100 Most Common German Words with Italian Translation (CGPT)

100 Most Common German Words with Italian Translation

Below is a list of the 100 most commonly used words in the German language, along with their Italian translations.

German	Italian
und	e
sein	essere
in	in
haben	avere
nicht	non
ja	sì
nein	no
was	cosa
wie	come
wo	dove
wann	quando
warum	perché
welche	quale
dieser	questo
hier	qui
dort	lì
gut	buono
schlecht	cattivo
groß	grande
klein	piccolo
alt	vecchio
neu	nuovo
viel	molto
wenig	poco
mehr	più
weniger	meno
(Der) Mensch	uomo
(Die) Frau	donna
(Das) Kind	bambino
(Der) Freund	amico
(Die) Familie	famiglia
(Der) Tag	giorno
(Die) Nacht	notte
(Die) Zeit	tempo
(Das) Jahr	anno
(Die) Woche	settimana
(Der) Monat	mese
(Das) Leben	vita
(Die) Arbeit	lavoro
(Die) Schule	scuola
essen	mangiare
trinken	bere
gehen	andare
kommen	venire
sehen	vedere
hören	sentire
sprechen	parlare
schreiben	scrivere
lesen	leggere
denken	pensare
wissen	sapere
lieben	amare
nehmen	prendere
geben	dare
arbeiten	lavorare
lernen	imparare
spielen	giocare
warten	aspettare
suchen	cercare
finden	trovare
fragen	chiedere
antworten	rispondere
bleiben	restare
fahren	guidare
laufen	correre
schlafen	dormire
helfen	aiutare
bringen	portare
kaufen	comprare
verkaufen	vendere
beginnen	iniziare
enden	finire
öffnen	aprire
schließen	chiudere
vergessen	dimenticare
erinnern	ricordare
hoffen	sperare
glauben	credere
spielen	suonare
tanzen	ballare
sitzen	sedere
stehen	stare in piedi
liegen	giacere
fallen	cadere
springen	saltare
lachen	ridere
weinen	piangere
sehen	guardare
ziehen	tirare
drücken	premere
verstehen	capire

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Coin Change Problem (Dynamic Programming)

youtube
I've asked to chatGPT why dp[i] +=dp[i-coin]

In point 2), we consider the case where we use the coin c to make change for the amount i. In this case, we can use the same number of possible combinations as we could for the amount i-c to make change for the amount i. Let me give you an example to illustrate this. Suppose we have the coins [1, 2, 5] and we want to make change for the amount 7. To compute the number of possible combinations of coins required to make change for the amount 7 using the coins up to 5, we can do the following: We start with dp[0] = 1, since there is only one way to make change for 0 (using no coins). We consider the first coin 1. For each amount i from 1 to 7, we check whether we can use the coin 1 to make change for the amount i. If we can, we update dp[i] by adding the value of dp[i-1] to it, since we can use one 1 coin and the number of possible combinations required to make change for the amount i-1 to make change for the amount i. For example, to make change for the amount 2, we can use one 1 coin and the number of possible combinations required to make change for the amount 1. Therefore, we update dp[2] by adding dp[1] to it. After considering the first coin, we have dp = [1, 1, 1, 1, 1, 1, 1]. We consider the second coin 2. For each amount i from 2 to 7, we check whether we can use the coin 2 to make change for the amount i. If we can, we update dp[i] by adding the value of dp[i-2] to it, since we can use one 2 coin and the number of possible combinations required to make change for the amount i-2 to make change for the amount i. For example, to make change for the amount 3, we can use one 2 coin and the number of possible combinations required to make change for the amount 1. Therefore, we update dp[3] by adding dp[1] to it. After considering the second coin, we have dp = [1, 1, 2, 2, 3, 3, 4]. We consider the third coin 5. For each amount i from 5 to 7, we check whether we can use the coin 5 to make change for the amount i. If we can, we update dp[i] by adding the value of dp[i-5] to it, since we can use one 5 coin and the number of possible combinations required to make change for the amount i-5 to make change for the amount i. For example, to make change for the amount 6, we can use one 5 coin and the number of possible combinations required to make change for the amount 1. Therefore, we update dp[6] by adding dp[1] to it. After considering the third coin, we have dp = [1, 1, 2, 2, 3, 4, 5].