# Minimum splits required to convert a number into prime segments

• Difficulty Level : Hard
• Last Updated : 30 Nov, 2021

Given a number in the form of a string s, the task is to calculate and display minimum splits required such that the segments formed are Prime or print Not Possible otherwise.
Examples:

Input: s = “2351”
Output :
Explanation: Given number is already prime.
Input: s = “2352”
Output:
Explanation: Resultant prime segments are 23,5,2
Input: s = “2375672”
Output :
Explanation: Resultant prime segments are 2,37567,2

Approach:
This problem is a variation of Matrix Chain Multiplication and can be solved using Dynamic programming.
Try all possible splits recursively and at each split, check whether the segments formed are prime or not. Consider a 2D array dp where dp[i][j] shows the minimum splits from index i to j and returns dp[0][n] where n is the length of the string.
Recurrence :

`dp[i][j] = min(1 + solve(i, k) + solve(k + 1, j)) where i <= k <= j`

Actually, in the exact recurrence written above, the left and right segments both are non-prime, then 1 + INT_MAX + INT_MAX will be negative which leads to an incorrect answer.
So, separate calculations for the left and right segments are required. If any segment is found to be non-prime, no need to proceed further. Return min(1+left+right) otherwise.
Base cases considered are :

• If the number is prime, return 0
• If i==j and the number is prime, return 0
• If i==j and the number is not prime, return INT_MAX

Below code is the implementation of above approach:

## C++

 `#include ``using` `namespace` `std;` `int` `dp[1000][1000] = { 0 };` `// Checking for prime``bool` `isprime(``long` `long` `num)``{``    ``if` `(num <= 1)``        ``return` `false``;``    ``for` `(``int` `i = 2; i * i <= num; i++) {``        ``if` `(num % i == 0) {``            ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}``// Conversion of string to int``long` `long` `convert(string s, ``int` `i, ``int` `j)``{``    ``long` `long` `temp = 0;``    ``for` `(``int` `k = i; k <= j; k++) {``        ``temp = temp * 10 + (s[k] - ``'0'``);``    ``}``    ``return` `temp;``}``// Function to get the minimum splits``int` `solve(string s, ``int` `i, ``int` `j)``{``    ``// Convert the segment to integer or long long``    ``long` `long` `num = convert(s, i, j);``    ``// Number is prime``    ``if` `(isprime(num)) {``        ``return` `0;``    ``}``    ``// If a single digit is prime``    ``if` `(i == j && isprime(num))``        ``return` `0;` `    ``// If single digit is not prime``    ``if` `(i == j && isprime(num) == ``false``)``        ``return` `INT_MAX;` `    ``if` `(dp[i][j])``        ``return` `dp[i][j];` `    ``int` `ans = INT_MAX;``    ``for` `(``int` `k = i; k < j; k++) {``        ``// Recur for left segment``        ``int` `left = solve(s, i, k);``        ``if` `(left == INT_MAX) {``            ``continue``;``        ``}` `        ``// Recur for right segment``        ``int` `right = solve(s, k + 1, j);``        ``if` `(right == INT_MAX) {``            ``continue``;``        ``}``        ``// Minimum from left and right segment``        ``ans = min(ans, 1 + left + right);``    ``}``    ``return` `dp[i][j] = ans;``}``int` `main()``{` `    ``string s = ``"2352"``;``    ``int` `n = s.length();` `    ``int` `cuts = solve(s, 0, n - 1);``    ``if` `(cuts != INT_MAX) {``        ``cout << cuts;``    ``}``    ``else` `{``        ``cout << ``"Not Possible"``;``    ``}``}`

## Java

 `import` `java.util.*;` `class` `GFG``{` `    ``static` `int` `dp[][] = ``new` `int``[``1000``][``1000``];` `    ``// Checking for prime``    ``static` `boolean` `isprime(``long` `num){``        ``int` `i;``        ``if` `(num <= ``1``)``            ``return` `false``;``        ``for` `(i = ``2``; i * i <= num; i++) {``            ``if` `(num % i == ``0``) {``                ``return` `false``;``            ``}``        ``}``        ``return` `true``;``    ``}` `    ``// Conversion of string to int``    ``static` `long` `convert(String s, ``int` `i, ``int` `j)``    ``{``        ``long` `temp = ``0``;``        ``int` `k;``        ``for` `(k = i; k <= j; k++) {``            ``temp = temp * ``10` `+ (s.charAt(k) - ``'0'``);``        ``}``        ``return` `temp;``    ``}` `    ``// Function to get the minimum splits``    ``static` `int` `solve(String s, ``int` `i, ``int` `j)``    ``{``        ``int` `k;` `        ``// Convert the segment to integer or long long``        ``long` `num = convert(s, i, j);` `        ``// Number is prime``        ``if` `(isprime(num)) {``            ``return` `0``;``        ``}` `        ``// If a single digit is prime``        ``if` `(i == j && isprime(num))``            ``return` `0``;``    ` `        ``// If single digit is not prime``        ``if` `(i == j && isprime(num) == ``false``)``            ``return` `Integer.MAX_VALUE;``    ` `        ``if` `(dp[i][j] != ``0``)``            ``return` `dp[i][j];``    ` `        ``int` `ans = Integer.MAX_VALUE;``        ``for` `(k = i; k < j; k++) {` `            ``// Recur for left segment``            ``int` `left = solve(s, i, k);``            ``if` `(left == Integer.MAX_VALUE) {``                ``continue``;``            ``}``    ` `            ``// Recur for right segment``            ``int` `right = solve(s, k + ``1``, j);``            ``if` `(right == Integer.MAX_VALUE) {``                ``continue``;``            ``}` `            ``// Minimum from left and right segment``            ``ans = Math.min(ans, ``1` `+ left + right);``        ``}``        ``return` `dp[i][j] = ans;``    ``}``    ` `    ``public` `static` `void` `main (String []args)``    ``{``    ` `        ``String s = ``"2352"``;``        ``int` `n = s.length();``    ` `        ``int` `cuts = solve(s, ``0``, n - ``1``);``        ``if` `(cuts != Integer.MAX_VALUE) {``            ``System.out.print(cuts);``        ``}``        ``else` `{``            ``System.out.print(``"Not Possible"``);``        ``}``    ``}``}` `// This code is contributed by chitranayal`

## Python3

 `# Python3 Implementation of the above approach``import` `numpy as np;``import` `sys` `dp ``=` `np.zeros((``1000``,``1000``)) ;` `INT_MAX ``=` `sys.maxsize;` `# Checking for prime``def` `isprime(num) :` `    ``if` `(num <``=` `1``) :``        ``return` `False``;``    ``for` `i ``in` `range``(``2``, ``int``(num ``*``*` `(``1``/``2``)) ``+` `1``) :``        ``if` `(num ``%` `i ``=``=` `0``) :``            ``return` `False``;``    ``return` `True``;` `# Conversion of string to int``def` `convert(s, i, j) :` `    ``temp ``=` `0``;``    ``for` `k ``in` `range``(i, j ``+` `1``) :``        ``temp ``=` `temp ``*` `10` `+` `(``ord``(s[k]) ``-` `ord``(``'0'``));` `    ``return` `temp;` `# Function to get the minimum splits``def` `solve(s, i, j) :` `    ``# Convert the segment to integer or long long``    ``num ``=` `convert(s, i, j);``    ``# Number is prime``    ``if` `(isprime(num)) :``        ``return` `0``;` `    ``# If a single digit is prime``    ``if` `(i ``=``=` `j ``and` `isprime(num)) :``        ``return` `0``;` `    ``# If single digit is not prime``    ``if` `(i ``=``=` `j ``and` `isprime(num) ``=``=` `False``) :``        ``return` `INT_MAX;` `    ``if` `(dp[i][j]) :``        ``return` `dp[i][j];` `    ``ans ``=` `INT_MAX;``    ` `    ``for` `k ``in` `range``(i, j) :``        ``# Recur for left segment``        ``left ``=` `solve(s, i, k);``        ``if` `(left ``=``=` `INT_MAX) :``            ``continue``;` `        ``# Recur for right segment``        ``right ``=` `solve(s, k ``+` `1``, j);``        ``if` `(right ``=``=` `INT_MAX) :``            ``continue``;``    ` `        ``# Minimum from left and right segment``        ``ans ``=` `min``(ans, ``1` `+` `left ``+` `right);``    ` `    ``dp[i][j] ``=` `ans;``    ` `    ``return` `ans;` `# Driver code   ``if` `__name__ ``=``=` `"__main__"` `:` `    ``s ``=` `"2352"``;``    ``n ``=` `len``(s);` `    ``cuts ``=` `solve(s, ``0``, n ``-` `1``);``    ``if` `(cuts !``=` `INT_MAX) :``        ``print``(cuts);``    ` `    ``else` `:``        ``print``(``"Not Possible"``);` `# This code is converted by Yash_R`

## C#

 `using` `System;` `class` `GFG``{`` ` `    ``static` `int` `[,]dp = ``new` `int``[1000,1000];`` ` `    ``// Checking for prime``    ``static` `bool` `isprime(``long` `num){``        ``int` `i;``        ``if` `(num <= 1)``            ``return` `false``;``        ``for` `(i = 2; i * i <= num; i++) {``            ``if` `(num % i == 0) {``                ``return` `false``;``            ``}``        ``}``        ``return` `true``;``    ``}`` ` `    ``// Conversion of string to int``    ``static` `long` `convert(String s, ``int` `i, ``int` `j)``    ``{``        ``long` `temp = 0;``        ``int` `k;``        ``for` `(k = i; k <= j; k++) {``            ``temp = temp * 10 + (s[k] - ``'0'``);``        ``}``        ``return` `temp;``    ``}`` ` `    ``// Function to get the minimum splits``    ``static` `int` `solve(String s, ``int` `i, ``int` `j)``    ``{``        ``int` `k;`` ` `        ``// Convert the segment to integer or long long``        ``long` `num = convert(s, i, j);`` ` `        ``// Number is prime``        ``if` `(isprime(num)) {``            ``return` `0;``        ``}`` ` `        ``// If a single digit is prime``        ``if` `(i == j && isprime(num))``            ``return` `0;``     ` `        ``// If single digit is not prime``        ``if` `(i == j && isprime(num) == ``false``)``            ``return` `int``.MaxValue;``     ` `        ``if` `(dp[i,j] != 0)``            ``return` `dp[i, j];``     ` `        ``int` `ans = ``int``.MaxValue;``        ``for` `(k = i; k < j; k++) {`` ` `            ``// Recur for left segment``            ``int` `left = solve(s, i, k);``            ``if` `(left == ``int``.MaxValue) {``                ``continue``;``            ``}``     ` `            ``// Recur for right segment``            ``int` `right = solve(s, k + 1, j);``            ``if` `(right == ``int``.MaxValue) {``                ``continue``;``            ``}`` ` `            ``// Minimum from left and right segment``            ``ans = Math.Min(ans, 1 + left + right);``        ``}``        ``return` `dp[i,j] = ans;``    ``}``     ` `    ``public` `static` `void` `Main(String []args)``    ``{``     ` `        ``String s = ``"2352"``;``        ``int` `n = s.Length;``     ` `        ``int` `cuts = solve(s, 0, n - 1);``        ``if` `(cuts != ``int``.MaxValue) {``            ``Console.Write(cuts);``        ``}``        ``else` `{``            ``Console.Write(``"Not Possible"``);``        ``}``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`2`

Time Complexity: O(n3/2)

Auxiliary Space: O(106)

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