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Learning DP Day 9
LIS and Kadane Algorithm
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13 files changed

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13 files changed

+658
-30
lines changed

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Box Stacking Problem/Code.cpp

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#include <bits/stdc++.h>
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using namespace std;
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#define F first
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#define S second
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#define PB push_back
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#define PF push_front
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#define P push
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#define INC(i,a,b) for (ll i = a; i <= b; i++)
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#define DEC(i,b,a) for (ll i = b; i >= a ; i--)
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#define inf LLONG_MAX
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#define neginf LLONG_MIN
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#define mod 1000000007
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#define eps 1e-9
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typedef ostringstream OS ;
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typedef stringstream SS ;
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typedef long long ll ;
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typedef unsigned long long ull;
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typedef pair < ll , ll > PLL ;
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typedef pair < char,ll > PCL ;
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typedef deque < double > DD ;
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typedef deque < PCL > DCL ;
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typedef deque < ll > DL ;
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typedef deque < PLL > DLL ;
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typedef deque < char > DC ;
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typedef deque < string > DS ;
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typedef vector < double > VD;
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typedef vector < PCL > VCL ;
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typedef vector < ll > VL;
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typedef vector < PLL > VLL ;
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typedef vector < char > VC ;
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typedef vector < string > VS ;
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typedef map < ll ,ll > MLL ;
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typedef map < char,ll > MCL;
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typedef map < ll,char > MLC;
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typedef map < string,ll> MSL;
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typedef priority_queue < PLL > PQLL ;
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typedef priority_queue < ll > PQL ;
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typedef stack < ll > SKL ;
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typedef stack < PLL > SKLL ;
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typedef queue < ll > QL ;
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typedef queue < PLL > QLL ;
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typedef set < ll > SL ;
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typedef set < PLL > SLL ;
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typedef set < char > SC ;
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typedef vector <VL> graph;
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string numtostr(ll n) {
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OS str1 ;
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str1 << n ;
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return str1.str();
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}
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ll strtonum(string s) {
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ll x ;
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SS str1(s);
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str1 >> x ;
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return x ;
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}
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ll GCD(ll a, ll b) {
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if ( b == 0 ) return a ;
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else return GCD(b,a%b);
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}
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ll LCM(ll a , ll b) {
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ll gcd = GCD(a,b);
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return (a/gcd)*b ;
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}
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vector < pair < ll,PLL> > boxes ;
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bool myfunc(pair < ll,PLL> x , pair < ll,PLL> y) {
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return ( (x.S.S * x.S.F) > (y.S.S * y.S.F)) ;
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}
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int main() {
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ios::sync_with_stdio(0);
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cin.tie(0);
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ll noOfBoxes ;
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cin >> noOfBoxes ;
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INC(i,1,noOfBoxes) {
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ll d1,d2,d3 ;
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cin >> d1 >> d2 >> d3 ;
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boxes.PB({d1,{max(d2,d3),min(d2,d3)}});
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boxes.PB({d2,{max(d1,d3),min(d1,d3)}});
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boxes.PB({d3,{max(d1,d2),min(d1,d2)}});
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}
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sort(boxes.begin(),boxes.end(),myfunc);
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VL lisBoxes ;
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lisBoxes.resize(boxes.size()+5,0);
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ll maxHeight = -1 ;
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INC(i,0,boxes.size()-1) {
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lisBoxes[i] = boxes[i].F ;
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maxHeight = max(maxHeight,lisBoxes[i]);
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}
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INC(i,1,boxes.size()-1) {
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INC(j,0,i-1) {
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if ( boxes[i].S.F < boxes[j].S.F && boxes[i].S.S < boxes[j].S.S && lisBoxes[j]+boxes[i].F > lisBoxes[i]) {
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lisBoxes[i] = lisBoxes[j]+boxes[i].F ;
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maxHeight = max(maxHeight,lisBoxes[i]);
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}
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}
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}
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cout << "Maximum Height is : " << maxHeight << endl;
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return 0 ;
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}

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Box Stacking Problem/README.md

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## Explanation
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[Box Stacking Problem](https://www.youtube.com/watch?v=kLucR6-Q0GA&list=PLEJXowNB4kPxBwaXtRO1qFLpCzF75DYrS&index=25)

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Kadane Algorithm Range/Code.cpp

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#include <bits/stdc++.h>
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using namespace std;
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#define F first
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#define S second
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#define PB push_back
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#define P push
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#define INC(i,a,b) for (ll i = a; i <= b; i++)
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#define DEC(i,b,a) for (ll i = b; i >= a ; i--)
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#define inf 999999999
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#define neginf -999999999
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typedef ostringstream OS ;
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typedef stringstream SS ;
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typedef long long ll ;
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typedef pair < ll , ll > PLL ;
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typedef pair < char,ll > PCL ;
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typedef vector < double > VDL;
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typedef vector < PCL > VCL ;
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typedef vector < ll > VL;
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typedef vector < PLL > VLL ;
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typedef vector < char > VC ;
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typedef map < ll ,ll > MLL ;
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typedef map < char,ll > MCL;
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typedef priority_queue < PLL > PQLL ;
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typedef priority_queue < ll > PQL ;
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typedef stack < ll > SKL ;
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typedef stack < PLL > SKLL ;
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typedef set < ll > SL ;
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typedef set < PLL > SLL ;
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typedef set < char > SC ;
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string numtostr(ll n) {
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OS str1 ;
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str1 << n ;
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return str1.str();
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}
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ll strtonum(string s) {
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ll x ;
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SS str1(s);
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str1 >> x ;
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return x ;
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}
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ll GCD(ll a, ll b) {
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if ( b == 0 ) return a ;
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else return GCD(b,a%b);
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}
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ll LCM(ll a , ll b) {
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ll gcd = GCD(a,b);
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return (a*b)/gcd ;
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}
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int main() {
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ios::sync_with_stdio(0);
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cin.tie(0);
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ll n ;
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cin >> n ;
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VL v ;
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INC(i,0,n-1) {
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ll a ;
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cin >> a ;
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v.PB(a);
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}
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pair < ll ,PLL > sum = {0,{0,0}};
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pair < ll ,PLL > best = {neginf,{-1,-1}}; /* you can use best as {0,{0,0}} if it is allowed to
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take empty subarray */
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INC(i,0,n-1) {
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if ( v[i] >= sum.F + v[i]) {
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sum.S.F = i ;
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sum.S.S = i ;
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sum.F = v[i] ;
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if ( v[i] > best.F) {
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best.S.F = sum.S.F ;
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best.S.S = sum.S.S ;
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best.F = sum.F ;
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}
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}
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else if ( v[i]+sum.F > v[i]) {
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sum.S.S = i ;
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if ( v[i]+sum.F > best.F) {
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best.S.F = sum.S.F ;
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best.S.S = sum.S.S ;
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best.F = v[i] + sum.F ;
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}
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sum.F = v[i]+sum.F ;
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}
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}
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cout << best.F << " " << best.S.F+1 << " " << best.S.S+1 << endl;
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return 0 ;
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}

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Kadane Algorithm Range/README.md

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## Explanation
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Some modification so that we can print the starting and ending index of the subarray which holds maximum sum .

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Kadane Algorithm/Code.cpp

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#include <bits/stdc++.h>
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using namespace std;
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#define F first
4+
#define S second
5+
#define PB push_back
6+
#define PF push_front
7+
#define P push
8+
#define INC(i,a,b) for (ll i = a; i <= b; i++)
9+
#define DEC(i,b,a) for (ll i = b; i >= a ; i--)
10+
#define inf LLONG_MAX
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#define neginf LLONG_MIN
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#define mod 1000000007
13+
#define eps 1e-9
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typedef ostringstream OS ;
15+
typedef stringstream SS ;
16+
typedef long long ll ;
17+
typedef unsigned long long ull;
18+
typedef pair < ll , ll > PLL ;
19+
typedef pair < char,ll > PCL ;
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typedef deque < double > DD ;
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typedef deque < PCL > DCL ;
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typedef deque < ll > DL ;
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typedef deque < PLL > DLL ;
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typedef deque < char > DC ;
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typedef deque < string > DS ;
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typedef vector < double > VD;
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typedef vector < PCL > VCL ;
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typedef vector < ll > VL;
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typedef vector < PLL > VLL ;
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typedef vector < char > VC ;
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typedef vector < string > VS ;
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typedef map < ll ,ll > MLL ;
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typedef map < char,ll > MCL;
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typedef map < ll,char > MLC;
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typedef map < string,ll> MSL;
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typedef priority_queue < PLL > PQLL ;
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typedef priority_queue < ll > PQL ;
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typedef stack < ll > SKL ;
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typedef stack < PLL > SKLL ;
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typedef queue < ll > QL ;
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typedef queue < PLL > QLL ;
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typedef set < ll > SL ;
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typedef set < PLL > SLL ;
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typedef set < char > SC ;
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typedef vector <VL> graph;
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string numtostr(ll n) {
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OS str1 ;
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str1 << n ;
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return str1.str();
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}
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ll strtonum(string s) {
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ll x ;
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SS str1(s);
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str1 >> x ;
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return x ;
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}
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ll GCD(ll a, ll b) {
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if ( b == 0 ) return a ;
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else return GCD(b,a%b);
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}
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ll LCM(ll a , ll b) {
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ll gcd = GCD(a,b);
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return (a/gcd)*b ;
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}
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int main() {
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ios::sync_with_stdio(0);
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cin.tie(0);
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ll n ;
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cin >> n ;
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VL v ;
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v.resize(n+5,0);
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INC(i,1,n) cin >> v[i] ;
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ll maxSum = neginf ;
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ll currSum = 0 ;
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INC(i,1,n) {
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currSum = max(currSum+v[i],v[i]);
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maxSum = max(maxSum,currSum);
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}
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cout << maxSum << endl;
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return 0 ;
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}

‎Concepts/Longest Increasing Subsequence and Kadane Algorithm/Kadane Algorithm/README.md

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## Explanation
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[Kadane Algorithm](https://www.geeksforgeeks.org/largest-sum-contiguous-subarray/)

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