[i]==cl && p[nx[i]]!=cl){
            b2=min(b2,dp[nx[i]]);
//            printf ("%d -> %d\n",i,b2);
            if (b2<b1)
            {
                int temp = b1;
                b1 = b2;
                b2 = temp;
                pb1=i;
            }
        }
//        printf ("%d %d %d ???\n",sum,b1,pb1);
        sum+=b1-1;
        if (pb1==-1) sum=-1;
        bool flag=0;
        FOR(i,0,n){
            if (p[i]>cl) continue;
            if (p[i]<cl || !isti[i]){
                nju[i]=sum+1;
                continue;
            }
            if (b1==b2 || b2==n){
                nju[i]=sum;
                continue;
            }
            nju[i]=sum;
            flag=1;
        }
        if (flag){
            for (int i=pb1;i>=0 && flag;--i){
                if (isti[i]) nju[i]++,flag=0;
            }
            for (int i=n-1;i>=0 && flag;--i){
                if (isti[i]) nju[i]++,flag=0;
            }
        }
//        FOR(i,0,n) printf ("%d %d %d\n",i,isti[i],nju[i]);
//        printf ("\n");
    }
    printf ("%d\n",nju[0]);
    
}

int main(){
    int znj;
    scanf ("%d",&znj);
    while(znj--) solve();
    return 0;
}








In Python3 :





#!/bin/python3

import sys

def bestlastrotation(s,groups,letters,memos):
    if len(letters) < 3:
        return groups[0]
    mn = letters[0]
    mn2 = letters[1]
    mn3 = letters[2]
    lens = len(s)
    
    groups2 = []
    for g in groups:
        i = g
        while s[i] == mn:
            i = (i + 1) % lens
        if s[i] == mn2 and s[g-1] != mn2:
            groups2.append([g,i])
    
    if len(groups2) == 0: return groups[0]
    if len(groups2) == 1: return groups2[0][0]
    
    
    for gg in groups2:
        j = gg[1]
        while s[j] == mn2 or s[j] == mn:
            j = (j + 1) % lens
        if s[j] != mn3:
            return gg[0]
        else:
            gg.append(j)
    
    if len(letters) < 4:
        return groups2[0][0]
    
    
    groupset = set(x[0] for x in groups2)
    
    ans = 0
    best = lens
    for g in groupset:
        s2 = (s[g:]+s[:g]).replace(mn,'')
        result = min_rotations(s2,memos)
        if best > result:
            best = result
            ans = g  
    
    
    return ans



def min_rotations(s,memos):
    if s in memos:
        return memos[s]
    
    letters = sorted(set(s))
    mn = min(letters)
    ans = 0
        
    while mn != max(letters):
        
        i = 0
        while s[i] == mn:
            i += 1
        if i > 0:
            s = s[i:]
        
        groups = []
        for i in range(len(s)):
            if s[i] == mn and s[i-1] != mn:
                groups.append(i)
        
        ans += len(groups)
        
        if len(groups) == 1:
            g = groups[0]
            s = s[g:] + s[:g]
        
        if len(groups) > 1:
            g = bestlastrotation(s,groups,letters,memos)
            s = s[g:] + s[:g]
        
        s = s.replace(mn,'')
        letters = letters[1:]
        mn = min(letters)
    
    memos[s] = ans
    return ans
    

q = int(input().strip())
for a0 in range(q):
    s = input().strip()
    # your code goes here
    print(min_rotations(s,dict()))
                        




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