CSES Coin Combinations 1

 Problem:

Consider a money system consisting of n$n$ coins. Each coin has a positive integer value. Your task is to calculate the number of distinct ways you can produce a money sum x$x$ using the available coins.

For example, if the coins are {2,3,5}$\{2,3,5\}$ and the desired sum is 9$9$, there are 8$8$ ways:

• 2+2+5$2+2+5$
  
• 2+5+2$2+5+2$
  
• 5+2+2$5+2+2$
  
• 3+3+3$3+3+3$
  
• 2+2+2+3$2+2+2+3$
  
• 2+2+3+2$2+2+3+2$
  
• 2+3+2+2$2+3+2+2$
  
• 3+2+2+2$3+2+2+2$
  

Input

The first input line has two integers n$n$ and x$x$: the number of coins and the desired sum of money.

The second line has n$n$ distinct integers c1,c2,…,cn$c_1,c_2,\dots ,c_n$: the value of each coin.

Output

Print one integer: the number of ways modulo 109+7${10}^9+7$.

Constraints

• 1≤n≤100$1\le n\le 100$
  
• 1≤x≤106$1\le x\le {10}^6$
  
• 1≤ci≤106$1\le c_i\le {10}^6$
  

Example

Input:
3 9
2 3 5

Output:
8




Full Explanation:




CODE:

#include <iostream>
#include<bits/stdc++.h>

using namespace std;

int main()
{
    int n=0,x=0;
    cin>>x>>n;

    int dice[x];

    for(int i=0 ; i<x ; i++){
        cin>>dice[i];
    }

    long long value[n+1];

    value[0] = 1;
    for(int i=1;i<=n;i++){

        value[i] = 0;

        for (auto c:dice){
            if(i-c >=0){
                value[i]+=(value[i-c]%1000000007);
            }
        }
    }

    cout<<value[n]%(1000000007);

    return 0;
}

CSES : Increasing Subsequence - dynamic Programming

 Problem Statement:

You are given an array containing n$n$ integers. Your task is to determine the longest increasing subsequence in the array, i.e., the longest subsequence where every element is larger than the previous one.

A subsequence is a sequence that can be derived from the array by deleting some elements without changing the order of the remaining elements.

Input

The first line contains an integer n$n$: the size of the array.

After this there are n$n$ integers x1,x2,…,xn$x_1,x_2,\dots ,x_n$: the contents of the array.

Output

Print the length of the longest increasing subsequence.

Constraints

• 1≤n≤2⋅105$1\le n\le 2\cdot {10}^5$
  
• 1≤xi≤109$1\le x_i\le {10}^9$
  

Example

Input:
8
7 3 5 3 6 2 9 8

Output:
4




Full Video Explanation:

Youtube Video Explanation




Code:(C++)

#include <bits/stdc++.h>
using namespace std;

int main() {

  int n;
  cin >> n;
  vector<int> dp;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    auto it = lower_bound(dp.begin(), dp.end(), x);
    if (it == dp.end()) {
      dp.push_back(x);
    } else {
      *it = x;
    }
  }
  cout << dp.size() << endl;
}