Monotonic Deque Visualization

Array: $[1, 3, -1, -3, 5]$, $k = 3$. Deque stores indices. $i=0$, val=$1$: deque empty, push $0$. Deque: $[0]$

$i=1$, val=$3$: $3 > 1$, pop $0$, push $1$.

Deque: $[1]$

$i=2$, val=$-1$: $-1 < 3$, push $2$. Deque: $[1, 2]$. Window complete. Max = $nums[1] = 3$.

$i=3$, val=$-3$: $-3 < -1$, push $3$. Deque: $[1, 2, 3]$.

Front $1$ still in window. Max = $3$.

$i=4$, val=$5$: $5 > -3, -1, 3$, pop all, push $4$. Front $1$ outside window anyway. Deque: $[4]$.

Max = $5$. The front always gives the maximum.