Dsa Search Binary Bound

In this tutorial, you'll learn about How to Fix Binary Search for Boundaries Errors. We cover key concepts, practical examples, and best practices.

Fix binary search for boundaries errors when first/last occurrence logic fails for missing target.

Quick Fix

Wrong

def first(a,t):
    l=0; r=len(a)-1
    while l<=r:
        m=l+(r-l)//2
        if a[m]>=t: r=m-1
        else: l=m+1
    return l

Returns insertion point when target not found, not -1.

Right

def first(a,t):
    l=0; r=len(a)-1; res=-1
    while l<=r:
        m=l+(r-l)//2
        if a[m]==t: res=m; r=m-1
        elif a[m]>t: r=m-1
        else: l=m+1
    return res
def last(a,t):
    l=0; r=len(a)-1; res=-1
    while l<=r:
        m=l+(r-l)//2
        if a[m]==t: res=m; l=m+1
        elif a[m]>t: r=m-1
        else: l=m+1
    return res

[2,4,10,10,10,18,20], first(10)->2, last(10)->4. O(log n).

Prevention

For first occurrence: don't stop at match, continue searching left half. For last: continue right.

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