Minsta initiala energi som krävs för att korsa gatan
Prova det på GfG Practice 
#practiceLinkDiv { display: ingen !viktigt; }
#practiceLinkDiv { display: ingen !viktigt; } Givet en matris som innehåller positiva och negativa tal. Arrayen representerar kontrollpunkter från ena änden till den andra änden av gatan. Positiva och negativa värden representerar mängden energi vid den kontrollpunkten. Positiva tal ökar energin och negativa tal minskar. Hitta den minsta initiala energi som krävs för att korsa gatan så att energinivån aldrig blir 0 eller mindre än 0.
Obs: Värdet på den minimala initiala energin som krävs kommer att vara 1 även om vi korsar gatan framgångsrikt utan att förlora energi till mindre än och lika med 0 vid någon kontrollpunkt. 1:an krävs för den första kontrollpunkten.
Exempel:
Input : arr[] = {4 -10 4 4 4}
Output: 7
Suppose initially we have energy = 0 now at 1st
checkpoint we get 4. At 2nd checkpoint energy gets
reduced by -10 so we have 4 + (-10) = -6 but at any
checkpoint value of energy can not less than equals
to 0. So initial energy must be at least 7 because
having 7 as initial energy value at 1st checkpoint
our energy will be = 7+4 = 11 and then we can cross
2nd checkpoint successfully. Now after 2nd checkpoint
all checkpoint have positive value so we can cross
street successfully with 7 initial energy.
Input : arr[] = {3 5 2 6 1}
Output: 1
We need at least 1 initial energy to reach first
checkpoint
Input : arr[] = {-1 -5 -9}
Output: 16
Recommended Practice Minimal energi Prova!Brute force approach:
- För varje möjlig initial energinivå (med början från 1) simulera korsningen av gatan med den energinivån och kontrollera om energinivån förblir positiv hela tiden.
- Returnera den lägsta initiala energinivån som säkerställer att energinivån aldrig blir noll eller negativ.
Nedan är koden för ovanstående tillvägagångssätt:
C++Java#includeusing namespace std ; // Function to check if energy level never becomes negative or zero bool check ( int arr [] int n int initEnergy ) { int energy = initEnergy ; for ( int i = 0 ; i < n ; i ++ ) { energy += arr [ i ]; if ( energy <= 0 ) { return false ; } } return true ; } // Function to calculate minimum initial energy // arr[] stores energy at each checkpoints on street int minInitialEnergy ( int arr [] int n ) { int minEnergy = 1 ; while ( ! check ( arr n minEnergy )) { minEnergy ++ ; } return minEnergy ; } // Driver code int main () { int arr [] = { 4 -10 4 4 4 }; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); cout < < minInitialEnergy ( arr n ); return 0 ; } Python3import java.util.* ; public class GFG { // Function to check if energy level never becomes // negative or zero static boolean check ( int [] arr int n int initEnergy ) { int energy = initEnergy ; for ( int i = 0 ; i < n ; i ++ ) { energy += arr [ i ] ; if ( energy <= 0 ) { return false ; } } return true ; } // Function to calculate minimum initial energy // arr[] stores energy at each checkpoints on the street static int minInitialEnergy ( int [] arr int n ) { int minEnergy = 1 ; while ( ! check ( arr n minEnergy )) { minEnergy ++ ; } return minEnergy ; } // Driver code public static void main ( String [] args ) { int [] arr = { 4 - 10 4 4 4 }; int n = arr . length ; System . out . println ( minInitialEnergy ( arr n )); } } // This code is contributed by akshitaguprzj3C## Function to check if energy level never becomes negative or zero def check ( arr n initEnergy ): energy = initEnergy for i in range ( n ): energy += arr [ i ] if energy <= 0 : return False return True # Function to calculate minimum initial energy # arr stores energy at each checkpoints on street def minInitialEnergy ( arr n ): minEnergy = 1 while not check ( arr n minEnergy ): minEnergy += 1 return minEnergy # Driver code arr = [ 4 - 10 4 4 4 ] n = len ( arr ) print ( minInitialEnergy ( arr n )) # THIS CODE IS CONTRIBUTED BY CHANDAN AGARWALJavaScriptusing System ; namespace EnergyCheck { class GFG { // Function to check if energy level never becomes negative or zero static bool Check ( int [] arr int n int initEnergy ) { int energy = initEnergy ; for ( int i = 0 ; i < n ; i ++ ) { energy += arr [ i ]; if ( energy <= 0 ) { return false ; } } return true ; } // Function to calculate minimum initial energy // arr[] stores energy at each checkpoints on street static int MinInitialEnergy ( int [] arr int n ) { int minEnergy = 1 ; while ( ! Check ( arr n minEnergy )) { minEnergy ++ ; } return minEnergy ; } // Driver code static void Main ( string [] args ) { int [] arr = { 4 - 10 4 4 4 }; int n = arr . Length ; Console . WriteLine ( MinInitialEnergy ( arr n )); } } }Utgång:
7
Tidskomplexitet: O(2^n)
Hjälputrymme: På)
Vi tar initial minimienergi 0 dvs; initMinEnergy = 0 och energi vid valfri kontrollpunkt som currEnergy = 0. Passera nu varje kontrollpunkt linjärt och lägg till energinivån vid varje i'te kontrollpunkt, dvs. currEnergy = currEnergy + arr[i]. Om currEnergy blir icke-positiv behöver vi åtminstone 'abs(currEnergy) + 1' extra initial energi för att passera denna punkt. Därför uppdaterar vi initMinEnergy = (initMinEnergy + abs(currEnergy) + 1). Vi uppdaterar även currEnergy = 1 eftersom vi nu har den extra minimienergi som krävs för nästa punkt.
Nedan är implementeringen av ovanstående idé.
C++Java// C++ program to find minimum initial energy to // reach end #includeusing namespace std ; // Function to calculate minimum initial energy // arr[] stores energy at each checkpoints on street int minInitialEnergy ( int arr [] int n ) { // initMinEnergy is variable to store minimum initial // energy required. int initMinEnergy = 0 ; // currEnergy is variable to store current value of // energy at i'th checkpoint on street int currEnergy = 0 ; // flag to check if we have successfully crossed the // street without any energy loss <= o at any checkpoint bool flag = 0 ; // Traverse each check point linearly for ( int i = 0 ; i < n ; i ++ ) { currEnergy += arr [ i ]; // If current energy becomes negative or 0 increment // initial minimum energy by the negative value plus 1. // to keep current energy positive (at least 1). Also // update current energy and flag. if ( currEnergy <= 0 ) { initMinEnergy += abs ( currEnergy ) + 1 ; currEnergy = 1 ; flag = 1 ; } } // If energy never became negative or 0 then // return 1. Else return computed initMinEnergy return ( flag == 0 ) ? 1 : initMinEnergy ; } // Driver Program to test the case int main () { int arr [] = { 4 -10 4 4 4 }; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); cout < < minInitialEnergy ( arr n ); return 0 ; } Python3// Java program to find minimum // initial energy to reach end class GFG { // Function to calculate minimum // initial energy arr[] stores energy // at each checkpoints on street static int minInitialEnergy ( int arr [] int n ) { // initMinEnergy is variable to store // minimum initial energy required. int initMinEnergy = 0 ; // currEnergy is variable to store // current value of energy at // i'th checkpoint on street int currEnergy = 0 ; // flag to check if we have successfully // crossed the street without any energy // loss <= o at any checkpoint boolean flag = false ; // Traverse each check point linearly for ( int i = 0 ; i < n ; i ++ ) { currEnergy += arr [ i ] ; // If current energy becomes negative or 0 // increment initial minimum energy by the negative // value plus 1. to keep current energy // positive (at least 1). Also // update current energy and flag. if ( currEnergy <= 0 ) { initMinEnergy += Math . abs ( currEnergy ) + 1 ; currEnergy = 1 ; flag = true ; } } // If energy never became negative or 0 then // return 1. Else return computed initMinEnergy return ( flag == false ) ? 1 : initMinEnergy ; } // Driver code public static void main ( String [] args ) { int arr [] = { 4 - 10 4 4 4 }; int n = arr . length ; System . out . print ( minInitialEnergy ( arr n )); } } // This code is contributed by Anant Agarwal.C## Python program to find minimum initial energy to # reach end # Function to calculate minimum initial energy # arr[] stores energy at each checkpoints on street def minInitialEnergy ( arr ): n = len ( arr ) # initMinEnergy is variable to store minimum initial # energy required initMinEnergy = 0 ; # currEnergy is variable to store current value of # energy at i'th checkpoint on street currEnergy = 0 # flag to check if we have successfully crossed the # street without any energy loss <= 0 at any checkpoint flag = 0 # Traverse each check point linearly for i in range ( n ): currEnergy += arr [ i ] # If current energy becomes negative or 0 increment # initial minimum energy by the negative value plus 1. # to keep current energy positive (at least 1). Also # update current energy and flag. if currEnergy <= 0 : initMinEnergy += ( abs ( currEnergy ) + 1 ) currEnergy = 1 flag = 1 # If energy never became negative or 0 then # return 1. Else return computed initMinEnergy return 1 if flag == 0 else initMinEnergy # Driver program to test above function arr = [ 4 - 10 4 4 4 ] print ( minInitialEnergy ( arr )) # This code is contributed by Nikhil Kumar Singh(nickzuck_007)JavaScript// C# program to find minimum // C# program to find minimum // initial energy to reach end using System ; class GFG { // Function to calculate minimum // initial energy arr[] stores energy // at each checkpoints on street static int minInitialEnergy ( int [] arr int n ) { // initMinEnergy is variable to store // minimum initial energy required. int initMinEnergy = 0 ; // currEnergy is variable to store // current value of energy at // i'th checkpoint on street int currEnergy = 0 ; // flag to check if we have successfully // crossed the street without any energy // loss <= o at any checkpoint bool flag = false ; // Traverse each check point linearly for ( int i = 0 ; i < n ; i ++ ) { currEnergy += arr [ i ]; // If current energy becomes negative or 0 // negativeincrement initial minimum energy // by the value plus 1. to keep current // energy positive (at least 1). Also // update current energy and flag. if ( currEnergy <= 0 ) { initMinEnergy += Math . Abs ( currEnergy ) + 1 ; currEnergy = 1 ; flag = true ; } } // If energy never became negative // or 0 then return 1. Else return // computed initMinEnergy return ( flag == false ) ? 1 : initMinEnergy ; } // Driver code public static void Main () { int [] arr = { 4 - 10 4 4 4 }; int n = arr . Length ; Console . Write ( minInitialEnergy ( arr n )); } } // This code is contributed by Nitin Mittal.PHP< script > // Javascript program to find minimum // initial energy to reach end // Function to calculate minimum // initial energy arr[] stores // energy at each checkpoints on street function minInitialEnergy ( arr n ) { // initMinEnergy is variable // to store minimum initial // energy required. let initMinEnergy = 0 ; // currEnergy is variable to // store current value of energy // at i'th checkpoint on street let currEnergy = 0 ; // flag to check if we have // successfully crossed the // street without any energy // loss <= o at any checkpoint let flag = 0 ; // Traverse each check // point linearly for ( let i = 0 ; i < n ; i ++ ) { currEnergy += arr [ i ]; // If current energy becomes // negative or 0 increment // initial minimum energy by // the negative value plus 1. // to keep current energy // positive (at least 1). Also // update current energy and flag. if ( currEnergy <= 0 ) { initMinEnergy += Math . abs ( currEnergy ) + 1 ; currEnergy = 1 ; flag = 1 ; } } // If energy never became // negative or 0 then // return 1. Else return // computed initMinEnergy return ( flag == 0 ) ? 1 : initMinEnergy ; } // Driver Code let arr = new Array ( 4 - 10 4 4 4 ); let n = arr . length ; document . write ( minInitialEnergy ( arr n )); // This code is contributed // by Saurabh Jaiswal < /script>
Produktion7Tidskomplexitet: O(n)
Hjälputrymme: O(1)
