Introduction to divisional DP (codevs 1017 problem solution)

Topic Portal: Maximum Product

The meaning of the question: Give a string of length N only composed of numbers, add k multiplication signs to it, make the product maximum, and output the maximum product.

Solution: Divisional DP, the specifics are not very clear, and this DP has not been systematically studied, but it can be clearly known that this provides the idea of ​​​​DP on the divisional topic. This problem is very simple, DP equation:

dp[i][j]=max{strToll(s+i-k, k)*dp[i-k][j-1] }

i indicates that the currently processed number string is the first i number of the original input number string

j means insert j multiplication signs into the i number

k means to separate a number of length k from the end of the number string

s is a pointer to the first character of the numeric string

strToll(char a[], b) means to convert the first b elements of the number string a into numbers

Simply put, it is to separate a part from the end of the string as a number and multiply it with the result of adding j-1 multiplication signs to the previous string

Code:

#include<iostream>
#include<algorithm>
#include<cstdio>
#define ll long long

using namespace std;
ll strToll(char p[], int n)
{
    ll sum = 0;
    for(char* q = p; q != p+n; ++ q)
        sum = sum*10 + (*q-'0');
    return sum;
}
ll dp[44][8];
char s[44];
ll DP(int N, int k)
{
    if(dp[N][k])    return dp[N][k];
    if(k == 0)  return dp[N][k] = strToll(s, N);
    for(int i = 1; i <= N-k; ++ i)
    {
        dp[N][k] = max(dp[N][k], strToll(s+N-i, i)*DP(N-i, k-1));
    }
    return dp[N][k];
}
intmain()
{
    #ifdef AFei
    freopen("in.txt", "r", stdin);
    #endif
    int N, k;
    scanf("%d%d%s", &N, &k, s);
    printf("%lld\n", DP(N, k));
    return 0;
}

The idea of ​​divisional DP allows us to use DP to solve this divisional type of problem