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Program to find number of operations required to remove palindromic sublists in C++
Suppose we have a list of numbers called nums. Now let us consider an operation where we delete some sublist which is a palindrome. We have to find the minimum number of operations required such that the list is empty.
So, if the input is like nums = [6, 2, 4, 4, 2, 10, 6], then the output will be 2, as we can remove the sublist [2, 4, 4, 2] first then the list is like [6, 10, 6] this is also a palindrome, so remove it to make list empty.
To solve this, we will follow these steps −
Define an array dp of size: 105 x 105.
Define a function dfs(), this will take i, j, an array v,
ret := inf
if i > j, then −
return 0
if i is same as j, then −
return 1
if j - i is same as 1, then −
return (if v[i] is same as v[j], then 1, otherwise 2)
if i + 1 <= j and v[i] is same as v[i + 1], then −
ret := 1 + dfs(i + 2, j, v)
if dp[i, j] is not equal to -1, then −
return dp[i, j]
ret := minimum of (ret, 1 + (minimum of (dfs(i + 1, j, v) and dfs(i, j - 1, v)))
if v[i] is same as v[j], then −
ret := minimum of ret and dfs(i + 1, j - 1, v)
for initialize k := i + 2, when k < j, update (increase k by 1), do −
if v[i] is same as v[k], then &minnus;
ret := minimum of ret and dfs((i + 1, k - 1, v) + dfs(k + 1, j, v))
return dp[i, j] = ret
From the main method do the following −
fill dp with -1
n := size of nums
return dfs(0, n - 1, nums)
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
int dp[105][105];
int dfs(int i,int j, vector <int>& v){
int ret= INT_MAX;
if(i > j)
return 0;
if(i == j)
return 1;
if(j - i == 1){
return v[i] == v[j] ? 1 : 2;
}
if(i + 1 <= j && v[i] == v[i + 1]){
ret = 1 + dfs(i + 2, j, v);
}
if(dp[i][j] != -1) return dp[i][j];
ret = min({ret, 1 + min(dfs(i + 1, j, v), dfs(i, j - 1, v))});
if(v[i] == v[j]){
ret = min(ret, dfs(i + 1, j - 1, v));
}
for(int k = i + 2; k < j; k++){
if(v[i] == v[k]){
ret = min(ret, dfs(i + 1, k - 1, v) + dfs(k + 1, j, v));
}
}
return dp[i][j] = ret;
}
int solve(vector<int>& nums) {
memset(dp , -1, sizeof dp);
int n = nums.size();
return dfs(0, n - 1, nums);
}
int main(){
vector<int> v = {6, 2, 4, 4, 2, 10, 6};
cout << solve(v);
}Input
{6, 2, 4, 4, 2, 10, 6}Output
2
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