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Greedy Knapsack | |
{ | |
for i=1 to n //step1 | |
{ | |
compute pi/wi; //step2 | |
// form 1 to n we have compute above code ---- O(n) (tim taken , since it runs n times) | |
} | |
sort objects in non- increasing order p/w; //step3 | |
// if i have n objects and i have to sort them, then | |
best sorting algorithm (compasion base sorting algo) is merge sort. -- O(nlogn) (time take for merge sort) | |
for i=1 to n //step4 | |
{ | |
if(m>0 && wi<=m) //step5 | |
m = m - wi; //step6 | |
P = P + pi; //step7 | |
else //step8 | |
break; //step9 | |
} | |
// for above code we have iterate from 1 to on sorted list -- O(n) (time taken) | |
if(m>0) //step10 | |
{ | |
P=P+ pi*(m/wi); //step11 | |
// this step will take constantant time so -- O(1) (time taken) | |
} | |
SO we total time taken will be = O(n) + O(nlogn) + O(n) +O(1) | |
so time complexity will be = O(nlogn) | |
} |
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