# String Reduction

### Problem Statement :

```Given a string consisting of the letters a, b and c, we can perform the following operation:

Take any two adjacent distinct characters and replace them with the third character.
Find the shortest string obtainable through applying this operation repeatedly.

For example, given the string aba we can reduce it to a 1 character string by replacing ab with c and ca with b: aba -> ca -> b.

Function Description

Complete the stringReduction function in the editor below. It must return an integer that denotes the length of the shortest string obtainable.

stringReduction has the following parameter:
- s: a string

Input Format

The first line contains the number of test cases t.

Each of the next t lines contains a string s to process.

Constraints

1 <= t <= 100
1 <= |s| <= 100

Output Format

For each test case, print the length of the resultant minimal string on a new line.```

### Solution :

```                            ```Solution in C :

In C++ :

#include<iostream>
#include<cmath>
#include<algorithm>
#include<vector>
#include<string>
#include<list>
#include<deque>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<utility>
using namespace std;

int main() {
string s;
int T=0, res=0;
int tab;

cin >> T;

for (int t = 0; t < T; t++) {
s.clear();
tab = 0;
tab = 0;
tab = 0;
res = 0;

cin >> s;
for (unsigned int i = 0; i < s.size(); i++) {
if (s[i] == 'a') tab++;
else if(s[i] == 'b') tab++;
else if(s[i] == 'c') tab++;
else cerr << "dupa!" << endl;
}

sort(tab, tab+3);

while (tab > 0) {
tab--;
tab--;
tab++;
sort(tab, tab+3);
}

cout << tab << endl;
}

return 0;
}

In Java :

/*
* Anand Oza
* October 29, 2011
*/

import java.io.IOException;
import java.io.StreamTokenizer;

public class Solution {
public static void main(String[] args) throws IOException {
StreamTokenizer in = new StreamTokenizer(new InputStreamReader(
System.in));
in.nextToken();
int T = (int) in.nval;

int ans;

for (int test = 0; test < T; test++) {
in.nextToken();
char[] c = in.sval.toCharArray();
int[] n = new int;
for (int i = 0; i < c.length; i++)
n[c[i] - 'a']++;
int x = (n + n) * (n + n) * (n + n);
if (x == 0)
ans = c.length;
else if ((n+n)%2==0 && (n+n)%2==0 && (n+n)%2==0)
ans = 2;
else
ans = 1;

System.out.println(ans);
}
}
}

In C :

#include <stdio.h>
#include <string.h>

int min( int a, int b ) { return a < b ? a : b; }

int T, n;
char s[ 105 ];

int a[ 105 ][ 105 ];
int b[ 105 ][ 105 ];
int c[ 105 ][ 105 ];
int f[ 105 ][ 105 ];

int len, i, l, r, m;

int main()
{
scanf( "%d", &T );

while( T-- ) {
scanf( "%s", s );
n = strlen( s );

for( i = 0; i < n; ++i ) {
if( s[i] == 'a' ) a[i][i] = 1; else a[i][i] = 0;
if( s[i] == 'b' ) b[i][i] = 1; else b[i][i] = 0;
if( s[i] == 'c' ) c[i][i] = 1; else c[i][i] = 0;
f[i][i] = 1;
}

for( len = 2; len <= n; ++len ) {
for( l = 0; l+len <= n; ++l ) {
r = l + len - 1;

f[l][r] = f[l][r-1]+1;
a[l][r] = b[l][r] = c[l][r] = 0;

for( m = l; m < r; ++m ) {
c[l][r] |= ( a[l][m] && b[m+1][r] || b[l][m] && a[m+1][r] );
b[l][r] |= ( a[l][m] && c[m+1][r] || c[l][m] && a[m+1][r] );
a[l][r] |= ( c[l][m] && b[m+1][r] || b[l][m] && c[m+1][r] );
f[l][r] |= min( f[l][r], f[l][m] + f[m+1][r] );
}

if( a[l][r] || b[l][r] || c[l][r] ) f[l][r] = 1;
}
}

printf( "%d\n", f[n-1] );
}

return 0;
}

In Python3 :

__author__ = 'jonghewk'

def reductions(string):
d = [0,0,0]
for letter in string:
if letter == 'a':
d+=1
elif letter == 'b':
d+=1
else:
d+=1

while True:
count =0
for i in d:
if i == 0:
count+=1
if count>=2:
break

d.sort(reverse=True)
d+=-1
d+=-1
d+=1

sum = 0
for i in d:
sum+=i
print(sum)

T = int(input())
cases = []
for i in range(T):
cases.append(input().strip())

for w in cases:
reductions(w)```
```

## Counting On a Tree

Taylor loves trees, and this new challenge has him stumped! Consider a tree, t, consisting of n nodes. Each node is numbered from 1 to n, and each node i has an integer, ci, attached to it. A query on tree t takes the form w x y z. To process a query, you must print the count of ordered pairs of integers ( i , j ) such that the following four conditions are all satisfied: the path from n

## Polynomial Division

Consider a sequence, c0, c1, . . . , cn-1 , and a polynomial of degree 1 defined as Q(x ) = a * x + b. You must perform q queries on the sequence, where each query is one of the following two types: 1 i x: Replace ci with x. 2 l r: Consider the polynomial and determine whether is divisible by over the field , where . In other words, check if there exists a polynomial with integer coefficie

## Costly Intervals

Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the

## The Strange Function

One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting

## Self-Driving Bus

Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever

## Unique Colors

You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti