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Dynamic programming common patterns

ap_Cooperative_dev answered on August 11, 2022 Popularity 6/10 Helpfulness 1/10

answer Dynamic programming common patterns

Dynamic programming common patterns

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1 Rod cutting problem

► Given a rod with certain length l
► Given the prices of different lengths
► How to cut the rod in order to maximize the profit?
► This is the rod cutting problem

We have to create a solution matrix:

dpTable[numOfLengths+1][originalLength+1]

Complexity: O(numOfLengths*originalLength)

#include <iostream>
using namespace std;

int maximum(int a , int b){
    return a>b?a:b;
}

int main() {
    int n;
    cin>>n;
    int v[4]={2,5,7,3};
    int l[4]={1,2,3,4};
    int m=4;

    int dp[m+1][n+1];
    for (int i=0;i<=m;i++){
        for(int j=0;j<=n;j++){

         if(i==0||j==0)
          dp[i][j]=0;
         else if(l[i-1]>j)
          dp[i][j]=dp[i-1][j];
         else
          dp[i][j]=maximum(dp[i-1][j],v[i-1]+dp[i][j-l[i-1]]);
        }
    }
        cout<<dp[m][n];
       // dp[m][n] is maximum profit
    return 0;
}
note : v[i-1] is i th element,we basically decide whether to choose i th
element or not, for each i such that 1<=i<=n
****IMP inside both loops use if else if else block to write recurrence.

for solution construction see sandy 8..... Gdri udemy-recursion..course

Popularity 6/10 Helpfulness 1/10 Language cpp

Source: Grepper

Tags: c++ dynamic-programming

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Contributed on Aug 11 2022

ap_Cooperative_dev

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