Min with Index

Often you need not the minimum value, but its position.

Store pairs $(\text{value}, \text{index})$ in the sparse table. The merge takes the pair with smaller value (or smaller index to break ties).

function build():
    for i = 0 to n - 1:
        st[i][0] = (arr[i], i)

    for j = 1 to K - 1:
        for i = 0 to n - (1 << j):
            left = st[i][j-1]
            right = st[i + (1 << (j-1))][j-1]
            if left[0] <= right[0]:
                st[i][j] = left
            else:
                st[i][j] = right

function query(l, r):
    k = LOG[r - l + 1]
    left = st[l][k]
    right = st[r - (1 << k) + 1][k]
    if left[0] <= right[0]:
        return left
    else:
        return right

Returns both the minimum value and its index in $O(1)$.